How to Learn Basic Algebra Fast and Free for Beginners — Rules, Equations, Solutions, Examples, Formulas, Problems and Answers

Latest update: April 13, 2024. Note: copyright info at end of page, there is history there. I never should have removed this tutorial.

This lesson is for people who think they can't learn algebra. Yes, you can.

Alternate titles for this page would be...

The Quick Basic Math Rules for Algebra

In Algebra How Do You Solve for X in Equations

In Algebra How Do You Simplify Equations

How to Learn Algebra Fast - How to Do Equations - Complete Beginner Algebra Lessons - Plus Problems with Solutions

Here is your online, complete, free, beginner algebra and equations tutorial. Easily and quickly learn algebra on your own. It is recommended that one does not attempt to do the entire tutorial in a single session; bookmark and return as desired.

If you already know arithmetic (including fractions and decimals), then you already know algebra. You just don't know you know yet. If you understand the answers to the following statements, proceed with this page; otherwise, it is probably not a good idea.

4 + 5 = 9

17 - 13 = 4

5 times 7 = 35

70 divided by 35 = 2

80 divided by 25 = 3.2

The Basics

Example #1

Algebra is nothing more than merely substituting letters for numbers. As an example:

       4 + 2 = 6

So, if we say the letter A is temporarily equal to 4, i.e.:

      A = 4

And the letter B is temporarily equal to 2, i.e.:

      B = 2

Then A plus B must equal 6, i.e.:

      A + B = 6

Example #2

      A = 5

      B = 3

So,

      A + B = ?

Well, if we replace the letter A with 5, then the question becomes:

      5 + B = ?

And then when we replace the letter B with 3, we have:

      5 + 3 = ?

Problem solved.

A side note: Algebra likes to use the letter X in place of the question mark. So the correct way to have stated the above question would have been to say:

      A = 5

      B = 3

      X = A + B

What is X? The answer is:

      X = 8

You have just learned the basic concept of algebra.

Example #3: Subtraction

      A = 19

      B = 14

      X = A - B

What is X?

We plug in the numbers and we get:

      X = 19 - 14

      X = 5

Multiplication and Division

Of course multiplication and division in algebra are just the same as in arithmetic.

Multiplication Example

(The asterisk sign (“*”) is used to replace the word “multiply.”)

      A = 20

      B = 5

      X = A * B

What is X? We plug in the numbers and we get:

      X = 20 * 5

      X = 100

Division Example

(The “/” sign is used to replace the word “divide.”)

      A = 20

      B = 5

      X = A/B

What is X? We plug in the numbers and we get:

      X = 20/5

      X = 4

Let's Mix Things Up

You now know all the arithmetic functions of algebra. Algebra lets you mix and combine these functions.

For example:

      A=1

      B=2

      C=3

      D=4

      X=A+B+C+D

      X=10

Let’s include subtraction:

      X=A + B + C - D

      X=(1+2+3) - 4, or X = 6 - 4, which is 2, or

      X = 6 - 4 = 2

Yes, there can be more than one equal sign in an equation. Instead of saying,

      A=42

      B=42

      C=42

      D=42

You can say,

      A=42

      A=B=C=D

Or just say,

      A=B=C=D=42

Side note. You have been solving equations since the first paragraph.

Some Random Example NASA Formulas

In Algebra How Do You Solve for V? Basic / beginner algebra volume formulas.

About the NASA Formula Examples

Note the "d²" in the volume formula for the cylinder. Yes, the upper "2" means the variable "d" is squared or itself times itself or "d" to the second power.

Note the "a³" in the volume formula for the cube. Likewise, the upper "3" means the variable "a" is cubed or itself times itself times itself or "a" to the third power.

Notice how some of the variables in the formulas are directly adjacent to each other. This is the standard used to indicate the variables are multiplied.

Examples

The rectangular prism formula or equation, V = a b h, means volume is equal to "a" times "b" times "h".

The top half of the volume for the sphere formula or equation, "πd³", means pi times d after d has been cubed. If d was equal to 5, then d³ would equal 125, making the equation π times 125 or 125π.

Yes, the horizontal slash in the sphere and cylinder formulas means divide by the lower number, 6 and 4 respectively.

As mentioned, "π" is the well-known symbol for pi. The approximate value of pi is 3.14159; this approximation serves most everyday purposes just fine.

More Multiplication Practice

Example #1

      A=1

      B=2

      C=3

      D=4

      X=A+B*C-D

What is X?

Simplify and solve.

When you see an equation has multiplication and division mixed into it, the rule is to do the multiplication and division first, then do the +’s and -‘s.

So the equation above really means,

      X = A + (B*C) - D or

      X = 1 + (2*3) - 4 or

      X = 1 + (6) - 4

      X = 3

The “(“ and “)” are used to indicate what parts of the equation to do first.

It should be noted X=A and A=X are mathematically equivalent.

Just Like the Pros

What you have been and are doing is just simplifying, i.e., breaking down the equation one piece at a time; just like the mathematicians do it. The mathematicians are no more able to look at an equation and instantly come up with the answer any better than the rest of us can. In other words, they can’t grasp the whole equation either. They just solve and proceed from line to line, trusting they solved the previous lines correctly.

Example #2

Here is another one:

      A=1, B=2, C=3, D=4, E=5, F=6

      ((D * B) + (F - 7)) + A) * C = X.

What is X?

This time there is more than one set of parentheses. When that happens, the rule is to do the innermost ones first. So let’s start solving this equation by breaking it down.

The (D*B) and the (F-7) are the innermost parts of the equation.

Let’s start with the (D*B).

      D * B = 4 * 2 = 8,

so we simplify the equation to,

      (8 + (F-7) + A) * C = X

Next is the (F-7).

      F - 7 = 6 - 7

This results in a number one less than zero, so we say negative one or -1.

(Another example would be 15-20. This results in a number 5 less than zero, so we say negative 5 or -5.)

The equation now looks like,

      (8 + (-1) + A) * C = X

Let’s get the A and C taken care of; the equation is now,

      (8 + (-1) + 1) * 3 = X

Next we add up the numbers inside the parenthesis.

-1 plus 1 equals zero of course.

Or you could have said: -1 plus 8 equals 7. The 8 is called a positive number, just as the -1 is called a negative number. Adding a positive number to a negative number is really just subtracting the negative number from the positive number. In other words:

      8 + (-1) = 8 - 1 = 7 or 1 + (-1) = 1 -1 = 0

Either way, our equation now looks like,

      (8 - 1 + 1) * 3 = X, which is

      (8) * 3 = 24 = X, or

      8 * 3 = 24 = X, or

      X = 24

Simplified a step at a time and solved.

If you didn’t know negative numbers before, now you do. For the sake of completeness, the next section is about what else one should know about negative numbers.

More About Negative Numbers

Numbers plus negative numbers result in lesser numbers. Keep in mind -10 is a lesser number than -5, etc.

Numbers minus negative numbers result in larger numbers. For example, whereas 9-5 = 4, but 9-(-5) = 14. In other words, minus minus results in a positive increase aka a lesser lesser or a larger larger. Minus a minus is exactly the same as plus a plus, e.g. -(-25)=25.

This is a good time to mention that in mathematics, two negatives equal a positive when applied to minus a minus subtraction, or any multiplication, or any division.

For multiplication:

Negative numbers times positive numbers equal negative numbers, e.g. -5 * 4 = -20.

Negative numbers times negative numbers equal positive numbers, e.g. -5 * -4 = 20.

You already knew positive numbers times positive numbers equal positive numbers.

For division, the same rules apply:

Negative numbers divided by positive numbers (or vice versa) equal negative numbers, e.g. -5/4 = -1.25 and 5/-4 = -1.25.

Negative numbers divided by negative numbers equal positive numbers, e.g. -5/-4 = 1.25.

You already knew positive numbers divided by positive numbers equal positive numbers.

More Example NASA Formulas

In Algebra How Do You Solve for V? Learning and doing volume formulas.

Using Spreadsheets

Spreadsheet software or applications will happily do the arithmetic and sort out the negatives versus the positives for you once you have replaced all the variables. It even knows to do the innermost before the outermost, etc. As an example, suppose you have simplified an equation to the following mess:

      X=((5-3)* 52)-21+((6+7)/(34-12))

If your spreadsheet software is MS Excel or you are using cloud Google Drive, you can exclude the X and just copy/paste the following into a single cell:

      =((5-3)* 52)-21+((6+7)/(34-12))

The spreadsheet will immediately solve the equation and give back the answer of 83.5bunchmoredigits. If you have the software or Google Drive access, go ahead and try it.

If you are experienced at spreadsheet calculations, you can, of course, do equations with the variables still in place; substituting the variables with cell locations or range names.

Another Division Example

Might as well keep it simple and use the previous variables.

      A = 5

      B = 34

      C = 21

      X=((A-3)* 52)-C+((6+7)/(B-12))

We replace the variables with the assigned numbers and we are right back where we started from:

      X=((5-3)* 52)-21+((6+7)/(34-12))

The arithmetic then gives us:

      X = 83.59090909...

Dividing by Zero

This is a good time to mention you cannot divide by zero.

For example:

      If A=1

      If A=2

      If A=3

      X = 5 + 10/(3-A)

Now if A=1, then

      X=5+10/(3-1)=5+10/2=5+5=10

Now if A=2, then

      X=5+10/(3-2)=5+10/1=5+10=15

If, however, we attempt to declare the variable A as A=3, the following occurs:

      X=5+10/(3-3)=5+10/0. (invalid)

At this point the equation becomes invalid. There is no answer to the question, “What is 10 divided by 0?”. An equation immediately becomes invalid when a divide-by-zero scenario occurs. Software applications are designed to recognize this when it happens. Plugging whatever-divided-by-zero into a spreadsheet used to give interesting results, before applications were modified to detect this.

What You've Learned

The basic concept of algebra is just plugging the numbers into the variables, and then doing the arithmetic. One merely keeps simplifying the equation until it is solved. You now have a full understanding of that concept. Yes, you have been using variables since the first paragraph.

Final Example

Here is the last example. It is presented in a different format. The question, however, remains the same. What is X? You already know everything needed to solve this equation.

      A=1, B=2, C=3, D=4, E=5

      T=-1, U=-2, V=-3

      (6X/8)+(2T+4)=((CD/2)-AD)+V

It should be noted 6X means the same as 6*X; and AD means the same as A*D. Other examples would be: 3A=3*A=A*3, 5Y=5*Y=Y*5, -2C=-2*C=C*-2, etc.

We plug the numbers into the variables, and the equation now is:

      (6X/8)+((2*-1)+4)=((3*4)/2)-(1*4)+-3

Some simplifying arithmetic gives us:

      (6X/8)+-2+4=(12/2)-4+-3

More arithmetic then gives us:

      6X/8 +2=6-4+-3

More arithmetic gives us:

      6X/8+2=-1

We can’t solve X as the equation is currently stated; so we will have to move things around and do more arithmetic.

Important Note

Whenever you change the actual value on one side of the equation, you must do the same on the other side of the equation. Example: 7=7. If you subtract 3 from the left side, then you must subtract 3 from the right side; thus 4=4. The same rule applies for addition, multiplication, and division.

Let’s subtract 2 from both sides of our equation.

      6X/8+2=-1

Then becomes:

      6X/8=-3

We have to get rid of the “divide by 8” part of the left side of the equation. So we multiply both sides of the equation by 8.

      6X/8=-3

Then becomes:

      6X=-24

We must make the X stand alone, so we divide both sides by 6.

      6X=-24

Then becomes:

      X = -4 (The Answer!)

How Do We Know If We Have the Right Answer?

To find out, we go back to the original equation and replace X with -4. We then simplify (reduce) the equation as before to its simplest form. If the simplest possible construct is valid; then, by definition, the statement “X=-4” is valid.

Here is the original equation.

      A=1, B=2, C=3, D=4, E=5

      T=-1, U=-2, V=-3

      (6X/8)+(2T+4)=((CD/2)-AD)+V

We don’t have to re-solve the parts that didn’t have the X in it to begin with, so we have:

      (6X/8)+2 = -1

We replace the X with -4, giving us:

      ((6*-4)/8)+2=-1

Simplifying gives:

      (-24/8)+2=-1

Which is:

      -3+2=-1

Which is:

      -1=-1

This construct is valid and simple enough to know X=-4 is valid.

To take it to the very end, you can multiply both sides by -1, giving us:

      1=1

What Would Have Happened, If Instead of Correctly Calculating X=-4, We Had Erroneously Calculated X=16?

The equation simplification/reduction would have proceeded smoothly to this point:

      (6X/8)+2 = -1 (as above)

When the 6X is replaced with 6*16, we get:

      (96/8)+2=-1 (false)

When further simplified says:

      12+2=-1 (false)

Which is

      14=-1 (false)

The resulting false statement by definition means the original calculation of "X=16" is a false statement.

The Adventure Continues...

There is a lot more (much, much more) to algebra, but it is really only an expansion of what you have already learned. Algebra is the basis of all other mathematics; including geometry, trigonometry, calculus, and so on. A good understanding of algebra is required to succeed at the other mathematics. Mathematics, itself, is the foundation of most other disciplines. This foundation is not just necessary for the sciences such as physics, electronics, chemistry, biology, astronomy, and so on. A mathematical foundation is necessary for many careers; including marketing, economics, architecture, and many, many others.

May all your calculations be prosperous ones!

- End of Lesson, but more to follow -

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I first published this tutorial at another website on 10/22/2010. However, to keep the information current, I then relocated it to websitewithnoname.com. I then made the mistake of moving it elsewhere. I have now moved it back to websitewithnoname.com A long road for trying to do good. This copyrighted tutorial has helped and served people well for years. If you find this tutorial currently printed or posted anywhere else but here, please let me know in comments. I originally wrote this page because of my knowing someone who was perfectly smart enough to understand algebra but had the mental block that they couldn't.

I never should have moved this page from here. Here are some of the previous comments when it was here:

Previous Comments from long ago:

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dorothy jordan 

5 years ago

Im so thankful for all the help an support,i have a big test coming up,was so worried,but now ,i feel so secure,thanks for ur help.

Kristen Howe profile image

Kristen Howe 

5 years ago from Northeast Ohio

Math was always a weak subject for me. This would be helpful and useful for anyone who's struggling with it. Voted up for useful!

Jean Bakula profile image

Jean Bakula 

7 years ago from New Jersey

Where were you when I was struggling with Algebra in 7th grade? And you even have pictures. I tried so hard, I used to stay after school for extra help. Finally the teacher agreed to pass me with a D if I would stop coming. I thought it was a good deal, although I was an A student in other subjects, I just couldn't grasp it. My son is now a teacher, and tells me she was a failure as a teacher for not trying harder!

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abseli 

7 years ago

Hi there! I could have sworn I've been to this website before but after browsing through some of the post I realized it's new to me. Anyways, I'm definitely delighted I found it and I'll be bookmarking and checking back frequently! make your computer run like brand new

Marderius profile image

Marderius 

7 years ago from Alabama

Well 2/3 x 5 7/8 ..first we can change 5 7/8 into an improper fraction giving us 47/8 now we can cross multiply... we will have 2/3 x 47/8= as you can see 2 can go into itself one time and into 8 four times.... now we have 1/3 x 47/4 giving us a final answer of 47/12 or 3 11/12 ! Hope this was helpful

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Carole Garfield 

7 years ago

I helping someone in fraction like 2/3 x 5 7/8 = Can someone take me through this

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carlarmes 

8 years ago from Bournemouth, England

my son found this hub useful, thank you for the content.

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Angela_1973 

9 years ago

Good hub on algebra, I hate it though, I speak like 5 languages but can never do math. Have a lot of respect for people in the science field

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kathryn1000 

9 years ago from London

That is really good.Congratulations.

*Algebra helps your brain*

To forget about troubles and pain.

So dive in and swim

While wearing a grin,

And soon you'll be back here again

How to Do Ternary or Trinary, Base 3 Numbering System Conversions Lesson / Tutorial Examples

Latest update: February 3, 2024

If you understand the everyday decimal (base 10) number system, then you already understand the ternary, base 3 counting and numbering system. You just don’t know you know yet. The complete lesson immediately follows the short semantics note about "ternary" versus "trinary".

Base 3 Conversion - Base 3 to Base 10 and Back - 0 1 2

How to Learn the Ternary Base 3 Numbering System

A complete lesson and examples.

Semantics Note

Ternary is the primary descriptor used to identify base 3 (using the digits 0 1 2) in mathematics as relates to numbering systems. Trinary is the primary descriptor used to identify base three as relates to logic (using the digits -1 0 +1); but the term has also been used in place of ternary. This page does not address the logic definition of trinary. This page is about and explains the base 3 number system; usually called ternary, but sometimes referred to as trinary.

A Quick Review of Base 10 Structure...

Base 10 Decimal Orders of Magnitude

1 · 10 · 100 · 1,000 · 10,000 · 100,000

Positional

100,000 · 10,000 · 1,000 · 100 · 10 · 1

We use the base 10 numbering/counting system in our day-to-day living. Base 10 has ten numbers (0-9) and orders of magnitude that are times ten.

• The lowest order number represents itself times one.
• The next order number represents itself times 10.
• The next order number represents itself times 10 x 10, or itself times 100.
• The next order of magnitude would be 10 x 10 x 10, or 1000.

And so on. A base 10 example would be the number 3528. This number means that there are:

• Eight 1’s,
• two 10’s,
• five 100’s,
• and three 1000's.

Which represents 8 + 20 + 500 + 3000 for a total of 3528.

The Ternary or Base 3 Numbering System...

...uses the same structure, the only difference being the orders of magnitude. Base 3 or ternary has three numbers: 0, 1, and 2.

The orders of magnitude are times three.

• The lowest order number represents itself times one.
• The next order number represents itself times 3.
• The next order number represents itself times 3 x 3, or itself times 9.
• The next order of magnitude would be 3 x 3 x 3, or itself times 27.
• The next order of magnitude would be 3 x 3 x 3 x 3, or itself times 81.

And so on.

Orders of Magnitude in Base 3

• 1 · 3 · 9 · 27 · 81 · 243 · 729 · 2,187 · 6,561

Positional

• 6,561 · 2,187 · 729 · 243 · 81 · 27 · 9 · 3 · 1

A basic, first example of a ternary number would be the base 3 number 11111. This would mean there are:

• one 1,
• one 3,
• one 9,
• one 27,
• and one 81.

Which represents 1 + 3 + 9 + 27 + 81 for a total of 121 in Base 10 decimal.

Another base 3 example would be the number 1120. This number means that there are:

• No 1’s,
• two 3’s,
• one 9,
• and one 27.

Which represents 0 + 6 + 9 + 27 for a total of 42 in base 10 decimal.

Another base 3 example would be the number 2101. This number means there are:

• One 1,
• No 3's,
• One 9,
• And two 27’s.

Which represents 1 + 0 + 9 + 54 for a total of 64 in base 10 decimal.

More Ternary (Base 3) to Base 10 Conversion Examples

9 · 3 · 1	9 · 3 · 1	27 · 9 · 3 · 1
0=0	110=12	220=24
1=1	111=13	221=25
2=2	112=14	222=26
10=3	120=15	1000=27
11=4	121=16	1001=28
12=5	122=17	1002=29
20=6	200=18	1010=30
21=7	201=19	1011=31
22=8	202=20	1012=32
100=9	210=21	1020=33
101=10	211=22	1021=34
102=11	212=23	1022=35

(Convenience relist)

Orders of Magnitude in Base 3

• 1 · 3 · 9 · 27 · 81 · 243 · 729 · 2,187 · 6,561

Positional

• 6,561 · 2,187 · 729 · 243 · 81 · 27 · 9 · 3 · 1

Other base numbering systems:  Try c. 2024: Search results for base (websitewithnoname.com)

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I first published this article at another website on 09/19/10. However, to keep the information current, relocating to websitewithnoname.com was best. This copyrighted article has served people well for years.

MPH to FPS: Mental Math Calculation Conversion Formula for Miles per Hour to Feet per Second

Latest update: January 10, 2023. Page URL indicates original publication date; meanwhile, times change and the updates continue.

How to Instantly Convert MPH to FPS While Driving

- The Quick and Easy Math Trick Formula Equation -

Simply divide miles-per-hour by 2, then multiply the result by 3 to find feet-per-second.

This is the easy, quick math formula or equation to use and gives a usable, fairly accurate answer. Your answer will be accurate within 5%. As an example, 100 mph converts to 150 fps. If one does the more complicated method of math calculation (detailed further down the page), the resulting answer would be 147 fps.

"How many feet per second..." 
is a math question usually relating to cars and driving.

Easy Table Conversion from MPH to FPS Examples Chart

Divide by 2, then multiply by 3.

MPH	FPS
10	15
15	22.5
20	30
25	37.5
30	45
35	52.5
40	60
45	67.5
50	75
55	82.5
60	90
65	97.5
70	105
75	112.5
80	120
90	135
100	150
120	180
140	210
160	240

The More Difficult (and More Accurate) Answer

To prove the quick math shortcut conversion calculation works:

1. First. convert MPH (miles-per-hour) to MPM (miles-per-minute) by dividing MPH by 60.
2. Then convert miles to feet. There are 5,280 feet in one mile, so multiply MPM by 5,280 to get FPM (feet-per-minute).
3. Lastly, convert FPM to FPS (feet-per-second) by dividing by 60.

Examples of the Longhand Math Converting Miles-per-Hour (MPH) to Feet-per-Second (FPS)

MPH to FPS Math Conversion Example One

You're going 25 mph. How many feet is that per second?

1. Conversion from mph to fps is as follows: If we divide by 60, we get miles-per-minute (mpm): 25/60 = .416667.
2. For accuracy's sake, now is a good time to convert miles to feet. There are 5,280 feet in a mile so we multiply mpm times 5,280 to get feet-per-minute: 416667 x 5280 = ~2199.99 feet-per-minute [note: "~" means approximate].
3. To convert from feet-per-minute to feet-per-second (fps), we divide the answer by 60: 2199.99/60 = ~36.667 feet-per second.
4. This answer is within 5% of the one you get doing the mental easy math way, which says 25 mph divided by 2 and then multiplied by 3 equals 37.5 fps.

MPH to FPS Math Conversion Example Two

65 mph. How many feet per second?

1. Conversion from mph to fps is as follows: If we divide by 60, we get miles-per-minute: 65/60 = 1.0843333333333.This makes sense. After all, 60 miles an hour is the well-known mile-a-minute.
2. For accuracy's sake, now is a good time to convert miles to feet. There are 5,280 feet in a mile, so we multiply the miles-per-minute times 5,280 to get feet-per-minute: 1.0843333333333 x 5280 = ~5725.28 feet-per-minute.
3. To convert from feet-per-minute to feet-per-second, we divide the answer by 60: 5725.28/60 = ~95.421 feet-per second, which is the answer.
4. This coincides within 5% of the table above, which says 65 mph equals 97.5 fps. 

MPH to FPS Math Conversion Example Three

120 mph is how many feet per second? Conversion from mph to fps is as follows.

1. If we divide by 60, we get miles-per-minute: 120/60 = 2.000. This again makes sense; 60 miles an hour is the usual mile-a-minute. So 120 mph would be 2-miles-a-minute.
2. To convert miles to feet. There are 5,280 feet in a mile, so we multiply the miles-per-minute times 5,280 to get feet-per-minute: 2 x 5280 = ~10560 feet-per-minute.
3. To convert from feet-per-minute to feet-per-second, we divide the answer by 60: 10560/60 = ~176 feet-per second.
4. This number is within 5% of the table above which says 120 mph equals 180 fps.

The Reverse FPS to MPH Math Conversion Examples

Quick way to find reverse, i.e., convert from feet-per-second to miles-per hour: divide fps by 3 and then multiply by 2 for mph.

Easy Table Conversion from FPS to MPH Examples Chart

FPS	MPH
10	6.67
20	13.33
25	16.67
40	26.68
50	33.33
75	50
100	66.67
150	100
200	133.33
500	333.33
1000	666.67

Doing 20 miles-per-hour? That is 30 feet-per-second.

The laws of physics seldom take a vacation.
Most of these cars would not be able to stop in time.

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How Much Does a Pint / Quart / Gallon Weigh in Pounds?

Latest update: February 26, 2024. Page URL indicates original publication date; meanwhile, times change and the updates continue.

How Many and How to Calculate Pints, Quarts, Gallons to and from Pounds

Alternate Titles or Questions

• How to Convert Pints to Quarts to Gallons to and from Pounds?
• Volume to Weight Conversions or Weight to Volume Conversions – 8:4:1:8.
• How many pounds in X pints, quarts, or gallons?
• How much does X gallons, quarts, or pints weigh?

A list of most-searched-for questions and answers is included. There is also a specific section relating to the calculating of the size/volume/weight of home water heaters.

Volume to Weight Conversions. Weight to Volume Conversions.
Simple math to convert or calculate pints, quarts, gallons, and pounds.

Be advised that this page is US-centric. As an example, this does not work in the UK where a pint is 1.25 pounds as opposed to US 1.043 pounds at room temperature (RT). There are also issues of temperature and density, both of which are addressed further down the page. The purpose of this page is for practical, everyday business-of-living uses only. For that it will serve you well.

First – The Quick Answers to Volume Amounts and Ratios

Volume Definitions

• 2 pints equals 1 quart.
• 4 quarts equals 1 gallon.
• 8 pints equals 1 gallon.

Or to Put It Another Way...

• 1 quart equals 2 pints.
• 1 gallon equals 8 pints.
• 1 gallon equals 4 quarts.

Converting Volume to Weight

Converting volume to weight has everything to do with the density of the liquid. Fortunately, this question usually has to do with:

• How much does the gasoline in your gas tank or a gas can weigh?
• How much does a specific container of water or other mostly-water grocery items weigh?
• Questions relating to home water heater size, calculated water volume and the resulting weight.

The rule of thumb, and the expression to remember is: "A pint's a pound the world around." The resulting estimates and extrapolations from this rule will serve you well for most everyday purposes. For scientific and industrial purposes where greater accuracy is required, a pint weighs a little bit more than a pound (1.043 lb.).

Basic Formulas

• A pint weighs a pound.
• There are two pints in a quart, so a quart weighs 2 pounds.
• There are four quarts in a gallon, so a gallon weighs 8 pounds. 
• And the eight pints in a gallon, also weighing 8 pounds.

This pretty much answers the question. Here are some other typical examples:

Some Household Examples

• A 1-quart bottle of Gatorade weighs 2 pounds. Note: there are 2 pints in a quart and 4 quarts in a gallon. As a side note: there are 16 fluid ounces in a pint, 32 fluid ounces in a quart; 1 and 2 pounds respectively.
• A 2-liter bottle of Pepsi would convert to a weight of a little over 4 pounds. Note: A liter is slightly more volume than a quart.

Some gallon examples

• A 1-gallon container would convert to a weight of 8 pounds.
• A 5-gallon container weighs 40 pounds.
• A 10-gallon container weighs 80 pounds.
• A full, 25-gallon SUV gas tank means you are hauling around 200 pounds of fuel.
• A typical city water tower can hold anywhere from 300,00 to 600,000 gallons of water, which converts to a weight of 2,400,000 to 4,800,000 pounds of water sitting on those "stilts".

The Density of the Liquid Significantly Affects the Rules Concerning Volume Conversion Calculations to Weight

A major component of converting fluid volume to a weight measurement is the density of the fluid. For gasoline, water, and most grocery items; the rule of a-pint's-a-pound will serve you just fine. However, as an example, the rule probably wouldn't work too well with any significant volume of engine oil. As an extreme example, the liquid metal/element mercury would totally throw the pint's-a-pound rule out the window. So of course would any molten metal or alloy.

Fluid density is also affected by temperature. This is why many people fill their gas tank first thing in the morning. There is more gas per gallon at 50 degrees Fahrenheit than at 90 degrees Fahrenheit. It should be noted the percentage difference is in the low single-digits.

Here is a worthwhile page from NASA about Density, Mass (weight), Volume for both solids and liquids.

List of Frequent Volume-to-Weight Conversion Q&A

The Most-Searched-for Questions and Answers for How Many Pounds

• How much does 1.5 quarts weigh? Answer is 3 pounds.
• How much does 2 quarts weigh? Answer is 4 pounds.
• How much does 3 quarts weigh? Answer is 6 pounds.
• How much does 5 quarts weigh? Answer is 10 pounds.
• How much does 6 quarts weigh? Answer is 12 pounds.
• How much does 10 quarts weigh? Answer is 20 pounds.
• How much does 16 quarts weigh? Answer is 32 pounds.
• How much does 5 gallons weigh? Answer is 40 pounds.
• How much does 10 gallons weigh? Answer is 80 pounds.
• How much does 15 gallons weigh? Answer is 120 pounds.
• How much does 20 gallons weigh? Answer is 160 pounds.
• How much does 50 gallons weigh? Answer is 400 pounds.
• How much does 55 gallons weigh? Answer is 440 pounds.

• How many pints is a pound? Answer is 1.0 pint.
• How many quarts is a pound? Answer is 0.5 quarts.
• How many gallons is a pound? Answer is 0.125 gallons.

The formulas for the volume of a sphere, the volume of a cube,
the volume of a cylinder, the volume of a rectangular prism.

More Water and Gasoline Volume-to-Weight Examples

Depending on what unit of measurement you use, volume will equal cubic English or cubic Metric; examples being cubic inches or cubic centimeters.

Side note: the tilde (~) is the mathematical symbol for approximate.

English

• 29 cubic inches equals ~1 pint, which equals ~1 pound.
• 58 cubic inches equals ~2 pints, which equals ~1 quart, which equals ~1/4 of a gallon, which equals ~2 pounds.
• 231 cubic inches equals ~4 quarts, which equals 1 gallon, which equals 8 pounds.

Metric

Most of the world uses metric. There is a reason for that. As an example, 1000 cubic centimeters equals one liter, 1000 grams equals one kilogram, etc.; all nice, neat, and tidy. The United States and others are trying to get with the program; metric is already included with English measurement on most U.S. consumer items. It's only a matter of time.

How Much Does the Water Weigh in a Full Water Heater?
– Water Tank Size Volume Formula and Answers –

Serendipitous energy.gov page on everything about water heaters, including how to buy one.

How to Calculate the Weight of the Water in a Home Water Heater

How much does the total amount of water in a water heater weigh, volume to weight conversion.

From the above NASA chart we see the volume formula for a cylinder is V = (πd2h)/4.

Water tank heaters come in all sizes. For the purposes of this example, we will say the water tank heater has a measured height of approximately 54 inches; what with this, that, and the other, the water part is probably around 48". The diameter measured as 18"; what with insulation, etc., 16 probably works.

So,
d = 16
h = 48

Thus (" * " meaning to multiply),
V = (3.14 * 16 * 16 * 48) divided by 4.

Since all numbers are inches, the answer will be in cubic inches. We reduce the formula as follows:

1. V = (3.14 * 256 * 48) divided by 4.
2. V = (3.14 * 12288)/4
3. V = 38514/4
4. V = 9646 cubic inches

231 cubic inches is equal to a gallon, so we divide 9646 by 231.
9646/231 = 41.76 gallons.

What with the inner measurements being estimates, looks like it is a 40 gallon water heater.

1. A gallon weighs 8 pounds.
2. So multiplying 40 times 8 gives 320.
3. A 40-gallon water heater contains 320 pounds of cold water.

Knowing the volume and weight of a 40-gallon water tank heater makes it easy to extrapolate the volume and approximate weight of other water heaters. Do remember that as volume increases, the discrepancy totals of the  "pints-a pound". designation versus the more accurate 1.043 lb. designation also increases. As an example: multiplying the 320 lb. calculation for a 40 gallon water heater by 1.043 gives a result of 333.76 lb. at RT versus the original approximation of 320 lb. at RT. When the water temperature is at hot water heater level, the actual weight will fall between the 320 lb. calculation and the 333.76 lb. calculation.

• 10 gallon water heater is 2310 cubic inches and the water weighs 80 pounds.
• 20 gallon water heater is 4620 cubic inches and the water weighs 160 pounds.
• 30 gallon water heater is 6930 cubic inches and the water weighs 240 pounds.
• 40 gallon water heater is 9240 cubic inches and the water weighs 320 pounds.
• 50 gallon water heater is 11550 cubic inches and the water weighs 400 pounds.
• 80 gallon water heater is 18480 cubic inches and the water weighs 640 pounds.
• 100 gallon water heater is 23100 cubic inches and the water weighs 800 pounds.

Do keep in mind the temperature versus density considerations and the expansion of water when heated, i.e., a fully hot water heater tank weighs slightly less than a cold or warm water tank heater that's been freshly refilled after usage. The difference between hot and cold water density versus volume is significant enough that most water heaters have a temperature pressure relief valve and a drainage tube or pipe to compensate for this.

Converting Cubic Inches to Cubic Feet...

...and the corresponding volume and weight ratios. It is surprising how much just one cubic foot of water weighs.

With the pint-equals-pound rule, one cubic foot of water weighs 60 pounds for approximation purposes.

A cubic foot is 12 inches times 12 inches times 12 inches. So 1728 cubic inches equals 1 cubic foot. To convert cubic inches to cubic feet, simply divide the cubic inches by 1728. So using the above examples, we would have:

• 2310 cubic inches equals 1.34 cubic feet equaling 10 gallons equaling 80 lb.
• 4620 cubic inches equals 2.68 cubic feet equaling 20 gallons equaling 160 lb.
• 6930 cubic inches equals 4.02 cubic feet equaling 30 gallons equaling 240 lb.
• 9240 cubic inches equals 5.36 cubic feet equaling 40 gallons equaling 320 lb.
• 11550 cubic inches equals 6.70 cubic feet equaling 50 gallons equaling 400 lb.
• 18480 cubic inches equals 10.72 cubic feet equaling 80 gallons equaling 640 lb.
• 23100 cubic inches equals 13.40 cubic feet equaling 100 gallons equaling 800 lb.

* A side note. I happened to stumble across this on Wikipedia: "Pound (mass), a unit of mass often abbreviated incorrectly as 'lbs' in the plural. Abbreviations of units of measure do not use an 's' on the end for plural."

May all your calculations be prosperous ones.

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