Ratio Calculator to Solve, Simplify, or Compare Ratios

Ratio Calculator Sign

This online ratio calculator will simplify a ratio (ratio simplifier), test for equality for two ratios (equivalent ratios calculator), and solve ratio equalities when given three of the four terms (ratio solver).

Plus, the results include a pie chart showing the percentage each side of the ratio represents, and a table containing the first one hundred ratios that are equal to the simplified ratio (ratio generator).

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Ratio Calculator

Solve, simplify, or compare ratios and generate a list of ratios equal to the result.

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Selected Data Record:

A Data Record is a set of calculator entries that are stored in your web browser's Local Storage. If a Data Record is currently selected in the "Data" tab, this line will list the name you gave to that data record. If no data record is selected, or you have no entries stored for this calculator, the line will display "None".

DataData recordData recordSelected data record: None

To simplify a ratio, enter the values for A and B only.

To check for equality, enter values for A, B, C, and D.

To solve a ratio equality, enter any 3 of the 4 values.

To enter a fraction or mixed number as one of the values, expand the appropriate "Ratio" label and the underlying calculator will convert either to a decimal for you.

Ratio A:B
Convert mixed number or fraction to decimal.
Value A
Value B

First ratio:

Enter the known values in the first ratio (A and/or B).

:
Ratio C:D
Convert mixed number or fraction to decimal.
Value C
Value D

Second ratio:

Enter the known values in the second ratio (C and/or D).

:
MissingMissingMissing valueMissing value :

Missing value:

This is the missing value.

Reduced:Reduced:Reduced:Reduced to simplest form:

Ratio reduced to simplest form:

This is the entered or solved ratio reduced to its simplest form.

A to 1:A to 1:A set to 1:A set to 1:

A set to 1:

This is the simplified ratio converted to 1:n form.

B to 1:B to 1:B set to 1:B set to 1:

B set to 1:

This is the simplified ratio converted to n:1 form.

If you would like to save the current entries to the secure online database, tap or click on the Data tab, select "New Data Record", give the data record a name, then tap or click the Save button. To save changes to previously saved entries, simply tap the Save button. Please select and "Clear" any data records you no longer need.

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Help and Tools

Learn

What a ratio is, and how to solve, simplify, check for equality, and scale ratios.

What is a Ratio?

A ratio is the mathematical relationship between two values that indicates how many times the first value contains the second value, and can be expressed in one of three ways.

  • 3 : 4
  • 3 to 4
  • 3/4

So in the above example, since 3 divided by 4 is equal to 0.75, the first value contains the second value 0.75 times. Or, the first value is 0.75 of the second value.

Or, as a practical example, suppose you have a class of 28 students consisting of 12 boys and 16 girls. In this case, the ratio of boys to girls is 12 to 16 (12:16 or 12/16). Since you can reduce the fraction 12/16 to 3/4, you could say that for every three boys in the class, there are four girls.

       
       
       
       

How to Simplify a Ratio

Since a ratio can be stated as a fraction (3:4 = 3/4), you simplify ratios the same way you simplify fractions, which is to find the greatest common factor (GCF) of the two numbers, and then divide both sides by the GCF.

For example, to simplify the ratio 12:16, you find that 12 and 16 have a greatest common factor 4. So dividing both numbers by 4 leaves you with a reduced ratio of 3:4.

12=12 ÷ 4=3
1616 ÷ 44

How to Determine if Two Ratios Are Equal

To determine if two ratios are equal, for each ratio, divide the first number by the second number. Then compare the two results to see if they are equal.

For example, if checking to see if 12:16 is equal to 54:72, dividing 12 by 16 equals 0.75, and 54 divided by 72 equals 0.75. Therefore the two ratios are equal.

12 : 16 = 12 = 0.75
16
54 : 72 = 54 = 0.75
72

The ratio 12:16 is equal to the ratio 54:72.

Or, if checking to see if 12:16 is equal to 20:25, dividing 12 by 16 equals 0.75, and 20 divided by 25 equals 0.80. Therefore the two ratios are not equal.

12 : 16 = 12 = 0.75
16
20 : 25 = 20 = 0.8
25

The ratio 12:16 is not equal to the ratio 20:25.

How to Solve for Ratio Equality

If you are given a ratio equality problem where one of the values is missing (A:B = C:D), you follow these steps:

  1. Convert the ratios to fractions.
  2. Multiply both sides of the equality by the unknown variable.
  3. Multiply both sides of the equality by the inverse of the fraction having both values.
  4. Solve for the unknown variable once you have it on one side of the equality all by itself.

Depending on which of the four values is unknown, getting the unknown variable by itself on one side of the equality will leave you with one of the following formulas to solve:

  • a = C/D X B
  • b = D/C X A
  • c = A/B X D
  • d = B/A x C

To illustrate how to solve for missing value, suppose you are presented with the following problem to solve:

A=C
1260
16d
BD

Since we know from the above formula list that d will be equal to B/A x C, we can solve for d like this:

d = B/A x C
d = 16/12 x 60
d = 1.3333333333333333 x 60
d = 80

Now that we know d is equal to 80, we can complete the equality.

A=C
1260
1680
BD

How to Scale a Ratio Up or Down

To scale up a ratio, multiply both sides of the ratio by the scale factor. For example, if you want to scale up the ratio 1:3 by a factor of 3, multiplying both sides by 3 leaves you with a scaled-up ratio of 3:9 ([1 x 3 = 3] : [3 x 3 = 9]).

To scale down a ratio, divide both sides of the ratio by the scale factor. For example, if you want to scale down the ratio 3:9 by a factor of 3, dividing both sides of the ration by 3 leaves you with a scaled-down ratio of 1:3 ([3 ÷ 3 = 1] : [9 ÷ 3 = 3]).

Use the following calculator to scale up or scale down ratios.

Scale Ratio Calculator
Ratio:
:
Direction:
Scale:
Scaled ratio:3 : 9
Rounded:3 : 9

Adjust Calculator Width:

Move the slider to left and right to adjust the calculator width. Note that the Help and Tools panel will be hidden when the calculator is too wide to fit both on the screen. Moving the slider to the left will bring the instructions and tools panel back into view.

Also note that some calculators will reformat to accommodate the screen size as you make the calculator wider or narrower. If the calculator is narrow, columns of entry rows will be converted to a vertical entry form, whereas a wider calculator will display columns of entry rows, and the entry fields will be smaller in size ... since they will not need to be "thumb friendly".

Show/Hide Popup Keypads:

Select Show or Hide to show or hide the popup keypad icons located next to numeric entry fields. These are generally only needed for mobile devices that don't have decimal points in their numeric keypads. So if you are on a desktop, you may find the calculator to be more user-friendly and less cluttered without them.

Stick/Unstick Tools:

Select Stick or Unstick to stick or unstick the help and tools panel. Selecting "Stick" will keep the panel in view while scrolling the calculator vertically. If you find that annoying, select "Unstick" to keep the panel in a stationary position.

If the tools panel becomes "Unstuck" on its own, try clicking "Unstick" and then "Stick" to re-stick the panel.