Ratio Calculator

What is a ratio?

A ratio compares two quantities and shows how many times one contains the other. It can be written as 3:4, "3 to 4," or the fraction 3/4. Ratios appear in recipes, map scales, screen sizes, mixing instructions, and odds.

This ratio calculator does two jobs. In "Solve A : B = C : D," enter any three values to find the missing fourth. In "Scale a ratio," enlarge or shrink a ratio by a factor while keeping its proportions.

Proportion calculator: solving A : B = C : D

Two equal ratios form a proportion. In a true proportion the cross products are equal, A × D = B × C, so any missing term can be found from the other three:

• A = B × C ÷ D
• B = A × D ÷ C
• C = A × D ÷ B
• D = B × C ÷ A

For example, to scale a 2:5 ratio so the first term is 14, solve 2 : 5 = 14 : D. D = 5 × 14 ÷ 2 = 35, so the answer is 14:35.

How to calculate a ratio and simplify it

To write a ratio in its simplest form, divide both terms by their greatest common factor. 640:480 has a greatest common factor of 160, so it simplifies to 4:3. If a term has decimals, first multiply both terms by the same power of 10 to make them whole numbers: 1.5:2 becomes 15:20, which simplifies to 3:4.

The calculator also shows the same ratio in other common forms:

• 1 : x divides both terms by A. 16:9 becomes 1:0.5625.
• x : 1 divides both terms by B. 16:9 becomes 1.7778:1.
• Percentage treats A and B as parts of a whole. In 16:9, A is 16 ÷ (16 + 9) = 64% of the total.

Scaling a ratio up or down

Multiplying or dividing both terms by the same number, called the scale factor, gives an equivalent ratio. Enlarging 640:480 by 1.5 gives 960:720, and shrinking it by 4 gives 160:120. This is how you resize an image without stretching it or multiply a recipe for more servings.

Aspect ratio calculator: common screen sizes

An aspect ratio is a width-to-height ratio. To find the height of a 16:9 image that is 1,600 pixels wide, solve 16 : 9 = 1600 : D. The answer is 900 pixels.

Frequently asked questions

How do you calculate a ratio?

Write the two quantities in order with a colon between them, then simplify. With 12 boys and 18 girls, the ratio of boys to girls is 12:18, which simplifies to 2:3 after dividing both by 6.

How do you find the missing number in a ratio?

Set up a proportion and cross-multiply. For 2 : 5 = x : 35, multiply 2 × 35 = 70 and divide by 5 to get x = 14. You can enter the three known values in the calculator and leave the unknown blank.

What is the difference between a ratio and a proportion?

A ratio compares two numbers, such as 3:4. A proportion says two ratios are equal, such as 3:4 = 6:8.

Can I turn a ratio into a percentage?

Yes. Divide one part by the total of both parts and multiply by 100. In 1:3, the first part is 1 ÷ 4 = 25% of the whole and the second is 75%.