Ratio Calculator

Simplify a ratio such as 12 : 8, find the missing number in a proportion, or share an amount in a given ratio. You get the answer in lowest terms with the working shown, all in your browser.

Type the parts of the ratio (for example 12 : 8). The third box is optional.

First part

Second part

Third part (optional)

Simplified ratio

3 : 2

12 : 8 simplifies to 3 : 2.

First part’s share: 60%
Second part’s share: 40%
First ÷ second: 1.5

Calculated instantly in your browser with standard formulas. Double-check anything important. Full disclaimer and terms of use.

What a ratio is

A ratio compares two or more amounts. A recipe that uses 2 cups of flour for every 1 cup of sugar has a flour to sugar ratio of 2 : 1. Ratios have no units of their own, so 2 : 1 works whether you measure in cups, grams or spoonfuls. The same ratio can be written as a fraction (2/1), a decimal (2) or a percentage share (about 66.7% flour and 33.3% sugar).

How to simplify a ratio

Find the greatest common factor of all the parts, the largest number that divides each of them exactly.
Divide every part by it. 12 : 8 has a greatest common factor of 4, so it simplifies to 3 : 2.
If a part has decimals, multiply all parts by 10, 100 or 1,000 until they are whole numbers first. 1.5 : 2.5 becomes 15 : 25, then 3 : 5.
A ratio in lowest terms has no common factor left, so 3 : 2 cannot be reduced any further.

How to find the missing number in a proportion

A proportion says two ratios are equal, such as 2 : 3 = 4 : 6. To find a missing number, cross-multiply: the first number times the last equals the second times the third (A × D = B × C). If 2 : 3 = 4 : ?, then 2 × ? = 3 × 4, so the missing number is 12 ÷ 2 = 6. This is the method behind scaling a recipe, converting a map scale and working out unit prices.

How to split an amount in a ratio

Add the parts of the ratio. For 3 : 2 the total is 5 parts.
Divide the amount by the number of parts. 100 ÷ 5 = 20 per part.
Multiply by each part: 3 × 20 = 60 and 2 × 20 = 40.
Check that the shares add back up to the amount: 60 + 40 = 100.

Common ratios

Where	Ratio	Meaning
Widescreen video and TVs	16 : 9	Width to height
Older screens and some photos	4 : 3	Width to height
Square photos	1 : 1	Width to height
Pancake batter	1 : 1 : 1	Flour, milk and eggs by weight, roughly
Concrete mix (general purpose)	1 : 2 : 3	Cement, sand and gravel by volume
Map scale 1 : 50,000	1 : 50,000	1 unit on the map is 50,000 units on the ground

Mistakes to avoid

Mixing units. 30 minutes : 2 hours is 30 : 120, which simplifies to 1 : 4, not 15 : 1.
Reading the order backwards. A ratio of boys to girls of 3 : 2 is not the same as girls to boys.
Mixing up a part with the whole. In the ratio 3 : 2 the first part is 3 out of 5 parts, which is 60%, not 3 out of 2.
Forgetting to simplify before comparing two ratios.

How to simplify a ratio in Excel or Google Sheets

With the two numbers in A1 and B1, use =A1/GCD(A1,B1) and =B1/GCD(A1,B1) to get the simplified parts. To show them as text, use =A1/GCD(A1,B1)&" : "&B1/GCD(A1,B1).

How to use the Ratio Calculator tool

Choose Simplify a ratio, Find the missing number or Split an amount.
Type the numbers. For a proportion, fill in three of the four boxes and leave one empty.
Read the answer, the shares as percentages and the working.
Use the copy icon to copy a result.

Frequently asked questions

How do I simplify a ratio?

Divide every part by their greatest common factor. For 12 : 8 the greatest common factor is 4, so 12 ÷ 4 : 8 ÷ 4 gives 3 : 2. The calculator also handles decimals: 1.5 : 2.5 becomes 3 : 5.

How do I find the missing number in a proportion?

Cross-multiply. If A : B = C : D, then A × D = B × C. For 2 : 3 = 4 : ?, the missing number is 3 × 4 ÷ 2 = 6.

How do I split an amount in a ratio?

Add the parts of the ratio, divide the amount by that total, then multiply by each part. Sharing 100 in the ratio 3 : 2 gives 100 ÷ 5 = 20 per part, so 60 and 40.

Can a ratio have three or more parts?

Yes. Use the third box for ratios such as 2 : 3 : 5. The calculator simplifies and splits three-part ratios in the same way.

Can I use zero or negative numbers?

A part can be 0 (for example 0 : 5 simplifies to 0 : 1) as long as at least one part is above 0. Negative numbers do not make sense in a ratio, so they are not accepted.