All calculators

Ratio Calculator

Enter a ratio as A : B = C : D. Leave one term blank to solve for it, or leave both right-hand terms blank to reduce the ratio to lowest terms.

Your ratio

A : B = C : D. Leave one term blank to solve for it, or leave both C and D blank to simplify A : B.
Working
C = (A × D) ÷ B = (3 × 72) ÷ 8 = 27
Share of the total
A 27.27%, B 72.73%
Missing term C
27
Full ratio
3 : 8 = 27 : 72
In lowest terms
3 : 8
As a decimal (A ÷ B)
0.375
In 1 : n form
1 : 2.6667
In n : 1 form
0.375 : 1

How to use this calculator

The four fields are the four terms of A : B = C : D. What the calculator does depends on which of them you leave empty.

What each pattern of entries does
To do thisEnterYou get
Solve for a missing termA 3, B 8, C blank, D 72C = 27, so 3 : 8 = 27 : 72
Simplify a ratioA 14, B 28, C and D blank1 : 2
Scale a ratio upA 2, B 5, C 8, D blankD = 20
Check two ratios matchAll four filled inEquivalent, or not

Leaving more than one term blank, other than C and D together, gives the calculator too little to work with, and it says so rather than guessing.

How ratios are solved and simplified

Two ratios are equal when their cross products are equal. That single fact is what lets any one of the four terms be recovered from the other three.

A : B = C : D when A × D = B × C
  • A × D — the first term times the last, e.g. 3 × 72 = 216
  • B × C — the middle two multiplied, e.g. 8 × 27 = 216
  • Equal cross products — the two ratios are equivalent

Rearranging gives the missing term directly. With C unknown, C = (A × D) ÷ B, so (3 × 72) ÷ 8 = 27.

Simplifying is a different operation: divide both terms by their greatest common divisor. 14 : 28 shares a divisor of 14, so it reduces to 1 : 2. Reducing never changes the relationship — 1 : 2, 7 : 14 and 14 : 28 are all the same ratio, which is why any of them can stand for the others.

A worked example

A recipe uses flour and water in the ratio 3 : 8 and you have 72 g of water. Enter 3 and 8 as A and B, leave C blank, and put 72 in D. Cross-multiplying gives(3 × 72) ÷ 8 = 27, so you need 27 g of flour.

The share figures answer the other common question. Three parts and eight parts make eleven, so flour is 27.27% of the mixture and water 72.73%. Scaling the whole recipe to 550 g means 150 g of flour and 400 g of water.

Frequently asked questions

How do I simplify a ratio?

Divide both terms by their greatest common divisor. For 14 : 28 that divisor is 14, so the ratio is 1 : 2. Enter 14 and 28 in A and B, leave C and D blank, and the calculator does exactly that.

How do I find a missing term in a ratio?

Cross-multiply. In 3 : 8 = C : 72, multiply 3 by 72 and divide by 8, which gives 27. The rule is the same wherever the gap is: the missing term is the product of the two terms diagonally opposite it, divided by the one beside it.

What do the 1 : n and n : 1 forms mean?

They are the same ratio rescaled so one side is exactly one. 3 : 8 is 1 : 2.6667 and 0.375 : 1. The first is how map scales and mixing ratios are written; the second is useful when you want the answer per unit of the second quantity.

How do I split an amount in a ratio?

Use the share of the total shown under the inputs. For 3 : 8 the shares are 27.27% and 72.73%, because there are 11 parts in total. Splitting £550 in that ratio gives £150 and £400.

Can I use decimals in a ratio?

Yes. 1.5 : 2 is a valid ratio and simplifies to 3 : 4, because scaling both sides by the same amount never changes a ratio. The calculator scales decimals up to whole numbers before reducing.

Is a ratio the same as a fraction?

They are closely related but read differently. The ratio 3 : 8 compares two parts, while the fraction 3/8 compares one part to the whole of the other. Mixing 3 : 8 means 3 parts in 11 total, which is 3/11 of the mixture rather than 3/8 of it.