Ratio Calculator

Solve, simplify, scale and compare ratios. Results update as you type.

Know three numbers? Enter them and leave the fourth empty. Works for any position.

:
=
:
3 : 4 = 600 : 800
3 : 4
600 : 800
Show the working
  1. Treat each ratio as a fraction: A/B = C/D.
  2. Cross-multiply: A × D = B × C.
  3. Get D on its own: D = (B × C) ÷ A.
  4. Put the numbers in: (4 × 600) ÷ 3 = 800.

Reduce a ratio to lowest terms. Decimals are fine too.

:
:
12 : 18 = 2 : 3

Every term divides evenly by 6, the biggest number that fits them all.

As a fraction
2/3
As a decimal
0.6667
Unit form
0.667 : 1
Share of the whole
40% / 60%

Make a ratio bigger or smaller without changing what it means.

:
:
2 : 3 × 4 = 8 : 12
Before
After

The proportions stay identical, only the size changes. Each term was multiplied by 4.

Two ratios, one question: do they say the same thing?

:
vs
:
Equivalent
6/9 = 14/21

Both boil down to 2 : 3, so they describe the same relationship.

6 : 9
14 : 21
Show the working
  1. Cross-multiply: 6 × 21 = 126 and 9 × 14 = 126.
  2. The products match, so the ratios are equivalent.

Ratios, explained simply

A quick visual tour, from the basics to solving for the number you're missing.

What is a ratio?

A ratio compares two (or more) quantities of the same kind. It tells you how much of one thing there is for every bit of another.

Flour
Sugar

Two scoops of flour for each scoop of sugar. You can write that three ways:

2 : 12 to 121

How to calculate a ratio

Three moves, and you're done.

  1. Name the two things you're comparing, e.g. 12 boys and 8 girls.
  2. Check the units match. Convert first if one is in minutes and the other in hours.
  3. Write them in order with a colon: boys : girls = 12 : 8. Order matters, so keep it consistent.
Boys : girls = 12 : 8, which is the same as 3 : 2

How to simplify a ratio

Find the biggest number that divides every term, then divide. It's the same idea as reducing a fraction.

12 : 18, grouped in sixes
:

Two groups against three groups. So 12 : 18 = 2 : 3. You divided both by 6, the greatest common factor.

How to find a missing value

When two ratios are equal, you can cross-multiply to find the unknown.

34 = 600?
  • Multiply across the diagonal: 4 × 600 = 2,400
  • Divide by the number left over: 2,400 ÷ 3
  • The missing value is 800

Turning a ratio into a fraction

Add the parts to get the whole, then put each part over that total.

3 : 2, so the whole is 5 parts
35 = 60%
25 = 40%

Careful: 3 : 2 as a part-to-part fraction is 3/2, which is 1.5. Part-to-whole uses the total on the bottom.

Ratios in real life

Mixing paint
Blue to white at 2 : 5. Using 10 cans of white? Multiply both by 2 and you need 4 cans of blue.
Trail mix for a crowd
Nuts to fruit at 3 : 1 for one jar. Making 5 jars means 15 : 5 cups.
Reading a map
A scale of 1 : 50,000 means 1 cm on paper is 50,000 cm (500 m) on the ground.

Practice

0 / 5 solved

Simplify 18 : 24.

Solve 5 : 8 = 15 : ?

Pancake batter mixes flour and milk 3 : 4 by volume. With 600 ml of milk, how many ml of flour?

A bag holds 2 red and 3 blue marbles. What fraction of the bag is red?

Are 6 : 9 and 14 : 21 equivalent? (yes or no)

Keep going

Ratios, fractions and percentages are three views of the same idea. Hop between them:

Fraction calculatorFraction to decimalPercentage calculator