Ratio Calculator

What a ratio says

A ratio compares two quantities: 3 : 4 means that for every three of the first there are four of the second. Unlike a fraction it does not have to refer to a whole — it is a relationship, which is why recipes, mixes, maps and screen sizes are all written this way.

Formula

• A : B = C : D means A × D = B × C, so D = C × B ÷ A
• Simplify by dividing both sides by their highest common factor
• Share of A = amount × A ÷ (A + B)

Worked example

With 3 : 4 = 15 : D, the missing value is 20, because 15 is five times 3 and the same scale applies to the other side. Splitting 70,000 in 3 : 4 gives 30,000 and 40,000.

How to use the ratio calculator

1. Enter the ratio you know as A and B.
2. Enter C, the new value for the first side, and D is worked out for you.
3. Add an amount to split it between the two sides in the same proportion.

Where ratios turn up

• Recipes and mixes: concrete at 1 : 2 : 4, rice and water at 1 : 2.
• Screens and photos: 16 : 9 and 4 : 5 are ratios of width to height.
• Business partnerships: profit shared in the ratio of what each partner put in.
• Maps and drawings: a 1 : 500 scale means one centimetre on paper is five metres on the ground.

Frequently asked questions

How do I simplify a ratio?

Divide both numbers by their highest common factor. 12 : 18 both divide by 6, giving 2 : 3. The calculator shows the simplest form as you type.

How do I split an amount in a ratio?

Add the parts together, divide the amount by that total, then multiply by each part. For 70,000 in 3 : 4, one part is 10,000, so the split is 30,000 and 40,000.

What is the difference between a ratio and a fraction?

A fraction compares a part to the whole; a ratio compares one part to another. In 3 : 4 the first quantity is three sevenths of the total, not three quarters.