Skip to content
Dark mode

Ratio calculator

Direct and inverse proportion, with every step shown.

Type of calculation

Result

Answer
28

How it is worked out

Step 1, find the value of one: 12 divided by 3 is 4.

Step 2, scale up to the quantity you want: 4 times 7 is 28.

Step 3, the answer: 3 goes with 12, so 7 goes with exactly 28.

This ratio calculator solves problems where three values are known and the fourth is missing. Enter the three values and it shows the answer together with every step of the working. Both kinds are covered: direct proportion, where more means more, and inverse proportion, where more means less.

How direct proportion works

Three apples cost £12. What do seven cost? First find the value of one: £12 divided by 3 is £4 an apple. Then scale up: £4 times 7 is £28. Those two steps, divide by the known quantity and multiply by the one you want, are the whole method.

When to use inverse proportion

Some problems work the other way round. Three workers take 12 days to finish a job. How long do seven take? Here you multiply first and divide second: 3 times 12 is 36 working days in total, divided by 7 workers is about 5.14 days. The deciding question: does the answer get bigger or smaller when the known quantity goes up? If smaller, it is inverse proportion.

Example: scaling a recipe

A cake recipe for 4 people needs 300 g of flour, and you are baking for 6. Find the amount for one person: 300 divided by 4 is 75 g. Then scale up: 75 times 6 is 450 g. Every other ingredient scales the same way. For shares expressed as percentages, use the percentage calculator.

Frequently asked questions

What is a ratio calculator for?

For finding a missing fourth value when three are known and the two quantities are in proportion, like prices, recipes or map scales.

How do I solve a direct proportion problem?

Divide the known value by the known quantity, then multiply by the quantity you want. If 3 apples cost £12, one costs £4 and seven cost £28.

What is the difference between direct and inverse proportion?

In direct proportion the answer grows when the known quantity grows. In inverse proportion it shrinks, as with more workers needing less time.

Does it show the working?

Yes, every step is shown on its own line so you can copy it into your exercise book.

How do I know which kind I need?

Ask whether the answer gets bigger or smaller when the known quantity goes up. Bigger means direct, smaller means inverse.


Updated on