Rule of Three Calculator

Solve a proportion in seconds. Enter three known values and get the fourth, for direct or inverse proportions.

Enter the three values you know and the fourth appears immediately, with the cross-multiplication written out underneath.

Example: if 3 shirts cost 45, then 5 shirts cost ?

Gives

How Does It Work?

  1. Choose direct or inverseDirect means both quantities move the same way — more items, more cost. Inverse means they move in opposite directions — more workers, less time.
  2. Enter the three values you knowRead it as a sentence: if A gives B, then C gives what?
  3. Read the fourth valueThe answer appears with the multiplication and division written out so you can check it.

What Is It Used For?

The rule of three is the quickest way to scale one known relationship up or down. It is the maths behind recipe conversions, unit prices, map scales, fuel estimates and dosage checks — anywhere two quantities keep a constant ratio.

  • Scaling a recipe from 4 servings to 7.
  • Working out the price of 5 items when 3 items cost a known amount.
  • Converting a map scale or a plan measurement to real distance.
  • Estimating how long a job takes with a different number of people (inverse).
  • Checking a per-unit price against a bulk price before you buy.

Examples

ProblemTypeAnswer
3 shirts cost 45 → 5 shirts cost?Direct75
200 g flour serves 4 → serves 6?Direct300 g
3 workers take 45 min → 5 workers?Inverse27 min
A car at 90 km/h takes 4 h → at 120 km/h?Inverse3 h

Frequently Asked Questions

What is the rule of three?

It is a way to find a missing fourth value when you know three values of a proportion. In a direct proportion you multiply the two diagonal values and divide by the remaining one — this is also called cross multiplication.

What is the difference between direct and inverse proportion?

In a direct proportion both quantities grow together: double the items, double the cost. In an inverse proportion one grows as the other shrinks: double the workers, halve the time. Choose the matching option above and the formula adjusts automatically.

How do I know which type I need?

Ask yourself what happens if the third value doubles. If the answer should also double, it is direct. If the answer should halve, it is inverse.

Can I use it for percentages?

Yes. A percentage is a proportion out of 100. If 180 is 100%, then 45 is (100 × 45) ÷ 180 = 25%. Our percentage calculator does this directly.

Does it handle decimals?

Yes — all three inputs accept decimal values, and results are shown to four decimal places when needed.

Free. No registration. This tool runs entirely in your browser, so the data you enter stays on your device.