Rule of three calculator

Solve a direct or inverse proportion. We show the working, not only the result.

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Your figures

Result

...equals 15.0000
Working
Si 2 → 6, entonces 5 → 15
Proportion
Directa (los dos suben a la vez)
Constant of proportionality
3.0000

What we assume

  • In a direct proportion the two quantities grow together: double one, double the other.
  • In an inverse one the product stays constant: double one, halve the other.
  • Picking the wrong type gives an answer that is mathematically correct and practically wrong.

How it is calculated

A rule of three links two proportional quantities to find a fourth value from three known ones.

Direct

Both quantities rise or fall together. If 2 kg cost 6, then 5 kg cost 15.

x = b x c / a

Inverse

When one goes up, the other goes down. If 4 workers take 6 days, 3 workers will take 8, because there are fewer hands for the same job.

x = a x b / c

How to tell which one you need

Ask yourself: if the first value doubles, does the other double or halve? Prices, distances and recipes are usually direct. Speeds, headcounts and flow rates are usually inverse.

An example

Direct: if 2 kg of tomatoes cost 6, then 5 kg cost 15.

Inverse: if 4 painters finish in 6 days, 3 painters will take 8 days.

Frequently asked questions

How do I know whether it is direct or inverse?

Check what happens when you double the first value. If the other doubles too, it is direct. If it halves, it is inverse. When in doubt, think of an extreme: with zero workers the job never finishes, so it is inverse.

Can I use it to scale a recipe?

Yes, that is the textbook direct proportion: if 4 people need 300 g, 6 people need 450 g.

What about a compound rule of three?

This one solves the simple case, with two quantities. For a compound one, apply it in steps: solve one proportion and feed the result into the next.

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Updated on 2026-08-26. Calculations run in your browser; nothing you type is sent to a server.

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