Rule of three calculator

Enter three values and get the fourth. Choose direct proportion when more of one means more of the other, or inverse when more means less.

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rule-of-three-calculator

Fill in the values above to see the result.

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How it works

Write the known pair

If A corresponds to B.

Add the third number

Then C corresponds to what? Choose direct or inverse.

Read X

The result appears with the formula and a sentence that states it.

Three numbers in, the fourth out

The rule of three is the everyday tool for scaling a quantity. If 4 kilos of tomatoes cost 20, how much do 10 kilos cost? If a recipe for 4 people uses 300 g of rice, how much do you need for 10? If a map scale says 2 cm corresponds to 5 km, what distance is 7 cm? In each case you know a pair of related values and one new number, and you want the value that goes with it. The rule of three gives it in one step.

Direct proportion

When both quantities grow together and shrink together, they are directly proportional. Double the kilos, double the price. The unknown is found by multiplying the second value of the known pair by the new number and dividing by the first value of the pair: X = B × C ÷ A. With A = 4, B = 20 and C = 10, X = 20 × 10 ÷ 4 = 50. Prices, ingredients, distances at constant speed and exchange rates all work this way.

Inverse proportion

When one quantity grows as the other shrinks, they are inversely proportional. If 4 workers finish a job in 6 days, how long will 8 workers need? More workers mean fewer days. The product stays constant, so X = A × B ÷ C = 4 × 6 ÷ 8 = 3 days. Time and speed for a fixed distance, workers and time for a fixed job, and the number of people sharing a fixed cost all follow the inverse rule.

How to tell which one applies

Ask what happens to the second quantity when the first one increases. If the second also increases, it is direct. If it decreases, it is inverse. Getting this wrong is the most common mistake with the rule of three, so read the situation before pressing any buttons: the calculator cannot know which relationship your problem has.

What it does not do

It assumes a perfectly proportional relationship. Many real situations are not proportional: bulk discounts, fixed fees, tax brackets, cooking times and anything with a minimum charge. Use the result as an estimate when the relationship is only approximately proportional. For percentages there is a dedicated percentage calculator.

Frequently asked questions

How do I solve a rule of three?
Write the known pair (A corresponds to B) and the new value C. For a direct proportion, X = B × C ÷ A. Enter the three numbers and the tool gives X.
What is the difference between direct and inverse proportion?
In a direct proportion both quantities rise together, like kilos and price. In an inverse one, one rises as the other falls, like workers and days to finish a job.
How do I know which type to choose?
Ask whether the second quantity goes up or down when the first goes up. Up means direct, down means inverse.
Can I use it for recipes?
Yes, if quantities scale with the number of servings. Cooking times, spices and pans often do not scale in proportion, so adjust with judgement.
Does it work with decimals?
Yes. You can use decimals, with a point or a comma.
Is my data sent anywhere?
No. The calculation is done in your browser.

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