Rule of Three Calculator

Solve proportions with the rule of three: enter three values and the fourth is calculated as you type. Covers direct and inverse proportionality, shows the formula with your numbers plugged in, and explains the result in a sentence.

Runs entirely in your browser. Nothing you put in here gets uploaded.

Setup

How the two quantities relate, which value to solve, and how results round.

Proportionality

More of one means more of the other in the same ratio. Twice the apples cost twice as much.

Solve for

Auto solves the field you leave empty.

Decimal places

Values

Fill in three values. The highlighted one is calculated for you.

Unit for A and C

Unit for B and X

applescorrespond to

€

then

applescorrespond to

€

Result

The formula with your numbers plugged in, the solved value, and the answer in words.

X = B × C ÷ A

X = 2 × 7 ÷ 3 = 4.67

Result (X)

4.67€

In words

If 3 apples correspond to 2 €, then 7 apples correspond to 4.67 €.

About the Rule of Three Calculator Tool

This tool solves proportions with the rule of three. Fill in three of the four values in the sentence and the fourth is calculated as you type, whichever one you leave out. It handles both direct proportionality, where the values grow together, and inverse proportionality, where one shrinks as the other grows.

The formula is always shown with your numbers plugged in, so you can see exactly how the answer was reached, and the result is also written out as a plain sentence. Optional unit labels like apples and € make that sentence read naturally.

What you can do

Solve a proportion for any of the four positions, not just the last one.
Switch between direct and inverse proportionality with one toggle.
See the cross multiplication formula with your own numbers filled in.
Read the answer as a full sentence, with your own unit labels.
Type decimals with a point or a comma, both are understood.
Copy the result or the sentence with one click, and set the decimal places.

How to use the Rule of Three Calculator

1Pick direct or inverse proportionality. The one line explanation tells you which fits.
2Type three of the four values into the sentence and leave the one you want to find empty, or pick it under Solve for.
3Optionally name the two quantities, like apples and €, so the answer reads as a sentence.
4Read the result next to the formula and copy it with the button.

Direct or inverse?

Direct proportionality means the two quantities move together. If 3 apples cost 2 €, then 7 apples cost more, and the tool computes X = B × C ÷ A. Prices, distances and recipe amounts usually work this way.

Inverse proportionality means one quantity shrinks as the other grows. If 4 workers need 6 hours, then 8 workers need less time, not more, and the formula becomes X = A × B ÷ C. Workers and time, speed and travel time, or pump count and fill time are typical inverse cases. If your answer looks upside down, you probably need the other mode.

Where the formula comes from

The rule of three is cross multiplication in disguise. In a direct proportion A : B = C : X the products across the equals sign match, so A × X = B × C, and dividing by A gives X. In an inverse proportion the products of each pair match instead, so A × B = C × X. The tool picks the right rearrangement for whichever value you left empty and shows it with your numbers, so you can follow the math or copy it into homework.

Some questions have no answer. When the value you solve for would require dividing by zero, the tool says so in plain words instead of showing an error code. For percentage questions like discounts and tips, the Percentage Calculator asks them directly, and for switching between measurement units there is the Unit Converter.

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