Rule of Three Calculator
Written by Thierno Sadou Diallo, formula verified per our methodology • Last checked on 9/5/2026
The rule of three is solved by cross-multiplication: if A corresponds to B, then C corresponds to (B × C) ÷ A. Example: if 3 kg costs $6, then 5 kg costs (6 × 5) ÷ 3 = $10.
Explanation
The rule of three (or "cross-multiplication") lets you solve a proportion with three known terms to find the fourth: it assumes a direct proportional relationship between the two quantities (doubling A doubles B). It's the tool behind many everyday calculations: converting a recipe for a different number of servings, calculating a price by weight, or scaling a percentage — in fact, the percentage calculator and the VAT calculator are both special cases of the rule of three where one term is fixed at 100. Caution: this method only applies to proportional quantities — it would be incorrect for quantities that don't vary linearly (for example, the time it takes several workers to finish a job isn't proportional to their number in the same way).
Example: price by weight
Inputs
A = 3 (kg), B = 6 ($), C = 5 (kg).
Calculation
The cross-multiplication is written: D = (B × C) ÷ A. First calculate the product B × C = 6 × 5 = 30, then divide by A: 30 ÷ 3 = 10.
Result
If 3 kg costs $6, then 5 kg costs $10.
Frequently asked questions
When can I use a rule of three?
Only when the two quantities are directly proportional: if one doubles, the other doubles too. That's true for a price by weight or a recipe, but false for quantities that follow a different relationship (for example, speed and travel time over a fixed distance, which are inversely proportional).
How do I scale a recipe with a rule of three?
Put the original quantity in A, the original number of servings in B, and the new number of servings in C: the result D gives the new quantity of the ingredient. Repeat this for each ingredient in the recipe.
What happens if the value A equals zero?
The calculation is meaningless: a reference value of zero can't correspond to any valid proportion (division by zero). The result then shows as unavailable rather than an incorrect number.