When does rule of three fail?

When the relation isn't proportional. Cooking time of an egg doesn't double for two eggs; economies of scale, tiered pricing, non-linear physics break proportionality.

Difference with percentage?

A percentage is a special rule of three with A = 100. For any other proportion, rule of three is more general.

Calculation & finance

Rule of three

Solve a rule of three (cross-multiplication): if A corresponds to B, then C corresponds to ? Enter the three known values, the fourth appears.

If A corresponds to B, then C corresponds to ? (D = B × C / A)

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Formula

D = B × C / A

How to use this tool

Rule of three computes a proportion: if 3 apples cost $2, what do 5 apples cost? Formula: D = B × C / A, where A ↔ B is the known pair and C ↔ D the unknown. Universal tool for scaling recipes, exchange rates, proportions, mixing ratios, etc.

Concrete examples

If 3 apples cost $2, then 5 apples cost $3.33
If 100 km uses 6 L of fuel, 250 km uses 15 L
A recipe for 4 requires 200 g flour; for 6, 300 g

Frequently asked questions

When does rule of three fail?: When the relation isn't proportional. Cooking time of an egg doesn't double for two eggs; economies of scale, tiered pricing, non-linear physics break proportionality.
Difference with percentage?: A percentage is a special rule of three with A = 100. For any other proportion, rule of three is more general.