How to solve a rule of three
- Choose whether the proportion is direct or inverse.
- Type A and B, the values that match each other.
- Type C, the value you want the equivalent of.
- See X and the step-by-step calculation.
Direct and inverse rule of three
The simple rule of three works when you have three values and want the fourth, which keeps a proportion. In the direct kind, if one quantity increases, so does the other: if 2 pounds cost 10, then 5 pounds cost 5 × 10 ÷ 2 = 25.
In the inverse kind, if one quantity increases, the other decreases: if 4 workers finish a job in 6 days, 8 workers finish it in 4 × 6 ÷ 8 = 3 days. The formula is A × B ÷ C instead of B × C ÷ A.
To tell which one to use, ask yourself: if C is larger than A, should X be larger or smaller than B? If larger, it's direct; if smaller, it's inverse. It works for recipes, map and blueprint scales, non-medical doses, fuel consumption and prices by quantity.
Good to know
- It assumes a strictly proportional relationship; it doesn't work when there are quantity discounts or other conditions.
- Don't use this tool to calculate medication doses: ask a professional.
- The result is shown with up to 6 decimals.
Frequently asked questions
How do you solve a simple direct rule of three?
Multiply B by C and divide by A. If 2 lb cost 10, 5 lb cost (10 × 5) ÷ 2 = 25.
When is it inverse?
When one quantity goes up and the other goes down, like workers and days of work, or speed and travel time.
How do I place the values?
A and B are the pair you already know (A matches B) and C is the value you want the equivalent X of.
Does it work for percentages?
Yes, but the percentage calculator is better for that, since it already covers the most common cases.
Are my numbers saved?
No. Everything is calculated in your browser.