Case 1
- Value A
- 3
- Value B
- 12
- Value C
- 5
- Type of proportion
- Direct (proportional)
20.0000
Open with these valuesRule of Three Calculator
20.0000
Result: 20.0000Three known numbers and one unknown: if 3 items cost 12, then 5 items cost (12 × 5) ÷ 3 = 20. That is the direct rule of three. Pick the inverse type when one quantity falls as the other rises — more workers, less time — and the calculator divides by C instead of by A.
The numbers at a glance
Held fixed: Value A 3.0000, Value B 12.0000, Type of proportion Direct (proportional).
| Value C | Result |
|---|---|
| 2.0000 | 8.0000 |
| 4.0000 | 16.0000 |
| 5.0000Your value | 20.0000 |
| 6.0000 | 24.0000 |
| 8.0000 | 32.0000 |
| 10.0000 | 40.0000 |
Worked examples
Case 2
- Value A
- 2.5
- Value B
- 5
- Value C
- 4
- Type of proportion
- Direct (proportional)
8.0000
Open with these valuesCase 3
- Value A
- 4
- Value B
- 6
- Value C
- 2
- Type of proportion
- Inverse (inversely proportional)
12.0000
Open with these valuesHow it's calculated
direct x = (B × C) ÷ A · inverse x = (A × B) ÷ C
- StepWrite your numbers as A : B = C : x, with x the value you are after.
- StepChoose direct when both quantities move together, inverse when one falls as the other rises.
- ResultDirect divides by A, inverse divides by C — the calculator does that step for you.
Reference table
| Proportion | Type | x |
|---|---|---|
| 3 : 12 = 5 : x | Direct | 20 |
| 2 : 5 = 8 : x | Direct | 20 |
| 2.5 : 5 = 4 : x | Direct | 8 |
| 4 : 6 = 2 : x | Inverse | 12 |
| 8 : 3 = 4 : x | Inverse | 6 |
Questions
What is the rule of three?
It is the method for finding an unknown value in a proportion. Given three numbers arranged as A : B = C : x, it solves for the fourth. It is the everyday name for cross-multiplication, and German calls it the Dreisatz.
How do I calculate the rule of three?
For a direct proportion, multiply B by C and divide by A: x = (B × C) ÷ A. For example 3 : 12 = 5 : x gives (12 × 5) ÷ 3 = 20. For an inverse proportion, use x = (A × B) ÷ C instead.
What is the difference between direct and inverse proportion?
In a direct proportion both quantities move the same way — more items cost more money. In an inverse proportion they move opposite ways — more workers means less time to finish the job. Pick the type that matches your situation, because the two give different answers from the same three numbers.
Why must A and C be greater than zero?
The rule of three divides by one of your inputs: by A in a direct proportion, by C in an inverse one. Dividing by zero has no answer, so both are kept above zero. B may be zero, because nothing ever divides by it.
Where is the rule of three used?
Anywhere a fixed ratio holds: scaling a recipe, converting currency, working out unit prices, mixing paint or fuel, reading a map scale. The inverse form covers speed-and-time and workers-and-duration problems, where one quantity rises as the other falls.
Sources and last check
Information, not professional advice.