Proportion Calculator
Enter any three values in A/B = C/D and instantly solve for the missing one. Works for ratios, scale problems, and any proportion equation.
What Is a Proportion?
A proportion is an equation stating that two ratios are equal. It takes the form A/B = C/D, read as "A is to B as C is to D." Proportions appear everywhere — scaling recipes, converting currencies, reading maps, and calculating percentages.
The four numbers in a proportion are called the terms. The outer terms (A and D) are called the extremes, and the inner terms (B and C) are the means. In any valid proportion, the product of the extremes equals the product of the means — this is called cross-multiplication.
How to Solve a Proportion
The key tool is cross-multiplication. If A/B = C/D, then:
To find any missing value, rearrange for the unknown:
B = (A × D) ÷ C
C = (A × D) ÷ B
D = (B × C) ÷ A
Worked Example
If 3/4 = ?/12, what is the missing value?
Cross-multiply: 3 × 12 = 4 × ? → 36 = 4? → ? = 9
Real-World Proportion Examples
🍕 Recipe Scaling
A recipe for 4 people uses 300 g flour. How much for 10 people?
🗺️ Map Scale
1 cm on a map = 50 km. A route measures 3.5 cm. How far is it?
💱 Currency Exchange
$1 = €0.92. How many euros is $250?
📐 Similar Triangles
Two similar triangles have sides 6 and 9. If the small one's other side is 8, find the large one's.
Direct vs. Inverse Proportion
This calculator handles direct proportion: as one quantity increases, the other increases at the same rate (A/B = C/D stays constant).
In inverse proportion, as one quantity increases, the other decreases (A × B = C × D is constant). For example: speed and travel time — going twice as fast takes half the time.