Math & numbers · Basic
Ratio Calculator
Simplify ratios to their lowest terms and solve proportion problems (A:B = C:?). Shows the GCD, simplified ratio, and step-by-step calculation — free and instant.
How it works
Simplifies a ratio A:B by dividing both values by their Greatest Common Divisor (GCD). Also solves proportions: given A:B = C:?, finds the missing fourth value using cross-multiplication.
Formula
Simplified: A/GCD : B/GCD Proportion: D = B × C / A
- GCD
- Greatest Common Divisor of A and B
- D
- The unknown fourth value in the proportion
Step by step
- 1For simplification: find the GCD of A and B using the Euclidean algorithm.
- 2Divide both A and B by the GCD to get the simplified ratio.
- 3For proportion: cross-multiply to get D = B × C / A.
Examples
Simplify 12 : 8
GCD(12, 8) = 4. 12/4 = 3, 8/4 = 2 → 3:2.
Inputs
- mode:
- simplify
- a:
- 12
- b:
- 8
Result
- result:
- 3 : 2
Proportion: 4:6 = 10:?
D = 6 × 10 / 4 = 60 / 4 = 15.
Inputs
- mode:
- proportion
- a:
- 4
- b:
- 6
- c:
- 10
Result
- result:
- 15
Frequently asked questions
How do you simplify a ratio?▾
Find the Greatest Common Divisor (GCD) of both numbers, then divide each by it. For example, 12:8 → GCD is 4 → divide both by 4 → 3:2.
How do you solve a proportion?▾
Use cross-multiplication: if A:B = C:D, then D = (B × C) / A. For example, if 4:6 = 10:D, then D = (6 × 10) / 4 = 15.