dopecalc

Ratio Calculator

Simplify a ratio to its lowest terms using the Greatest Common Divisor (GCD). Also scale a ratio by a given factor.

Simplify Ratio

Scale Ratio (optional)

About this Calculator

Simplify a ratio to its lowest terms using the Greatest Common Divisor (GCD). Also scale a ratio by a given factor.

Formula & Calculations

Formula

Simplified ratio a:b = (a/GCD(a,b)) : (b/GCD(a,b)). Scaled ratio = (a*k) : (b*k).
Where:
  • a : b=A ratio comparing two quantities
  • GCD=The Greatest Common Divisor used to simplify the ratio to its lowest terms
  • k=An optional scale factor to multiply both terms of the simplified ratio

Assumptions

  • Both numbers should be integers for meaningful simplification.
  • The GCD method ensures the simplified ratio is in lowest terms with integer components.
  • At least one of the two numbers must be non-zero.

Calculation Examples

Example 1

Inputs:12 : 18
Result:2 : 3

GCD(12, 18) = 6. Divide both by 6: 12/6 = 2, 18/6 = 3.

Example 2

Inputs:3 : 4 scaled by factor 5
Result:15 : 20

Multiply both terms of the simplified ratio by 5.

Frequently Asked Questions

How do you simplify a ratio?

Find the GCD of both numbers using the Euclidean algorithm, then divide both terms by the GCD. The resulting ratio is equivalent to the original but in lowest terms.

Can ratios have decimals?

Traditional ratios use whole numbers. If you have a decimal ratio like 1.5:3, multiply both sides by 10 to get 15:30, then simplify to 1:2.