Ratio Calculator
Simplify a ratio to its lowest terms or scale a ratio by a multiplier. Useful for mixing, recipes, maps, and more.
How to use this tool
- Enter the two values in the ratio (A and B).
- Optionally enter a scale multiplier (default 1 = just simplify).
- Read the simplified and scaled ratio.
Simplify any ratio to its lowest terms and optionally scale it up or down by a multiplier.
Formula
Simplified ratio: divide both A and B by their Greatest Common Divisor (GCD).
GCD(A, B) is found via the Euclidean algorithm: repeatedly replace the larger number with the remainder of dividing the two, until the remainder is 0.
Simplified A = A ÷ GCD(A, B) | Simplified B = B ÷ GCD(A, B)
Scaled A = Simplified A × Scale | Scaled B = Simplified B × Scale
How it works
This calculator reduces a ratio to its lowest terms by dividing both values by their greatest common divisor, computed using the Euclidean algorithm. An optional scale multiplier then proportionally enlarges both simplified terms, making it easy to work with recipes, maps, or mixing ratios at a different quantity. Results are exact for whole-number inputs; floating-point inputs may yield non-integer simplified values.
Worked example
Worked example
- Inputs: A = 6, B = 9, Scale = 1.
- GCD(6, 9): 9 mod 6 = 3; 6 mod 3 = 0 → GCD = 3.
- Simplified A = 6 ÷ 3 = 2; Simplified B = 9 ÷ 3 = 3.
- Scaled A = 2 × 1 = 2; Scaled B = 3 × 1 = 3.
Simplified ratio: 2 : 3 | Scaled ratio: 2 : 3
Key terms
- Ratio
- A comparison of two quantities expressed as A : B, showing their relative sizes.
- Greatest Common Divisor (GCD)
- The largest integer that divides both A and B without a remainder; used to reduce a ratio to its simplest form.
- Euclidean algorithm
- An efficient method for finding the GCD by repeatedly taking remainders until zero is reached.
- Simplest form
- A ratio where A and B share no common factor greater than 1 — the most reduced representation.
- Scale multiplier
- A number applied to both simplified ratio terms to produce an equivalent ratio at a different magnitude.
Frequently asked questions
- How do I simplify a ratio?
- Divide both parts of the ratio by their greatest common divisor (GCD). For 6:9, GCD=3, so 6/3 : 9/3 = 2:3.
- What are common uses for ratios?
- Ratios appear in recipes (flour to water), mixing (paint, concrete), maps (scale), finance (debt-to-income), and photography (aspect ratio).