Simplify Ratio Calculator — Reduce A:B to Lowest Terms
Enter two or three positive whole numbers and get the equivalent ratio in its simplest form — all parts are divided by their GCD so the result uses the smallest possible integers.
- 1
Greatest common divisor
GCD(12, 18) = 6The GCD is the largest integer that divides both parts without remainder. - 2
Divide each part by GCD
12 ÷ 6 : 18 ÷ 6 = 2 : 3
How does this calculator work?
Simplified A:B = (A ÷ GCD(A,B)) : (B ÷ GCD(A,B)). For three parts use GCD(GCD(A,B),C). GCD is found via the Euclidean algorithm. Example: 12:18 → GCD = 6 → 2:3. The simplified ratio expresses the same proportional relationship using the smallest whole numbers.
Formula
How this is calculated
A ratio A:B is in simplest form when GCD(A, B) = 1 — the parts share no common factor greater than 1. To reduce it, compute the GCD using the Euclidean algorithm (repeatedly replace with the remainder until zero), then divide all parts by that GCD. For a three-part ratio A:B:C, compute GCD(GCD(A, B), C) and divide all three parts.
For example, 12:18 → GCD(12, 18) = 6 → 2:3. Both ratios express the same relationship: for every 2 units of A there are 3 units of B. The simplified form uses the fewest integers while preserving the proportion exactly.
Only positive whole numbers are accepted. Ratios involving fractions or decimals can be converted: multiply all parts by the LCM of their denominators to clear fractions, then simplify.
Frequently asked questions
Find the GCD of all parts and divide each part by it. For example, 15:25 → GCD = 5 → 3:5. Verify by confirming no integer greater than 1 divides all of the resulting parts.
Yes. For A:B:C, compute GCD(A, B) first, then GCD(that result, C). Divide all three parts by this final GCD. For example 6:9:12 → GCD = 3 → 2:3:4.
A fraction a/b represents part of a whole (a out of b), while a ratio a:b compares two independent quantities. Simplifying uses the same GCD method, but a ratio can have more than two parts and does not imply a single whole to divide.
Also known as
TG we-Calculate Editorial Team. (2026). Simplify Ratio Calculator — Reduce A:B to Lowest Terms [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/simplify-ratio-calculator
TG we-Calculate Editorial Team. "Simplify Ratio Calculator — Reduce A:B to Lowest Terms." TG we-Calculate. 2026. https://we-calculate.com/calculator/simplify-ratio-calculator.
TG we-Calculate Editorial Team, "Simplify Ratio Calculator — Reduce A:B to Lowest Terms," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/simplify-ratio-calculator
@misc{wecalculate_simplify_ratio_calculator, title = {Simplify Ratio Calculator — Reduce A:B to Lowest Terms}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/simplify-ratio-calculator}}, year = {2026}, note = {TG we-Calculate} }
Did this calculator help you?