Ratio of Three Numbers Calculator — Simplify A : B : C
Enter any three positive numbers to get the simplified A : B : C ratio in lowest terms and the percentage each number represents of the combined total. A colour-coded bar visualises the three-way split.
Simplified ratio: 2 : 3 : 5
- 1
GCD of A and B
GCD(2, 3) = 1 - 2
GCD of all three
GCD(1, 5) = 1 - 3
Simplified ratio A : B : C
2 : 3 : 5 - 4
Total A + B + C
2 + 3 + 5 = 10
How does this calculator work?
Divide all three numbers by their GCD to get the simplified ratio. For 6 : 9 : 15, GCD = 3 gives 2 : 3 : 5. The percentage split (here 20% : 30% : 50%) shows each part's share of the combined total A + B + C.
Formula
How this is calculated
Simplifying a three-number ratio works the same way as a two-number ratio: divide all three values by their greatest common divisor. GCD(A, B, C) is calculated by applying the two-value GCD rule twice — first GCD(A, B), then GCD(that result, C). For example, 6 : 9 : 15 gives GCD(6, 9) = 3, then GCD(3, 15) = 3, so the simplified ratio is 2 : 3 : 5.
Each part can also be expressed as a percentage of the combined total (A + B + C). For 2 : 3 : 5 the total is 10, giving 20 %, 30 %, and 50 % respectively. This percentage view is natural when distributing profits among three partners, reading a three-ingredient recipe proportion, or interpreting a three-segment survey result.
GCD-based simplification applies cleanly only to whole-number inputs. With decimal inputs the ratio is displayed as entered, and the percentage breakdown and visual bar still reflect the correct proportions. All three values must be strictly positive; a zero part would create a degenerate ratio.
Frequently asked questions
Find GCD(A, B) first using the Euclidean algorithm, then find GCD(result, C). For example, GCD(12, 8, 20): GCD(12, 8) = 4, then GCD(4, 20) = 4.
Add all three parts to get the total, then divide each by the total and multiply by 100. For 2 : 3 : 5 the total is 10, so percentages are 20%, 30%, and 50%.
Yes. Enter each person's share weight as A, B, and C. The percentage breakdown tells each person their share of the total, and you can multiply total amount by each percentage to find the actual monetary value.
Also known as
TG we-Calculate Editorial Team. (2026). Ratio of Three Numbers Calculator — Simplify A : B : C [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/ratio-of-3-numbers-calculator
TG we-Calculate Editorial Team. "Ratio of Three Numbers Calculator — Simplify A : B : C." TG we-Calculate. 2026. https://we-calculate.com/calculator/ratio-of-3-numbers-calculator.
TG we-Calculate Editorial Team, "Ratio of Three Numbers Calculator — Simplify A : B : C," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/ratio-of-3-numbers-calculator
@misc{wecalculate_ratio_of_3_numbers_calculator, title = {Ratio of Three Numbers Calculator — Simplify A : B : C}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/ratio-of-3-numbers-calculator}}, year = {2026}, note = {TG we-Calculate} }
Did this calculator help you?