Triangle Ratio Calculator — Sides from a Ratio and Perimeter
Enter the ratio of the three sides and the perimeter to find the actual side lengths, angles, and area of the triangle. Works for any ratio — whole numbers, decimals, or fractions.
Actual side a = Perimeter × r₁ / (r₁ + r₂ + r₃)
- 1
Sum of ratio parts
3 + 4 + 5 = 12 - 2
Scale factor (P ÷ ratio sum)
36 ÷ 12 = 3Each ratio part is multiplied by this factor to get the actual side length. - 3
Side a = P × r₁ ÷ ratio sum
36 × 3 ÷ 12 = 9
How does this calculator work?
For sides in ratio r₁:r₂:r₃ with perimeter P: a = P·r₁/(r₁+r₂+r₃), b = P·r₂/(r₁+r₂+r₃), c = P·r₃/(r₁+r₂+r₃). Enter the three ratio parts and perimeter to get actual side lengths, all angles, and area instantly.
Formula
How this is calculated
When the sides of a triangle are in the ratio r₁ : r₂ : r₃, the actual sides are proportional fractions of the total perimeter P. The sum of the ratio parts r₁ + r₂ + r₃ represents the whole perimeter, so each side equals P × rₙ / (r₁ + r₂ + r₃). For example, a 3:4:5 ratio with perimeter 36 gives sides 9, 12, 15.
Once the three side lengths are known, the calculator computes the area via Heron's formula (Area = √[s(s−a)(s−b)(s−c)], s = P/2) and all three interior angles via the Law of Cosines. The triangle is classified as equilateral, isosceles, or scalene based on the ratio parts.
Note that not every ratio r₁:r₂:r₃ produces a valid triangle: the resulting sides must satisfy the triangle inequality (sum of any two sides > third side). If the ratio implies one side is too long, the calculator shows a warning rather than an impossible result.
Frequently asked questions
Yes — ratio parts can be any positive number, including decimals. A 1.5:2:2.5 ratio gives the same triangle shape as 3:4:5 (just multiply by the same constant). Only the perimeter determines the actual size.
A 3:4:5 ratio produces a right triangle (angle C = 90°) because 3² + 4² = 5². Multiples such as 6:8:10 or 9:12:15 also produce right triangles. Enter ratio 3:4:5 and any perimeter to confirm the 90° angle.
Say you know side a. Then perimeter P = a × (r₁ + r₂ + r₃) / r₁. Compute P and enter it in the perimeter field. The other sides follow automatically.
Also known as
TG we-Calculate Editorial Team. (2026). Triangle Ratio Calculator — Sides from a Ratio and Perimeter [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/triangle-ratio-calculator
TG we-Calculate Editorial Team. "Triangle Ratio Calculator — Sides from a Ratio and Perimeter." TG we-Calculate. 2026. https://we-calculate.com/calculator/triangle-ratio-calculator.
TG we-Calculate Editorial Team, "Triangle Ratio Calculator — Sides from a Ratio and Perimeter," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/triangle-ratio-calculator
@misc{wecalculate_triangle_ratio_calculator, title = {Triangle Ratio Calculator — Sides from a Ratio and Perimeter}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/triangle-ratio-calculator}}, year = {2026}, note = {TG we-Calculate} }
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