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Triangle Calculator

Find the area, perimeter, angles and type of a triangle from its three sides, using Heron's formula and the Law of Cosines.

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Triangle Calculator
Solve any triangle from 3 known values — sides, angles, area
Triangle
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Disclaimer. This calculator is provided for educational and general-purpose use. Verify critical or high-stakes calculations independently before relying on them. Read full disclaimer →

About Triangle Calculator

A triangle is fully determined by any three elements (sides or angles) where at least one is a side. Area = half times base times height. For two sides and included angle: Area = 0.5 times a times b times sin(C). For all three sides, use Heron's formula: Area = square root of s(s-a)(s-b)(s-c) where s is the semi-perimeter (perimeter divided by 2).

Law of Sines: a divided by sin(A) equals b divided by sin(B) equals c divided by sin(C) - use when you know two angles and a side. Law of Cosines: c squared = a squared plus b squared minus 2ab times cos(C) - use for two sides and included angle or all three sides known. Sum of all interior angles always equals 180 degrees. This tool handles all valid triangle configurations and shows all computed properties.

Frequently Asked Questions

For a triangle where all three sides (SSS) are known, Heron's formula gives the area as the square root of s(s-a)(s-b)(s-c), where s is the semi-perimeter (perimeter divided by 2). For example, a classic 3-4-5 right triangle has s=6, so area = sqrt(6×3×2×1) = sqrt(36) = 6, which matches the simpler 0.5×base×height calculation for that same right triangle.
It solves SSS (three known sides) and right-triangle problems given the hypotenuse and one other side (RHS). Other classic configurations like SAS, ASA or AAS aren't supported yet — if you select one of those modes, the tool will ask you to use SSS or the right-triangle mode instead.
Type (acute, right or obtuse) is based on the largest computed angle: right if any angle is essentially 90°, obtuse if the largest angle exceeds 90°, otherwise acute. Shape (scalene, isosceles or equilateral) is based on comparing the three side lengths for equality.
When you only know the three side lengths and not the angles, the Law of Cosines (c² = a² + b² − 2ab·cos(C)) lets you solve algebraically for each angle from the sides alone. This is what makes it possible to fully solve an SSS triangle — area, all three angles, and perimeter — from side lengths only.
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