Triangle Solver (SSS)
Enter the three side lengths of a triangle to calculate all three angles and the area, using the law of cosines and Heron's formula.
Last updated: September 5, 2026
Frequently asked questions
What are the angles of a 3-4-5 triangle?
90°, 53.13°, and 36.87° - a 3-4-5 triangle is a right triangle, since 3² + 4² = 5² satisfies the Pythagorean theorem, and the angle opposite the longest side (5) is exactly 90°.
What's the area of a 3-4-5 triangle?
6 - using Heron's formula: s = (3+4+5)/2 = 6, area = √(6×(6-3)×(6-4)×(6-5)) = √(6×3×2×1) = √36 = 6.
What is the law of cosines?
c² = a² + b² − 2ab·cos(C), a generalization of the Pythagorean theorem that works for any triangle, not just right triangles. Rearranged to solve for an angle: cos(C) = (a² + b² − c²) / (2ab).
Why does this need three sides, and not angles or other combinations?
This tool solves the SSS (side-side-side) case specifically. Other cases like SAS (two sides and the included angle) or ASA (two angles and the included side) need different starting formulas - the law of cosines shown here works directly from three known sides.
What happens if the three sides I enter can't form a real triangle?
The calculator can't produce a valid result - by the triangle inequality, the sum of any two sides must be greater than the third side (e.g., 2, 3, and 10 can't form a triangle since 2+3 < 10). If your sides fail this check, double-check your measurements.
How do I find the largest angle in a triangle from its side lengths?
The largest angle is always opposite the longest side - plug the longest side in as 'c' in the law of cosines rearrangement, cos(C) = (a² + b² − c²)/(2ab), then take the inverse cosine of the result.
Do the three angles always add up to 180°?
Yes, for any triangle in standard flat (Euclidean) geometry - this is a useful check: after this calculator solves all three angles, they should sum to 180° (allowing for tiny rounding differences).