Triangle Calculator
Solve any triangle from three values — all sides and angles, area, perimeter, heights and radii, drawn to scale.
Enter any three values, at least one of them a side. Side a is opposite angle A.
Which three values?
- Three sides (SSS) — angles from the law of cosines.
- Two sides and the angle between them (SAS) — third side from the law of cosines.
- One side and two angles (ASA, AAS) — the third angle is 180° minus the others; sides from the law of sines.
- Two sides and an angle not between them (SSA) — there may be no triangle, one, or two different triangles. The calculator shows both when they exist.
law of sines: a ÷ sin A = b ÷ sin B = c ÷ sin C
Example
Sides a = 7 and b = 5 with the angle C = 49° between them give c = √(49 + 25 − 70 cos 49°) ≈ 5.30, angles A ≈ 85.6° and B ≈ 45.4°, and an area of ½ × 7 × 5 × sin 49° ≈ 13.21.
Area from three sides
Heron’s formula: with s = (a + b + c) ÷ 2, the area is √(s(s − a)(s − b)(s − c)). The calculator also gives the triangle’s type, the height to side a, and the radii of the inscribed and circumscribed circles.
Frequently asked questions
How do I find the angles of a triangle from its sides?
Use the law of cosines: cos A = (b² + c² − a²) ÷ 2bc, and similarly for the other angles.
Why are there sometimes two triangles?
With two sides and an angle that is not between them (SSA), the third vertex can sit in two places. This is called the ambiguous case.