Triangle Calculator

Trigonometry homework, a carpentry cut, a plot of land with three measured sides — this triangle calculator solves any triangle from three known values. It finds the missing sides and angles, the area (Heron's formula), perimeter, heights, and the inscribed and circumscribed circle radii, tells you whether the triangle is scalene, isosceles or equilateral and acute, right or obtuse, and draws it to scale. The tricky ambiguous SSA case is handled properly, with both possible triangles shown.

How to use it

Enter three values — for example three sides, or two sides and the angle between them.
Leave the other three boxes empty.
Read the solved triangle and its drawing.

Example

With sides a = 7, b = 8 and the angle between them C = 60°, the cosine rule gives c² = 49 + 64 − 2 × 7 × 8 × cos 60° = 57, so c ≈ 7.55. The area is ½ × 7 × 8 × sin 60° ≈ 24.25 square units. For a plot measured in feet or metres, convert the area with theland area converter, or find areas of other shapes with thearea & volume calculator.

Frequently asked questions

What do I need to solve a triangle?

Any three values including at least one side: three sides (SSS), two sides and the angle between them (SAS), two angles and a side (ASA or AAS), or two sides and an angle not between them (SSA). Three angles alone only fix the shape, not the size.

Why does SSA sometimes give two triangles?

With two sides and an angle opposite one of them, the other side can swing to two different positions — the “ambiguous case”. The calculator shows both triangles when that happens, or tells you if no triangle is possible.

Which formulas are used?

The cosine rule (a² = b² + c² − 2bc cos A) for SSS and SAS, the sine rule (a/sin A = b/sin B = c/sin C) for the other cases, and Heron’s formula for the area.

How do I use Pythagoras’ theorem here?

For a right-angled triangle, enter the two shorter sides and set the angle between them (C) to 90°. The calculator gives the hypotenuse c, which equals √(a² + b²).