Triangle Calculator

Solve a triangle from SSS, SAS, ASA, AAS or RHS: sides, angles, area by Heron’s formula, heights, medians, bisectors and radii.

Your result will appear here

Fill in the fields and press Calculate, or pick one of the examples.

About the Triangle Calculator

Solves a triangle completely from any set of measurements that determines it uniquely: three sides (SSS), two sides and the included angle (SAS), two angles and a side (ASA or AAS), or the hypotenuse and a leg of a right triangle (RHS).

You get all sides and angles, the area by Heron’s formula, the perimeter, the three heights, medians and angle bisectors, and the radii of the inscribed and circumscribed circles. The diagram is drawn to scale.

Limitations

The ambiguous case SSA (two sides and a non-included angle) is not offered because it can describe two different triangles.

How to use it

Choose which measurements you know.
Enter them; angles are in degrees.
Press Calculate.

Example

SSS: a = 3, b = 4, c = 5

→ Area 6, angles 36.87°, 53.13°, 90°

Formulas used

A = \sqrt{s(s-a)(s-b)(s-c)},\quad s = \tfrac{a+b+c}{2}

Heron’s formula.

c^{2} = a^{2} + b^{2} - 2ab\cos C

Law of cosines.

\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} = 2R

Law of sines; R is the circumradius.

Questions and answers

Why does it say my lengths do not form a triangle?

By the triangle inequality each side must be shorter than the sum of the other two. Sides 1, 2 and 3 would lie flat along a line.

Pythagorean Theorem CalculatorFind the missing side of a right triangle from the other two with the Pythagorean theorem, shown step by step.Area CalculatorArea of squares, rectangles, triangles, circles, trapezoids, parallelograms, rhombuses, ellipses and regular polygons.Angle CalculatorConvert between degrees, radians, gradians and turns, find reference, complementary and supplementary angles, and the angle between lines.

About the Triangle Calculator

Limitations

How to use it

Formulas used

Questions and answers

Related tools

About the Triangle Calculator

Limitations

How to use it

Formulas used

Questions and answers