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Triangle Calculator

Solve any triangle from three known sides or angles.

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What do you know?

Solution

Area

—

Perimeter—
Semi-perimeter—
Height to side a—
Circumradius—
Inradius—
Type by sides—
Type by angles—

Quick Tool Overview

The Triangle Calculator solves a triangle from any three known values — three sides, two sides and an angle, or two angles and a side — returning every remaining side and angle plus the area, perimeter and height. It says which method it used and rejects impossible inputs with a reason.

What it does
Solves a triangle completely from three known values
You give it
Any three sides or angles that define the triangle
You get back
All sides and angles, area, perimeter, height and the type
Best for
Trigonometry homework, surveying, carpentry and roof pitches
Calculators Free, unlimited use No sign-up Runs in your browser

About the Triangle Calculator

Give the calculator any three values that define a triangle — three sides, two sides and an angle, or two angles and a side — and it solves for everything else: all three sides, all three angles, the area, the perimeter and the height.

It picks the right method for what you gave it and says which one it used, whether that is the law of cosines for three sides, the law of sines for an angle-side pair, Pythagoras for a right triangle or Heron's formula for the area. The triangle is classified by both sides and angles, and impossible inputs are rejected with a reason, since three sides only form a triangle if the two shorter ones exceed the longest, and three angles must total 180 degrees.

Key features of the Triangle Calculator

Picks the right method

Law of cosines for three sides, law of sines for an angle-side pair, Pythagoras for a right triangle — and it tells you which it used.

Heron's formula for area

The area is found from the three sides alone, with no height needed.

Classified by sides and angles

Scalene, isosceles or equilateral, and acute, right or obtuse, reported together.

Impossible triangles explained

Three sides only form a triangle if the two shorter exceed the longest, and angles must total 180 — the calculator says which rule you broke.

Everything at once

Sides, angles, area, perimeter and height come back in one solve rather than one value at a time.

How to use the Triangle Calculator

  1. 1

    Choose what you know

    Select the combination you have: three sides, two sides and an angle, or two angles and a side.

  2. 2

    Enter the values

    Fill in the three known measurements. Angles are in degrees.

  3. 3

    Read the full solution

    Every remaining side and angle is calculated, with the area, perimeter, height and triangle type.

Frequently asked questions

c squared equals a squared plus b squared minus 2ab times the cosine of C. It finds a third side from two sides and the angle between them, and reduces to Pythagoras when that angle is 90 degrees.

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