Triangle Calculator

Enter three sides to get area, perimeter and all three angles, or use base and height / SAS when that is all you know.

Pick one length unit; area is reported in that unit squared.

How it works

Three sides use Heron’s formula: s is the semi-perimeter and area is √[s(s−a)(s−b)(s−c)]. Angles come from the law of cosines. Sides that fail the triangle inequality (each pair must be longer than the third side) are rejected.

Base and height use ½bh. SAS uses ½ab sin(C) with C in degrees. Area is a length² quantity — never mixed with the raw side lengths.

Formula

s = (a + b + c) / 2
Area = √[s(s − a)(s − b)(s − c)]
cos C = (a² + b² − c²) / (2ab)
Area = ½bh  or  ½ab sin(C)

Worked examples

A 3-4-5 triangle
sides 3, 4, 5 → area 6, perimeter 12, right angle opposite 5
Base and height
base 10, height 4 → area 20

Useful notes

SSS also reports angles opposite a, b and c.
For a right triangle with two legs, the right-triangle page also gives the hypotenuse.

FAQ

How do I find the area of a triangle?: If you know base and height, area is half their product. If you know all three sides, use Heron. If you know two sides and the included angle, use ½ab sin(C).
Why was my triangle rejected?: The sides must satisfy the triangle inequality: the sum of any two sides is greater than the third. 1, 2 and 9 cannot form a triangle.
What unit is the area in?: The square of the length unit you selected. Sides in cm give area in cm².

Related tools

See all Geometry tools.