$Triangle Area$

Triangle Area

Find the area of a triangle from the base and height, three sides (Heron's formula), two sides and the included angle, a side and two angles, for equilateral and right triangles.

What is known:

Side a

Height h to side a

Units:

Lengths are positive numbers (whole or decimal), angles are in degrees.

Test yourself

The triangle area calculator finds the area in six ways: from the base and height, from three sides (Heron's formula), from two sides and the included angle, from a side and two adjacent angles, for an equilateral triangle and for a right triangle from its legs. The solution is shown step by step.

Triangle area formulas

What is known	Formula
Base and height	S = ½ · a · h
Three sides (Heron)	S = √(p(p − a)(p − b)(p − c)), p = (a + b + c)/2
Two sides and the included angle	S = ½ · a · b · sin γ
Side and two adjacent angles	S = a² · sin β · sin γ / (2 sin(β + γ))
Equilateral triangle	S = a²√3 / 4
Right triangle, legs a and b	S = ½ · a · b
From the inradius	S = p · r
From the circumradius	S = abc / (4R)

Example 1. Sides 5, 6 and 7 cm.
p = (5 + 6 + 7)/2 = 9, S = √(9 · 4 · 3 · 2) = √216 ≈ 14.7 cm².

Example 2. a = 8 cm, b = 6 cm, the angle between them is 30°.
S = ½ · 8 · 6 · sin 30° = 12 cm².

When a triangle exists

Three segments form a triangle only if each of them is shorter than the sum of the other two (the triangle inequality): a < b + c, b < a + c, c < a + b. For example, segments 1, 2 and 3 do not form a triangle. The calculator checks this condition.