Triangle Area Calculator

Multiply the base by the height and divide by 2. The height must be the perpendicular distance from the base to the opposite vertex, not the slant side. For base 10 and height 6, the area is 10 × 6 ÷ 2 = 30 square units.

Heron's formula gives the area of any triangle from its three side lengths: A = √(s(s − a)(s − b)(s − c)), where s = (a + b + c) ÷ 2 is the semiperimeter. It works for scalene, isosceles, and equilateral triangles without needing a height.

When you know two sides and the angle between them, area = ½ × a × b × sin(angle). The angle must be the one between the two sides, not opposite either. For a = 8, b = 10, angle = 60°: ½ × 8 × 10 × sin(60°) ≈ 34.641 square units.

For three lengths to actually form a triangle, the sum of any two sides must be greater than the third. If you enter 3, 4, and 100, no triangle is possible because 3 + 4 < 100. The calculator flags this case in Heron mode.

A triangle's interior angle is always strictly between 0° and 180° (the three angles sum to exactly 180°). Values at or beyond the boundary describe a degenerate triangle with zero area or a self-intersecting shape that is not a triangle.

Yes, any of the three methods works for right triangles. For a right triangle, base × height ÷ 2 is the simplest because the two legs are already perpendicular. For more right-triangle math (legs, hypotenuse, angles), use the right triangle calculator.