Triangle Area Calculator

Calculate the area of a triangle using the formula: Area = (Base × Height) ÷ 2

Example: A triangle with base = 5 units and height = 8 units has an area of 20 square units.

Another worked example

Base = 12 units, height = 7 units:

Area = (12 × 7) ÷ 2 = 84 ÷ 2 = 42 square units

Why the formula divides by 2

Any triangle is exactly half of a parallelogram with the same base and height — draw a second, upside-down copy of the triangle attached along its longest visible edge and the two together tile a base × height rectangle-like parallelogram perfectly. That's the geometric reason the area formula is base × height ÷ 2 rather than just base × height (which would give you the parallelogram's area).

What "height" means here

Height must be the perpendicular distance from the base to the opposite vertex — not the length of one of the triangle's slanted sides. For a triangle that isn't right-angled, that perpendicular height is usually shorter than either non-base side, and using a side length by mistake will overstate the area. If you only know the three side lengths and no perpendicular height, this formula can't be applied directly; Heron's formula is the correct tool for that case.

Input rules

Base and height must both be positive numbers in the same unit of measurement — the calculator does not convert between units, and it rejects zero, negative, or non-numeric entries with an error message rather than returning a meaningless result.