Calcometry

Triangle Area Calculator

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Area from base × height ÷ 2, or from three side lengths with Heron's formula.

Triangle dimensions

Switch modes to use base & height, or three side lengths (Heron's formula).

Method

Triangle area

20

Base 10 × height 4 ÷ 2

Formula
base × height ÷ 2

Related calculators

Triangle area

The most common way to find a triangle's area is base × height ÷ 2, where height is measured perpendicular to the base. This works for any triangle as long as you know a base and the corresponding height.

When you only know the three side lengths (and not the height), Heron's formula solves it instead: first find the semi-perimeter s = (a + b + c) / 2, then area = √(s(s−a)(s−b)(s−c)). If the three lengths cannot form a valid triangle (one side is too long relative to the other two), the area comes out to 0.

Example: a triangle with base 10 and height 4 has area 10 × 4 ÷ 2 = 20. A 3-4-5 right triangle, using Heron's formula with s = 6, gives area = √(6×3×2×1) = √36 = 6 — matching the simpler ½ × 3 × 4 = 6 you'd get treating the legs as base and height.

Common questions

When should I use Heron's formula instead of base × height?

Use Heron's formula when you know all three side lengths but not a perpendicular height — common for surveying or when working from measured sides alone.

Why did I get an area of 0 in Heron's mode?

The three lengths you entered don't satisfy the triangle inequality (each side must be shorter than the sum of the other two), so no valid triangle exists.