Triangle Perimeter Calculator
Find a triangle's perimeter and its area with Heron's formula from three side lengths.
Perimeter
12
Perimeter = a + b + c. The 3-4-5 triangle has a perimeter of 12 and an area of 6.
Area (Heron's formula)
6
Semi-perimeter (s)
6
Heron's formula finds the area from the three sides: with s = perimeter / 2, area = √(s(s−a)(s−b)(s−c)).
How it works
The perimeter of any triangle is simply the sum of its three sides, a + b + c. Type in the three lengths and this tool adds them up. For the familiar 3-4-5 triangle, that's a perimeter of 12.
The same three sides also pin down the area, thanks to Heron's formula. It first finds the semi-perimeter s = (a + b + c) / 2, then computes the area as √(s(s−a)(s−b)(s−c)). No angles or heights needed — the 3-4-5 triangle works out to an area of exactly 6.
Before doing any of that, the calculator checks the triangle inequality: the two shorter sides have to add up to more than the longest side, or no triangle can close. If your lengths fail that test, it tells you instead of returning a meaningless number.
Frequently asked questions
What is the triangle inequality?
It's the rule that any two sides of a triangle must add up to more than the third side. If they don't — say sides of 1, 2, and 5 — the shorter sides can't reach far enough to meet, so no triangle exists. This tool checks that automatically.
How does Heron's formula find the area without a height?
Heron's formula uses only the three side lengths. It computes the semi-perimeter s = (a + b + c) / 2, then the area equals the square root of s(s−a)(s−b)(s−c). It's ideal when you know the sides but not any angles or altitudes.
Do the sides need the same units?
Yes. Enter all three lengths in the same unit — all centimeters, all inches, whatever you like. The perimeter comes out in that unit and the area in the corresponding square unit.