Triangle Area Calculator
Find a triangle's area from three sides (Heron's formula) or from base and height.
How to use this calculator
Choose your method. If you know the three side lengths, pick Heron's and enter a, b and c. If you know the base and the perpendicular height, pick that mode and enter the two values. Press Calculate area and the tool returns the area in square units, with the working shown. When you enter three sides, it also checks that they can actually form a triangle — any side longer than the other two combined is impossible, and the tool flags that rather than returning a wrong answer.
The formulas explained
There are two standard routes to a triangle's area:
base × height: ½ × b × h · three sides: √(s(s−a)(s−b)(s−c)), where s = (a+b+c) ÷ 2
The base-and-height method is the simplest when you have a perpendicular height. When you only know the side lengths, Heron's formula uses the semi-perimeter s — half the perimeter — to find the area without needing any angles or heights. It works for every triangle, which is why it is so useful in surveying and construction where measuring sides is easier than measuring heights.
A worked example
For a triangle with sides 3, 4 and 5: the semi-perimeter is (3 + 4 + 5) ÷ 2 = 6. Heron's formula gives √(6 × (6−3) × (6−4) × (6−5)) = √(6 × 3 × 2 × 1) = √36 = 6 square units. This is a right triangle, so the base-and-height method agrees: ½ × 3 × 4 = 6.
Frequently asked questions
What is Heron's formula?
A way to find a triangle's area from its three sides using the semi-perimeter: area = √(s(s−a)(s−b)(s−c)).
How do you find the area of a triangle?
Half the base times the height, or Heron's formula if you only know the three sides.
What is the semi-perimeter?
Half the perimeter — the three sides added and divided by two.