Area of a Triangle Calculator

Find the area of a triangle three ways: from base and height, from the three side lengths, or from the coordinates of its corners.

Area —

How to Find the Area of a Triangle

Pick the method that matches what you know.

1

Base and height

If you know a base and the perpendicular height, use ½ × base × height.

2

Three sides

If you know all three side lengths, Heron’s formula gives the area.

3

Coordinates

If you know the corner points, the shoelace formula gives the area from the coordinates.

Frequently Asked Questions

What is the formula for the area of a triangle?
The most common triangle area formula is area = ½ × base × height, where the height is measured perpendicular to the chosen base. For a triangle with a base of 10 cm and a height of 6 cm the area is ½ × 10 × 6 = 30 cm². When you know the three sides instead of a height, use Heron’s formula. When you only have coordinates, the shoelace formula gives the area directly.
What is Heron’s formula?
Heron’s formula gives the area of a triangle from its three sides alone. With sides a, b, c and semi-perimeter s = (a + b + c) ⁄ 2, the area is √[s(s − a)(s − b)(s − c)]. For the 3-4-5 triangle, s = 6 and the area is √(6 × 3 × 2 × 1) = √36 = 6. The three sides must satisfy the triangle inequality, or the product under the root turns negative and no triangle exists.
How do I find the area from coordinates?
The shoelace formula turns three vertex coordinates into an area: area = ½ |x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂)|. For (0, 0), (4, 0) and (0, 3) that gives ½ |0(0 − 3) + 4(3 − 0) + 0(0 − 0)| = ½ × 12 = 6. The absolute value makes the order of the points irrelevant. If the result is 0 the three points are collinear, so they do not form a triangle at all.
Is my data sent anywhere?
Nothing you type is sent anywhere. The triangle area calculator runs entirely in your browser with JavaScript, so your side lengths, heights and coordinates never leave your device. There is no account, no upload step and nothing is logged. The page keeps working offline once it has loaded.

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