Triangle Area Calculator

The most common is one half times base times perpendicular height. This tool also offers Heron's formula from three sides and the SAS formula from two sides and their included angle, and all three return the same area for the same triangle.

With sides a, b, and c, let s be half the perimeter, so s equals (a plus b plus c) divided by 2. The area is the square root of s times (s minus a) times (s minus b) times (s minus c). It needs no height, only the three side lengths.

When you know two sides and the angle between them, the area equals one half times side a times side b times the sine of the included angle. The tool also finds the third side with the law of cosines so it can report the perimeter.

The perimeter needs all three side lengths. The three-sides and SAS methods know or can derive every side, so they show a perimeter, while the base-and-height method knows only the base and cannot.

Three lengths only form a real triangle if each pair of sides adds up to more than the third side. Values that break this triangle inequality, such as 1, 2, and 5, are rejected with a message instead of a wrong answer.

The SAS method takes the included angle in degrees, so 30 means 30 degrees. It is converted to radians internally before the sine and cosine are taken, and it must be strictly between 0 and 180 degrees.

The engine rounds the area and perimeter to six decimal places. The 3-4-5 triangle gives a clean area of 6, while irrational results like the SAS perimeter above are shown to six places.

Yes. Each field accepts decimals down to steps of 0.1 and values up to 1000, so you can mix whole numbers and fractional measurements freely. All inputs must be greater than zero.

No. The calculation runs in your browser, so the numbers you type never leave your device and nothing is stored on a server.