Triangle calculator
Area and angles from three side lengths.
About this calculator
Enter the three sides in any one unit, and the area will be in that unit squared. It also tells you what kind of triangle you have.
Three lengths only make a triangle if any two sides together are longer than the third. The calculator tells you if yours do not.
How it works
Heron's formula gives the area and the law of cosines gives the angles.
Worked example
- Side a: 3
- Side b: 4
- Side c: 5
Area: 6 (Scalene, right)
The story behind it
Where the idea came from: Heron of Alexandria, first century AD.
You only need three sides to find a triangle's area, thanks to Heron, who set out the method in his book Metrica. He was an engineer and wrote for practical people measuring land and buildings. This calculator still uses his formula for the area, and the law of cosines for the angles.
Why you can trust this calculator
- It runs in your browser. Nothing you type into it is sent anywhere.
- The method is explained on this page, so you can check it yourself.
- Free to use, with no sign-up.
- Results are estimates, so please double-check anything important.
- Spotted a mistake? Tell us and we'll look into it.
After 15 years as a mathematics educator, I built CalculStore to give students, teachers, professionals and anyone working with numbers simple, reliable tools.
Meet the founder