This geometry calculator uses Heron's formula to find a triangle's area, perimeter, semiperimeter, and angles from three side lengths.
Math
3 Sides Triangle Area Calculator
Use Heron's formula to calculate a triangle's area from three valid side lengths.
Calculator
About this calculator
Formula notes
s = (a + b + c) / 2; area = sqrt(s x (s - a) x (s - b) x (s - c)); each angle uses the law of cosines.
Worked examples
- Example: sides 3, 4, and 5 form a right triangle with area 6, perimeter 12, and a 90 degree angle opposite the 5 side.
- Sides 6, 8, and 10 give area 24, perimeter 24, and a right angle opposite the 10 side.
How to use it
- Enter the three side lengths.
- Confirm the units match your measurement.
- Read area, perimeter, semiperimeter, and the three angles.
Frequently asked questions
Which triangle does this handle?
Any triangle whose three sides satisfy the triangle inequality; the angles are derived from the side lengths.
What if the sides cannot form a triangle?
The tool rejects the input because the triangle inequality would be violated.
Limits and interpretation
- The result assumes a Euclidean triangle; the tool rejects sides that violate the triangle inequality.
- Area is reported in square metres after unit conversion, so check the unit you entered.