Heron’s formula, known since ancient Greece, needs no height or angles, only the sides.
How to use the Heron’s Formula Calculator
- Side a
- Side b
- Side c
Results update as you type, and every field accepts the units shown in its menu.
How it works
Compute the semi-perimeter s and plug it into the formula. Angles come from the law of cosines.
Inputs explained
| Field | What to enter |
|---|---|
| Side a | Units: m, cm, mm, km, in, ft … |
| Side b | Units: m, cm, mm, km, in, ft … |
| Side c | Units: m, cm, mm, km, in, ft … |
What each result means
- Semi-perimeter = ([Side a] + [Side b] + [Side c])÷2
- Angle A = deg(acos(([Side b]^2 + [Side c]^2 – [Side a]^2)÷(2×[Side b]×[Side c])))
- Angle B = deg(acos(([Side a]^2 + [Side c]^2 – [Side b]^2)÷(2×[Side a]×[Side c])))
- Angle C = 180 – [Angle A] – [Angle B]
Example values
How the main result changes when Side a changes and everything else stays at the example values above:
| Side a (m) | Area (m²) |
|---|---|
| 3.5 | 13.95 |
| 5.25 | 20.83 |
| 7 | 26.83 |
| 8.75 | 31.67 |
| 10.5 | 34.94 |
| 14 | 33.67 |
Formula
s = (a + b + c) ÷ 2Area = √(s(s − a)(s − b)(s − c))Worked example
Inputs — Side a: 7 m; Side b: 8 m; Side c: 9 m.
Results — Semi-perimeter = 12 m; Area = 26.83 m²; Angle A = 48.19 °; Angle B = 58.412 °; Angle C = 73.398 °.
Key terms
- Semi-perimeter
- Half of the perimeter.
Frequently asked questions
Why is there no result?
The sides break the triangle inequality: each side must be shorter than the other two combined.
Who was Heron?
Heron of Alexandria, a Greek mathematician and engineer of the 1st century.
What formula does the Heron’s Formula Calculator use?
s = (a + b + c) ÷ 2.