# Heron’s Formula Calculator

URL: https://speedycalculator.com/calculators/math/herons-formula/
Last updated: 2026-10-25

> The Heron’s formula calculator finds the area of a triangle from its three side lengths, along with the perimeter and the three angles. It also checks that the sides can form a triangle.

## Inputs

- Side a (m, cm, mm, km, in, ft, yd, mi)
- Side b (m, cm, mm, km, in, ft, yd, mi)
- Side c (m, cm, mm, km, in, ft, yd, mi)

## Results

- Semi-perimeter
- Area
- Angle A
- Angle B
- Angle C

## Formula

```
s = (a + b + c) ÷ 2
Area = √(s(s − a)(s − b)(s − c))
```

## Explanation

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

FieldWhat to enterSide aUnits: m, cm, mm, km, in, ft …Side bUnits: m, cm, mm, km, in, ft …Side cUnits: 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)3.513.955.2520.83726.838.7531.6710.534.941433.67

## 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.

## FAQ

**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.