# Triangle Height Calculator

URL: https://speedycalculator.com/calculators/math/triangle-height/
Last updated: 2026-10-30

> The triangle height calculator finds all three heights (altitudes) of a general, equilateral, isosceles or right triangle from its sides, plus the area, perimeter and angles.

## Inputs

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

## Results

- Area
- Height to side a
- Height to the second side
- Height to the third side
- Perimeter
- Angle α (opposite a)
- Angle β (opposite b)
- Angle γ (opposite c)

## Formula

```
hₐ = 2A/a,  h_b = 2A/b,  h_c = 2A/c,  A from Heron's formula
```

## Explanation

A triangle's height (altitude) is the perpendicular distance from a vertex to the opposite side. Every triangle has three, one for each side. Heights are needed for areas, for roof pitches and for the strength of triangular frames.

### How to use the Triangle Height Calculator

- **Triangle type**
- **Side a**
- **Side b**
- **Side c**

Results update as you type, and everything is calculated in your browser.

### How it works

Pick the type of triangle so only the necessary sides are asked for. The area is computed with Heron's formula and each height is twice the area divided by its base.

### Inputs explained

FieldWhat to enterTriangle typeChoose one: General (three sides), Equilateral, Isosceles (legs a, base b), Right (legs a and b)Side aUnits: cm, m, mm, in, ft, yd …Side bUnits: cm, m, mm, in, ft, yd …Side cUnits: cm, m, mm, in, ft, yd …

### What each result means

- **Area** = sqrt(([a] + [b] + [c])×(-[a] + [b] + [c])×([a] - [b] + [c])×([a] + [b] - [c]))÷4
- **Height to side a** = 2×[Area]÷[a]
- **Height to the second side** = 2×[Area]÷[b]
- **Height to the third side** = 2×[Area]÷[c]
- **Perimeter** = [a] + [b] + [c]
- **Angle α (opposite a)** = deg(acos(([b]^2 + [c]^2 - [a]^2)÷(2×[b]×[c])))
- **Angle β (opposite b)** = deg(acos(([a]^2 + [c]^2 - [b]^2)÷(2×[a]×[c])))
- **Angle γ (opposite c)** = 180 - [Angle α (opposite a)] - [Angle β (opposite b)]

### Example values

How the main result changes when **Side a** changes and everything else stays at the example values above:

Side a (cm)Height to side a (cm)2.55.84623.755.998355.87886.255.62617.55.2618104.1325

## Worked example

Inputs — Triangle type: General (three sides); Side a: 5 cm; Side b: 6 cm; Side c: 7 cm.

Results — Area = 14.696938 cm²; **Height to side a = 5.878775 cm**; Height to the second side = 4.898979 cm; Height to the third side = 4.199125 cm; Perimeter = 18 cm; Angle α (opposite a) = 44.415309 °; Angle β (opposite b) = 57.12165 °; Angle γ (opposite c) = 78.463041 °.

## Key terms

- **Altitude**: A perpendicular segment from a vertex to the line of the opposite side.

## FAQ

**How many heights does a triangle have?**
Three, one to each side.

**Can a height be outside the triangle?**
Yes – in an obtuse triangle two heights fall outside.

**What is the height of an equilateral triangle?**
a√3/2.

**Where do the three heights meet?**
At the orthocenter.


## Sources

- [OpenStax – Algebra and Trigonometry 2e](https://openstax.org/details/books/algebra-and-trigonometry-2e)
- [OpenStax – Prealgebra 2e](https://openstax.org/details/books/prealgebra-2e)
- [Wolfram MathWorld – Altitude](https://mathworld.wolfram.com/Altitude.html)