# Isosceles Triangle Calculator

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

> The isosceles triangle calculator finds the height, area, perimeter, base angles, vertex angle and the height to a leg of an isosceles triangle from its leg and base, leg and vertex angle, or base and height.

## Inputs

- What do you know?
- Leg a (cm, m, mm, in, ft, yd, km, mi)
- Base b (cm, m, mm, in, ft, yd, km, mi)
- Vertex angle (°, rad, π rad, grad, turn)
- Height h (cm, m, mm, in, ft, yd, km, mi)

## Results

- Leg a
- Base b
- Height to the base
- Area
- Perimeter
- Base angles
- Vertex angle
- Height to a leg

## Formula

```
h = √(a² − b²/4),  A = b·h/2,  P = 2a + b
Base angle = arccos(b/(2a)),  vertex angle = 180° − 2·base angle
```

## Explanation

An isosceles triangle has two equal sides (legs) and two equal base angles. Roof gables, A-frames, pediments and many bridges and logos use it because it is symmetric about its height.

### How to use the Isosceles Triangle Calculator

- **What do you know?**
- **Leg a**
- **Base b**
- **Vertex angle**
- **Height h**

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

### How it works

Choose what you know. The height to the base splits the triangle into two right triangles, which gives all the other quantities.

### Inputs explained

FieldWhat to enterWhat do you know?Choose one: Leg a and base b, Leg a and vertex angle, Base b and height hLeg aUnits: cm, m, mm, in, ft, yd …Base bUnits: cm, m, mm, in, ft, yd …Vertex angleUnits: °, rad, π rad, grad, turnHeight hUnits: cm, m, mm, in, ft, yd …

### What each result means

- **Height to the base** = sqrt([Leg a]^2 - [Base b]^2÷4)
- **Area** = [Base b]×[Height to the base]÷2
- **Perimeter** = 2×[Leg a] + [Base b]
- **Base angles** = deg(acos([Base b]÷(2×[Leg a])))
- **Vertex angle** = 180 - 2×[Base angles]
- **Height to a leg** = [Base b]×[Height to the base]÷[Leg a]

### Example values

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

Leg a (cm)Area (cm²)3.756.755126.2516.44887.520.62161028.6182

## Worked example

Inputs — What do you know?: Leg a and base b; Leg a: 5 cm; Base b: 6 cm.

Results — Leg a = 5 cm; Base b = 6 cm; Height to the base = 4 cm; **Area = 12 cm²**; Perimeter = 16 cm; Base angles = 53.130102 °; Vertex angle = 73.739795 °; Height to a leg = 4.8 cm.

## Key terms

- **Vertex angle**: The angle between the two equal sides.

## FAQ

**What makes a triangle isosceles?**
Two equal sides (and so two equal angles).

**How do I find the base angles?**
arccos(b/(2a)), or (180° − vertex angle)/2.

**Is an equilateral triangle isosceles?**
Yes, under the usual inclusive definition.

**Does the height bisect the base?**
Yes – it is also a median and an angle bisector.


## 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 – Isosceles triangle](https://mathworld.wolfram.com/IsoscelesTriangle.html)