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
| Field | What to enter |
|---|---|
| What do you know? | Choose one: Leg a and base b, Leg a and vertex angle, Base b and height h |
| Leg a | Units: cm, m, mm, in, ft, yd … |
| Base b | Units: cm, m, mm, in, ft, yd … |
| Vertex angle | Units: °, rad, π rad, grad, turn |
| Height h | Units: 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) |
|---|---|
| 3.75 | 6.75 |
| 5 | 12 |
| 6.25 | 16.4488 |
| 7.5 | 20.6216 |
| 10 | 28.6182 |
Formula
h = √(a² − b²/4), A = b·h/2, P = 2a + b
Base angle = arccos(b/(2a)), vertex angle = 180° − 2·base angle
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.
Frequently asked questions
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.