Triangle Height Calculator
The height of a triangle measured to side a — the perpendicular distance from the opposite corner — worked out from the three sides, with the area and angles alongside.
Height and area are two views of the same fact: area = ½ × base × height, so height = 2 × area ÷ base.
How the triangle height calculator works
Height and area are two views of the same fact: area = ½ × base × height, so height = 2 × area ÷ base. The area comes from the three sides by Heron's formula, which means any triangle has a height to each of its three sides, and the shortest side has the longest height. This page measures to side a; enter your sides in a different order to measure to another.
Formula: a² = b² + c² − 2bc·cos A; a / sin A = b / sin B = c / sin C; area = ½ab·sin C
Worked examples
| Inputs | Height to side a | Note |
|---|---|---|
| 3, 4, 5 measured to side a | 4 | height 4 — side a is a leg of the right angle |
| An equilateral triangle of side 6 | 5.1962 | height 5.196 = 6√3 ÷ 2 |
| A 5-5-6 isosceles triangle | 4 | height to the base is 4 |
FAQFrequently asked questions
What is the height of a triangle?
The perpendicular distance from one side to the opposite corner. Every triangle has three, one to each side.
How do I find the height without the area?
From the three sides: Heron's formula gives the area, then height = 2 × area ÷ the side you are measuring to.
Which side is the base?
Any of them. This page measures to side a — reorder your sides to measure to a different one.
Can the height fall outside the triangle?
Yes, in an obtuse triangle the foot of the height can land beyond the end of the side, on its extension.
What is the height of an equilateral triangle?
Side × √3 ÷ 2, about 0.866 times the side.
Where these figures come from
- NIST Digital Library of Mathematical Functions — reference definitions for elementary and special functions
- Wolfram MathWorld — definitions and formulas for every topic on this page
- NIST/SEMATECH e-Handbook of Statistical Methods — the statistical formulas (mean, variance, z, confidence intervals, sample size)
- National curriculum in England — Mathematics — the terms and methods taught in UK schools
Last checked: September 2026. Formulas are fixed by mathematics and do not change with tax years or regulations.