Triangle Area Calculator
The area of any triangle from base and height, from three sides (Heron's formula) or from two sides and the angle between them.
Base × height ÷ 2 works when you know the perpendicular height.
How the triangle area calculator works
Base × height ÷ 2 works when you know the perpendicular height. With three sides use Heron's formula: s = (a + b + c) ÷ 2 and A = √(s(s−a)(s−b)(s−c)). With two sides and the included angle, A = ½ab sin C.
Formula: A = ½bh; A = √(s(s−a)(s−b)(s−c)); A = ½ab·sin C
Worked examples
| Inputs | Area | Note |
|---|---|---|
| base 6, height 4 | 12 | 12 |
| sides 3, 4, 5 | 6 | right-angled, area 6 |
| sides 5 and 7, angle 60° | 15.155445 | 15.16 |
FAQFrequently asked questions
Which height do I use?
The perpendicular distance from the base to the opposite corner — not the slanted side.
What is Heron's formula?
A way to get the area from the three sides alone: A = √(s(s−a)(s−b)(s−c)) with s the half-perimeter.
Can any three lengths make a triangle?
Only if each side is shorter than the other two added together (the triangle inequality).
How do I know if a triangle is right-angled from its sides?
If the two shorter sides squared add up to the longest side squared (3-4-5, 5-12-13).
What is ½ab sin C?
The area when you know two sides and the angle between them; sin 90° = 1 gives back ½ × base × height.
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)
- Common Core State Standards — Mathematics — the terms and methods taught in US schools
Last checked: September 2026. Formulas are fixed by mathematics and do not change with tax years or regulations.