Reviewed by CalcMulti Editorial Team·Last updated: ·← Geometry Hub
The area of a triangle is half the product of its base and perpendicular height: A = ½ × base × height. This formula works for all triangles — right, acute, obtuse, equilateral, and isosceles — as long as you use the perpendicular height (altitude), not a slanted side.
When you know all three sides but not the height, use Heron's formula: A = √(s(s−a)(s−b)(s−c)) where s = (a+b+c)/2 is the semi-perimeter. When you know two sides and the included angle, use A = ½ × a × b × sin(C).
This calculator supports all three methods. Enter whichever measurements you have and it will show the full calculation step by step.
A = ½ × b × h
| Method | Formula | Use When |
|---|---|---|
| Base & Height | A = ½ × b × h | You know base and perpendicular height |
| Heron's Formula | A = √(s(s−a)(s−b)(s−c)), s = (a+b+c)/2 | You know all three side lengths |
| SAS (2 sides + angle) | A = ½ × a × b × sin(C) | You know two sides and the angle between them |
| Equilateral triangle | A = (√3/4) × s² | All three sides are equal |
| Right triangle | A = ½ × leg₁ × leg₂ | Two perpendicular sides (legs) known |
A = πr² — radius, diameter, or circumference input
Trapezoid Area Calculator½(a+b)×h — parallel sides and height
Right Triangle CalculatorPythagorean theorem + all angles and sides
Polygon Area CalculatorArea of regular polygons 3–12 sides
Perimeter CalculatorPerimeter of triangles, rectangles, circles
Surface Area Calculator3D shapes — cube, cylinder, sphere, cone
This calculator is for educational purposes only and does not constitute professional advice. Results are based on standard mathematical formulas. Always verify critical calculations with a qualified professional before making important decisions.