Triangle Area Calculator
Calculate triangle area from base and height, three sides, two sides and an included angle, angles and a side, coordinates, right-triangle legs, or circle radii with three sides.
Triangle area from the data you know
English competitors usually cover more than one triangle formula on a triangle area calculator page. This page keeps the calculator focused on area while supporting the main known-data cases: base-height, Heron's formula, SAS, ASA, AAS, coordinates, right triangles, equilateral triangles, and radius checks.
| Known values | Method | Validation |
|---|---|---|
| Base and height | Base and height | Both values must be positive. |
| Three sides | Heron's formula | Triangle inequality must hold. |
| Two sides and included angle | SAS | The angle must be between 0 and 180 degrees. |
| Coordinates | Coordinate determinant | The three points cannot be collinear. |
| Incircle or circumcircle radius plus sides | Radius consistency check | The radius must match the same three sides. |
Core triangle area formulas
A is area; b is base; h is height.
s is semiperimeter; a, b, and c are side lengths.
a and b are sides around included angle C.
r is inradius and s is semiperimeter.
R is circumradius.
What the result includes
- Area in the square of the selected unit.
- Perimeter when sides are known or recoverable.
- Angles and all side lengths for methods that define one triangle.
- Incircle and circumcircle radii when sides are available.
Frequently Asked Questions
Sources and References
Calculations are based on the listed reference sources. Links open in a new tab.
Related Tools
Calculate triangle area from three side lengths using Heron's formula, with semiperimeter, triangle inequality checks, heights, angles, and incircle/circumcircle radii.
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Calculate surface area and volume for common 3D shapes including cube, rectangular prism, sphere, cylinder, and cone.