Triangle Area Calculator
Area from three sides, with angles, inradius and circumradius.
Inputs
Result
Formula
| Heron | A = √(s(s−a)(s−b)(s−c)) |
| Semi-perimeter | s = (a + b + c) ÷ 2 |
| Cosine rule | cos A = (b² + c² − a²) ÷ 2bc |
| Inradius | r = A ÷ s |
| Circumradius | R = abc ÷ 4A |
| Height on a | ha = 2A ÷ a |
Sides of 3, 4 and 5 m: semi-perimeter 6.000 m, area 6.0000 m², angles of 36.87°, 53.13° and 90.00°, a right-angled triangle, inradius 1.0000 m, circumradius 2.5000 m and a height of 2.4000 m on side c.
FAQ
With only three side lengths, how do I set out the angles?
Use the 3-4-5 method or the cosine rule. 3-4-5 is the practical squareness check: measure 3 m along one leg and 4 m along the other, and if the diagonal reads 5 m the corner is square — within 2 mm is plenty for building work. For other angles compute the third side and strike it from two tapes.
When does Heron's formula lose accuracy?
On slender triangles where one side approaches the sum of the other two, because s−c becomes a difference of two large similar numbers and most significant digits are lost. For such shapes on site, use base × height ÷ 2 or coordinates — both are far more stable.
What use are inradius and circumradius on site?
The inradius sets the largest round object that fits inside a triangular area — how big a circular tank fits on a triangular plinth, for instance. The circumradius locates the centre through three columns that are not collinear, which is more accurate on a triangular plot than bisecting diagonals.
Related calculators
Results are estimating aids only and are not a design basis. Construction and final accounts must follow the drawings, the applicable standards and an approved method statement. Anything affecting structural safety, shoring or falsework must be checked by a suitably qualified engineer.