Triangle Area Calculator
Area from three sides, using Heron's formula.
Work out Triangle Area. Area from three sides, using Heron's formula. Refuses impossible figures instead of printing NaN.
Area
6
Scalene, right · perimeter 12
This uses Heron's formula: with s as half the perimeter, the area is √(s(s−a)(s−b)(s−c)). It needs no height and no angle, which is why it is the one to reach for when all you have is a tape measure. The angles come from the law of cosines and always sum to 180°, which is a useful check on your own working. Any two sides must add to more than the third — the triangle inequality. Lengths that only just satisfy it give a very thin triangle, and lengths that exactly equal it give a straight line rather than a triangle at all.
How the Triangle Area Calculator works
Enter three side lengths for the area, all three angles, the perimeter, and the inradius and circumradius. Heron's formula needs no height and no angle, which is why it is the one to reach for when all you have is a tape measure.
Also known as: heron's formula calculator · area of a triangle from 3 sides · scalene triangle area calculator · triangle calculator from sides
Frequently asked questions
What is Heron's formula?
With s as half the perimeter, the area is √(s(s−a)(s−b)(s−c)). It gives the area from three side lengths alone, with no height or angle required.
Why do my three lengths not form a triangle?
Because any two sides must add to more than the third — the triangle inequality. Sides of 1, 2 and 10 cannot reach far enough to meet. If they add to exactly the third, the points lie in a straight line rather than forming a triangle.
How do I find the area if I have the base and height?
Half base times height. Heron's formula is for when you do not have a height, which is most real measuring situations — a height means finding a perpendicular, and a tape measure gives you sides.
What are the inradius and circumradius?
The inradius is the radius of the largest circle fitting inside the triangle, area ÷ s. The circumradius is the circle passing through all three corners, abc ÷ 4×area. For a right triangle the circumradius is exactly half the hypotenuse.
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