Solving a triangle from three sides
When you know all three sides, everything else can be calculated. The calculator uses Heron's formula for the area: with s = (a + b + c) ÷ 2, the area is √(s(s − a)(s − b)(s − c)). The angles come from the law of cosines: cos A = (b² + c² − a²) ÷ 2bc, and the same pattern for B and C.
The triangle inequality
Three lengths can form a triangle only if each side is shorter than the sum of the other two. If they do not, the calculator tells you.
Types of triangles
- By sides: equilateral (all equal), isosceles (two equal) or scalene (all different).
- By angles: acute (all angles under 90°), right (one angle of 90°) or obtuse (one angle over 90°).
Try 3, 4 and 5: it is the classic right triangle with an area of 6.
Frequently asked questions
What is Heron's formula?
A way to find the area of a triangle from its three sides, without needing the height.
Can I enter two sides and an angle?
This tool needs three sides. For a right triangle with two known sides, use the Pythagorean Theorem Calculator.
Why do the angles add up to 180°?
That is a property of every triangle in a flat plane.