Triangle Calculator
Free triangle calculator: solve any triangle from three sides, two sides and the angle between them, or two angles and a side: sides, angles and area.
What it does
Any triangle is fixed by three pieces of information that include at least one side: three sides (SSS), two sides and the angle between them (SAS), or two angles and the side between them (ASA). This calculator solves it with the laws of cosines and sines, giving all sides and angles, the area by Heron's formula, the perimeter and whether the triangle is acute, right or obtuse and equilateral, isosceles or scalene.
How to use it
- Choose what you know: three sides, two sides and an angle, or two angles and a side.
- Type the three values (angles in degrees).
- See the area, all sides and angles, the perimeter and the type of triangle.
The arithmetic runs in your browser. Nothing you type is sent anywhere and nothing is stored, so you can use these with real numbers.
Frequently asked questions
What is Heron's formula?
It gives the area from the three sides: with s = (a + b + c) / 2, the area is √(s(s − a)(s − b)(s − c)). For sides 3, 4 and 5, s = 6 and the area is √(6 × 3 × 2 × 1) = 6.
Why can't some sides form a triangle?
Each side must be shorter than the sum of the other two (the triangle inequality). Sides 1, 2 and 3 lie flat on a line and enclose no area.
Why isn't two sides and any angle enough?
If the angle is not between the two sides (SSA), there can be two different triangles, one or none. That is why this calculator asks for the angle between the sides.
How are the sides and angles named?
Each side takes the lowercase letter of the opposite angle: side a is opposite angle A, b opposite B and c opposite C. The three angles always add up to 180°.
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