About the Triangle Calculator
Triangle Calculator finds every measurement of a triangle from the few you know. Choose what you know: three sides (SSS), two sides and the angle between them (SAS), two angles and the side between them (ASA), two angles and a side not between them (AAS), or any two values of a right triangle. The tool then shows all three sides and angles, the area, the perimeter, the type of triangle, the three heights, the inradius and the circumradius, and draws the triangle to scale with its corners labelled. It says plainly when the numbers cannot form a triangle. Two sides and an angle that is not between them, known as SSA, can have two answers, so it is not offered. Results are rounded only for display, and angles are in degrees.
Updated September 2026
How to use the Triangle Calculator
- 1Choose what you know from the list, for example three sides.
- 2Type the values in the boxes. Angles are in degrees.
- 3For a right triangle, fill in any two of a, b, c, A and B.
- 4Read the sides, angles, area, perimeter, type, heights and radii.
- 5Check the drawing, and copy the results if you need them.
Which triangle method to use
Match the method to the measurements you have, and be careful about which angle sits between which sides. In SAS the angle must lie between the two sides you enter. In ASA the side must lie between the two angles. In AAS the side is opposite one of the angles.
Sides are named after the opposite corner: side a is opposite angle A, and so on, and the drawing labels all of them so that you can check your entries against your figure.
Right triangles and Pythagoras
A right triangle has one angle of exactly 90 degrees, which the tool calls C, and the side opposite it, c, is the hypotenuse. The other two sides are the legs. Give any two of the five values a, b, c, A and B and the rest follow.
If you enter a leg that is as long as or longer than the hypotenuse, the tool tells you the hypotenuse must be the longest side. A 3-4-5 triangle is the best known example, with angles of about 36.87, 53.13 and 90 degrees.
The law of sines and cosines in plain words
- Law of cosines: c² = a² + b² − 2ab cos C. It finds a third side from two sides and the angle between them, and it finds angles from three sides.
- Law of sines: a ÷ sin A = b ÷ sin B = c ÷ sin C. It finds the other sides once you know a side and its opposite angle.
- The angles of every triangle add up to 180 degrees.
Area, height and radii
The height on a side is twice the area divided by that side. The inradius is the radius of the largest circle inside the triangle, found as area divided by half the perimeter. The circumradius is the radius of the circle through all three corners, and equals abc divided by four times the area.
For plain area formulas of other shapes, see Area Calculator. To change the length units of your answer, use Unit Converter, and Fraction Calculator when your sides are fractions.
Features
- SSS, SAS, ASA, AAS and right triangle modes
- All sides and angles, area and perimeter
- Triangle type: equilateral, isosceles or scalene, acute, right or obtuse
- Three heights, inradius and circumradius
- To-scale drawing with labelled corners
- Clear messages when no triangle exists
- Runs in your browser
Frequently asked questions
How do I find the hypotenuse?
In a right triangle, square the two shorter sides, add them, and take the square root. For sides 3 and 4 that is √(9 + 16) = 5. Choose Right triangle, type a = 3 and b = 4, and c appears.
How do I find the area of a triangle with three sides?
Use Heron's formula: with s as half the perimeter, the area is √(s(s − a)(s − b)(s − c)). For sides 3, 4 and 5, s is 6 and the area is √(6 × 3 × 2 × 1) = 6. The calculator uses this formula whenever it knows the three sides.
What is the Pythagorean theorem?
It says that in a right triangle the square of the hypotenuse equals the sum of the squares of the other two sides: a² + b² = c². It lets you find a missing side of a right triangle from the other two, and the right triangle mode applies it for you.
How do I solve a triangle with two angles and a side?
Subtract the two angles from 180 degrees to get the third, then use the law of sines to find the other sides. Choose ASA if the side is between the angles, or AAS if it is opposite one of them. The two angles must add up to less than 180 degrees.
Why can't some sides make a triangle?
The two shorter sides must together be longer than the longest side. Sides 1, 2 and 3 fail because 1 + 2 equals 3, so the sides would lie flat in a line, and sides 1, 1 and 3 fail because they cannot reach across. The calculator tells you when this happens.
What is SAS, SSS and ASA?
They describe what you know. SSS is three sides, SAS is two sides and the angle between them, and ASA is two angles and the side between them. AAS is two angles and a side that is not between them. Each of these fixes the triangle completely.