Triangle Calculator
Solve any triangle given sides and angles. Calculate area, perimeter, heights, inradius, and circumradius using the Law of Cosines and Law of Sines.
How to Use This Calculator
- Choose a solve mode: SSS (3 sides), SAS (2 sides + included angle), ASA (2 angles + included side), or AAS (2 angles + non-included side).
- Enter the known values in the fields provided.
- Click Calculate Triangle to solve for all sides, angles, area, and other properties.
- A visual diagram of the triangle will be drawn to scale.
Formulas
c² = a² + b² − 2ab·cos(C)
Law of Sines:
a/sin(A) = b/sin(B) = c/sin(C)
Area (SAS): Area = ½ab·sin(C)
Area (Heron's): Area = √(s(s−a)(s−b)(s−c)), where s = (a+b+c)/2
Inradius: r = Area / s
Circumradius: R = abc / (4 · Area)
Height on side a: h₁ = 2 · Area / a
Examples
Right Triangle (3-4-5)
SSS: a=3, b=4, c=5 — Area = 6, Perimeter = 12, Angles = 36.87°, 53.13°, 90°.
SAS Triangle
a=5, b=7, C=60° — c = 6.245, Area = 15.155, Perimeter = 18.245.
Equilateral Triangle
a=b=c=10 — All angles = 60°, Area = 43.301, Inradius = 2.887.
Frequently Asked Questions
How do I find the area of a triangle?
If you know two sides and the included angle, use Area = ½ab·sin(C). If you know all three sides, use Heron's formula: Area = √(s(s−a)(s−b)(s−c)) where s is the semi-perimeter (a+b+c)/2.
What is the Pythagorean theorem?
For right triangles only: a² + b² = c², where a and b are the legs and c is the hypotenuse (longest side opposite the right angle).
How do I solve a triangle with SAS?
Use the Law of Cosines first to find the third side: c² = a² + b² − 2ab·cos(C). Then use the Law of Sines to find the remaining angles.
What is the Law of Cosines?
The Law of Cosines generalizes the Pythagorean theorem for any triangle: c² = a² + b² − 2ab·cos(C). It relates the lengths of the sides to the cosine of one of its angles.