Triangle Calculator
Solve any triangle given sides and angles. Calculate area, perimeter, angles, and height using the law of cosines and sines.
Enter any 3 values (at least one side). Leave the rest blank.
Area
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All values
Not enough information or invalid triangle.
What is Triangle Calculator?
A triangle calculator solves any triangle given at least three values (with at least one being a side). It computes all missing sides and angles, as well as the area, perimeter, height, inradius, and circumradius using the law of cosines, law of sines, and Heron's formula.
How to use
- 1 Enter any three known values — sides a, b, c and/or angles A, B, C — leaving unknowns blank.
- 2 At least one side must be provided; angles alone don't define a unique triangle size.
- 3 Results including area, perimeter, and all six triangle values appear automatically.
- 4 If the combination is impossible or ambiguous, an error message will appear.
Formula
Example calculation
For a triangle with sides a=3, b=4, c=5: the law of cosines gives angle C = arccos((9+16-25)/24) = 90°. This is a right triangle with area = (3×4)/2 = 6 and perimeter = 12.
Frequently asked questions
What information do I need to solve a triangle?
You need at least 3 pieces of information, and at least one must be a side length. Valid combinations include SSS, SAS, ASA, and AAS. AAA (all angles) defines shape but not size.
What is the law of cosines used for?
The law of cosines is used when you know three sides (SSS) or two sides and the included angle (SAS). It's a generalization of the Pythagorean theorem for non-right triangles.
What is Heron's formula?
Heron's formula calculates triangle area from the three side lengths without needing height. It uses the semi-perimeter s = (a+b+c)/2: Area = √(s(s-a)(s-b)(s-c)).
What is the inradius of a triangle?
The inradius is the radius of the largest circle that fits inside the triangle. It equals Area / s, where s is the semi-perimeter.
What is the circumradius of a triangle?
The circumradius is the radius of the circle that passes through all three vertices of the triangle. It equals a / (2·sin(A)), where a is any side and A is the opposite angle.