Triangle Calculator
Triangle Properties
6
Area
12
Perimeter
36.8699° / 53.1301° / 90°
Angles (°)
Right
Type
What is a Triangle Calculator?
A triangle calculator computes a triangle's area, perimeter, and all three interior angles from a minimal set of known measurements. This tool supports four input modes: three sides (SSS), two sides plus an included angle (SAS), two angles plus an included side (ASA), and right triangle with two known values. It uses Heron's formula for area and the law of cosines for angles.
How to Use
- Select a calculation type from the dropdown (e.g., Three Sides (SSS)).
- Enter the known side lengths or angles into the input fields.
- Area, perimeter, all three angles, and triangle type are calculated and displayed instantly.
- If the sides violate the triangle inequality, no result is shown.
Frequently Asked Questions
What is Heron's formula?
Heron's formula calculates triangle area from the three side lengths without needing height: Area = √(s(s−a)(s−b)(s−c)), where s = (a+b+c)/2 is the semi-perimeter. It works for any triangle type.
How do I know if three sides form a valid triangle?
The triangle inequality theorem: each side must be less than the sum of the other two sides. If any side ≥ sum of other two, no triangle can be formed. For example, sides 3, 4, 10 cannot form a triangle (3+4=7 < 10).
What is the law of cosines?
The law of cosines generalizes the Pythagorean theorem: c² = a² + b² − 2ab·cos(C). It's used to find an angle when all three sides are known, or to find a side when two sides and an included angle are known.
What types of triangles are there?
By sides: equilateral (all equal), isosceles (two equal), scalene (all different). By angles: acute (all angles < 90°), right (one angle = 90°), obtuse (one angle > 90°). A right triangle with sides 3-4-5 is the most famous example.
Area Formula
Area = √(s(s-a)(s-b)(s-c))