Introduction
A triangle always has three angles that add up to 180 degrees. If you know some of the sides or angles, you can find the rest. This triangle angle calculator does that work for you. Enter the values you know — like three sides (SSS), two sides and an angle (SAS), or two angles and a side (ASA) — and the tool solves for every missing angle and side. It also gives you the area, perimeter, triangle type, and a step-by-step solution so you can see exactly how each answer was found.
How to Use Our Triangle Angle Calculator
Enter the sides and angles you know about your triangle, and this calculator will find all missing angles, sides, area, perimeter, and other properties instantly.
Given: Pick what information you already have. Choose "3 sides" if you know all three side lengths, "2 sides and 1 angle" if you know two sides and one angle, "2 angles and 1 side" if you know two angles and one side, or "2 angles only" if you just know two angles.
Known Angle: When you pick "2 sides and 1 angle," use this dropdown to tell the calculator which angle you know. Choose α, β, or γ depending on which angle is between your two known sides.
Angle Unit: Select whether your angles are in degrees, radians, or gradians. The calculator will convert all results to match your choice.
Angle α: Enter the angle at vertex A. This is the angle opposite side a.
Angle β: Enter the angle at vertex B. This is the angle opposite side b.
Angle γ: Enter the angle at vertex C. This is the angle opposite side c.
Side a: Enter the length of side a, which sits across from angle α.
Side b: Enter the length of side b, which sits across from angle β.
Side c: Enter the length of side c, which sits across from angle γ.
Calculate: Click this button to solve the triangle. The calculator will show all three angles, all three sides, a solved triangle diagram, and properties like area, perimeter, inradius, circumradius, and triangle type. A step-by-step solution explains the math used.
Reset: Click this button to clear all fields and start over with a new triangle.
Triangle Angle Calculator
A triangle is a shape with three straight sides and three angles. The three angles of any triangle always add up to 180 degrees. If you know some sides or angles, you can find the rest using math rules like the Law of Cosines and the Law of Sines.
How Triangles Work
Each angle in a triangle sits across from a side. The biggest angle is always across from the longest side, and the smallest angle is across from the shortest side. If you know at least three pieces of information (with at least one side), you can solve the entire triangle — meaning you can find every missing angle and side.
Types of Triangles by Angles
- Acute triangle: All three angles are less than 90°.
- Right triangle: One angle is exactly 90°.
- Obtuse triangle: One angle is greater than 90°.
Types of Triangles by Sides
- Equilateral: All three sides are equal. All angles are 60°.
- Isosceles: Two sides are equal. The two angles across from those sides are also equal.
- Scalene: All three sides are different lengths. All three angles are different too.
Key Formulas Used
The Law of Cosines helps when you know three sides (SSS) or two sides and the angle between them (SAS). It works like this: c² = a² + b² − 2ab·cos(γ). The Law of Sines says that a/sin(α) = b/sin(β) = c/sin(γ). This is useful when you know two angles and a side (ASA or AAS).
Triangle Inequality Rule
Not every set of three numbers can form a triangle. The sum of any two sides must be greater than the third side. For example, sides of 2, 3, and 10 cannot make a triangle because 2 + 3 = 5, which is less than 10.