Triangle Angle Calculator
Find missing triangle angles from two known angles or three side lengths using AA and SSS methods.
Select a calculation method, enter the required values, and get all three angles instantly. All results are in degrees.
Triangle Angle Calculator
Find missing triangle angles from two known angles or three side lengths using AA and SSS methods.
Enter any two angles to find the third. Uses the rule that all three angles of a triangle sum to 180°.
About the Triangle Angle Calculator
Every triangle has three interior angles that always sum to exactly 180 degrees. This fundamental theorem of Euclidean geometry underlies both methods available in this calculator: the two-angle method (AA) and the three-side method (SSS).
The AA method is the simplest: if you know any two angles of a triangle, you can find the third by subtracting their sum from 180°. So if angle A is 30° and angle B is 60°, then angle C = 180° − 30° − 60° = 90°. This method is widely used in geometry proofs, architectural drawing, and navigation — any time you have measured two angles directly and need to confirm or compute the third.
The SSS method uses the law of cosines, a generalization of the Pythagorean theorem that works for any triangle. Given sides a, b, and c opposite to angles A, B, and C respectively, the formula is: cos(A) = (b² + c² − a²) / (2bc). Rearranging gives A = arccos((b² + c² − a²) / (2bc)). Once angle A is determined, angle B = arccos((a² + c² − b²) / (2ac)), and angle C = 180° − A − B. This method is used in surveying, navigation, structural analysis, and any field where direct angle measurement is impossible but all three side lengths can be measured.
For a valid triangle the following must hold: every side must be positive, the sum of any two sides must exceed the third side (triangle inequality), and each angle must be positive with all three summing to 180°. If the SSS inputs violate the triangle inequality, the arccos argument falls outside [−1, 1] and the result is undefined — the calculator will display an error in that case.
Special cases worth noting: an equilateral triangle (all sides equal) has all three angles equal to 60°. An isosceles triangle (two equal sides) has two equal base angles that can be found from SSS once you enter the three sides. A right triangle has one 90° angle, which the calculator will correctly report when the sides satisfy a² + b² = c².
All results are expressed in degrees. If you need results in radians, multiply each degree value by π / 180. The calculator uses standard double-precision floating-point arithmetic, giving results accurate to at least ten significant digits for all valid inputs.
Triangle angle calculator examples
Four examples demonstrating both calculation methods with classic triangle types.
| Known Values | Result | Explanation |
|---|---|---|
| AA: Angle A = 30°, Angle B = 60° | C = 90° | C = 180° − 30° − 60° = 90°. This is a 30-60-90 right triangle, a fundamental shape in geometry and trigonometry. |
| AA: Angle A = 50°, Angle B = 50° | C = 80° | C = 180° − 50° − 50° = 80°. An isosceles triangle with equal base angles of 50° and a vertex angle of 80°. |
| SSS: a = 10, b = 10, c = 10 | A = B = C = 60° | All three sides are equal, so this is an equilateral triangle. All angles are 60° by symmetry. |
| SSS: a = 3, b = 4, c = 5 | A ≈ 36.87°, B ≈ 53.13°, C = 90° | The classic 3-4-5 right triangle. cos(C) = (9 + 16 − 25) / 24 = 0, so C = 90°. The other angles follow from the law of cosines. |
How to use the Triangle Angle Calculator
- Choose a method: Two Known Angles (AA) if you know two angles, or Three Known Sides (SSS) if you know all side lengths.
- Enter the required values in the input fields. For AA enter angle A and angle B in degrees. For SSS enter the lengths of sides a, b, and c.
- Click Calculate Angles. All three angles appear instantly in degrees.
- Verify the result: the three angles should sum to exactly 180° for a valid triangle.
- Click Reset to clear all fields and start a new calculation.
Triangle Angle Calculator FAQ
How do I find the third angle of a triangle if I know two angles?
Subtract the sum of the two known angles from 180°. For example, if angle A = 45° and angle B = 75°, then angle C = 180° − 45° − 75° = 60°. This works because all interior angles of a triangle always sum to exactly 180° in Euclidean geometry.
What is the law of cosines and when do I use it?
The law of cosines states cos(A) = (b² + c² − a²) / (2bc), where a, b, c are side lengths and A is the angle opposite side a. Use it when you know all three sides (SSS case) but no angles. It generalizes the Pythagorean theorem: when A = 90°, the formula reduces to a² = b² + c², which is the Pythagorean theorem.
Why does the calculator show an error for some side length inputs?
Not every set of three positive numbers can form a triangle. The triangle inequality requires that the sum of any two sides must be strictly greater than the third side. For example, sides 1, 2, 10 cannot form a triangle because 1 + 2 < 10. If you enter invalid side lengths the calculator will alert you rather than return a meaningless result.
Can this calculator handle obtuse triangles?
Yes. An obtuse triangle has one angle greater than 90°. The law of cosines handles obtuse triangles correctly because arccos returns values in the range [0°, 180°], which covers all possible interior angles. The two-angle method also works: simply ensure both input angles are positive and their sum is less than 180°.
What is a 3-4-5 triangle?
A 3-4-5 triangle is a right triangle whose sides are in the ratio 3:4:5, satisfying 3² + 4² = 5². Its angles are approximately 36.87°, 53.13°, and 90°. It is the simplest Pythagorean triple and is widely used in construction to check for right angles — a carpenter's square based on this ratio is called a speed square.
Are the results in degrees or radians?
All results are displayed in degrees. If you need radians, multiply each degree value by π/180 (approximately 0.01745). For example, 90° equals 90 × π/180 = π/2 radians. The calculator uses degree-based arccos internally by converting the raw radian result from Math.acos and multiplying by 180/π.