The angles of a triangle always add up to 180°. Knowing them is essential when cutting roof rafters, laying out triangular structures or checking whether a triangle is acute, right or obtuse.
How to use the Triangle Angle Calculator
- What do you know?
- Side a
- Side b
- Side c
- Angle γ (between a and b)
- Angle α
- Angle β
Results update as you type, and everything is calculated in your browser.
How it works
With three sides each angle comes from the law of cosines. With two sides and the included angle, the third side is computed first. With two angles, the third is 180° minus their sum.
Inputs explained
| Field | What to enter |
|---|---|
| What do you know? | Choose one: Three sides (SSS), Two sides and the angle between them (SAS), Two angles |
| Side a | Units: cm, m, mm, in, ft, yd … |
| Side b | Units: cm, m, mm, in, ft, yd … |
| Side c | Units: cm, m, mm, in, ft, yd … |
| Angle γ (between a and b) | Units: °, rad, π rad, grad, turn |
| Angle α | Units: °, rad, π rad, grad, turn |
| Angle β | Units: °, rad, π rad, grad, turn |
Example values
How the main result changes when Side a changes and everything else stays at the example values above:
| Side a (cm) | Angle α (opposite a) (°) |
|---|---|
| 2.5 | 20.3641 |
| 3.75 | 32.3822 |
| 5 | 44.4153 |
| 6.25 | 56.8471 |
| 7.5 | 69.9853 |
| 10 | 100.2866 |
Formula
α = arccos((b² + c² − a²)/(2bc)), α + β + γ = 180°
Worked example
Inputs — What do you know?: Three sides (SSS); Side a: 5 cm; Side b: 6 cm; Side c: 7 cm.
Results — Angle α (opposite a) = 44.415309 °; Angle β (opposite b) = 57.12165 °; Angle γ (opposite c) = 78.463041 °; Type by angles = Acute.
Key terms
- Interior angle
- An angle inside the triangle at a vertex.
Frequently asked questions
Why do triangle angles add to 180°?
A line through one vertex parallel to the opposite side shows the three angles form a straight angle.
Can a triangle have two right angles?
No – the third angle would be 0°.
How do I find an angle from three sides?
Use the law of cosines solved for the angle.
What is an exterior angle?
180° minus an interior angle; it equals the sum of the two remote interior angles.