Formula used
For any triangle, the interior angles add up to a fixed total: A + B + C = 180°. In radians the total is π, and in gradians it is 200.
When two angles are known, the missing angle is: Missing = Total − (Known1 + Known2).
How to use this calculator
- Select a mode (compute, any-two, validate, or right-triangle).
- Choose your angle units and enter the available angles.
- Leave exactly one angle blank in “any-two” mode.
- Optionally enable exterior angles and triangle classification.
- Click Calculate, then download CSV or PDF if needed.
Example data table
| Case | Angle A (°) | Angle B (°) | Angle C (°) | Result / Note |
|---|---|---|---|---|
| Find third (A,B) | 35 | 65 | — | C = 80° |
| Any two (A,C) | 50 | — | 60 | B = 70° |
| Validate | 60 | 60 | 60 | Valid equilateral triangle |
| Right triangle | 25 | 90 | — | C = 65° |
1) The 180° angle-sum rule
Every triangle in a flat plane has interior angles that add to 180°. This calculator uses that fact to compute the unknown value quickly: C = 180° − (A + B). This rule assumes Euclidean geometry, used in most classroom and field work. If you enter angles in radians, it converts them first, then converts results back.
2) Detecting impossible inputs
Not every pair of angles can form a triangle. If A + B is 180° or more, the third angle becomes zero or negative, which is invalid. The tool flags these cases and explains why the triangle cannot exist, preventing misleading results clearly.
3) Degrees, radians, and DMS display
Angles are commonly measured in degrees, but engineering and programming often prefer radians. The calculator supports both, plus an optional Degrees–Minutes–Seconds display for cleaner reporting. Conversions are handled with high precision to keep rounding errors small.
4) Validation with a tolerance
Real data is rarely perfect. When you check all three angles, the calculator compares their sum to 180° using a user-defined tolerance, such as ±0.1°. This helps when angles come from measurement, drawings, or floating-point computations, and it reduces false “invalid” warnings.
5) Triangle type from angles
Once angles are known, the tool classifies the triangle as acute (all < 90°), right (one ≈ 90°), or obtuse (one > 90°). It also indicates likely symmetry, such as isosceles patterns when two angles match within tolerance.
6) Exterior-angle quick checks
Exterior angles are useful for geometry checks in construction layouts and drawings. With the exterior toggle, the calculator reports each exterior angle as 180° − interior. It’s a fast way to confirm supplementary relationships without extra math.
7) Practical use and common mistakes
Use the “Load Example” button to see typical values, then replace them with your measurements. Double-check units before calculating, and avoid mixing degrees with radians. If results look strange, review whether you entered an exterior angle by mistake.
FAQs
1) What is the formula for the third angle?
The third interior angle equals 180° minus the sum of the other two angles. In radians, use π instead of 180°. The calculator applies the correct total based on your selected units.
2) Why does the calculator say “invalid triangle”?
If the known angles add to 180° or more, the remaining angle becomes zero or negative. A triangle cannot exist with those values, so the tool blocks the result and shows a clear warning.
3) Can I enter only one angle?
No. With only one angle, there are infinitely many possible triangles. You need at least two angles to determine the third, unless you have extra information like a right angle plus another angle.
4) What does tolerance mean in validation?
Tolerance is an allowed error range when checking whether A + B + C equals 180°. For example, ±0.1° accepts small measurement or rounding differences while still flagging clearly incorrect inputs.
5) What’s the difference between interior and exterior angles?
Interior angles are inside the triangle. An exterior angle is formed by extending a side; at each vertex it is supplementary to the interior angle. The calculator can show exterior angles as 180° minus interior.
6) Does this work for spherical triangles?
No. On a sphere, angle sums can exceed 180° and depend on surface area. This tool is for standard plane geometry used in school math, drafting, and typical engineering sketches.