3 Angle Triangle Calculator

A triangle’s interior angles always add to a fixed total: 180° in degrees, or π in radians.

This calculator also checks whether the final sum is within your tolerance, then labels the triangle as acute, right, or obtuse based on its angles.

1. Enter any two angles (A, B, or C).
2. Pick the unit: Degrees or Radians.
3. Set a tolerance if you will enter all three angles.
4. Click Calculate to show results above the form.
5. If available, use Download CSV or Download PDF.

When Two Angles Are Known

Any triangle is fully determined by its three angles, and the sum is fixed: 180° (degrees) or π (radians). If you enter two angles, the missing one is computed as Third = Total − (First + Second). This is the fastest way to confirm homework, check drawings, or verify survey notes.

Why the Third Angle Must Be Positive

A valid triangle requires each interior angle to be greater than 0. If your known angles already add to the full total, the computed third angle becomes zero, which forms a straight line, not a triangle. If the known angles exceed the total, the result becomes negative, indicating an input mistake.

Tolerance and Real‑World Rounding

Measurements often include rounding, especially when angles come from instruments, CAD sketches, or quick calculations. The tolerance field lets you define how close the sum must be to 180° or π. A strict setting like 0.0001 works for computed values, while a slightly larger tolerance can help when values were rounded to one or two decimals.

Classifying Acute, Right, and Obtuse

Angle size tells you the triangle’s type. If any angle is near 90°, the triangle is right. If one angle is greater than 90°, it is obtuse. If all three are less than 90°, it is acute. This calculator labels the type automatically so you can interpret the geometry immediately.

Equiangular and Isosceles Checks

Equal angles reveal symmetry. A triangle with angles 60°, 60°, 60° is equiangular (often called equilateral in side terms). If two angles match within tolerance, the triangle is isosceles by angles, which is useful when checking mirror‑symmetric designs and repeated components.

Degree–Radian Conversion Reference

Engineers and scientists often switch units. Use degrees = radians × (180/π) and radians = degrees × (π/180). Common anchors are π/2 = 90°, π/3 = 60°, and π/6 = 30°. The results panel shows both your chosen unit and degree equivalents.

Worked Mini‑Examples You Can Try

Try A = 40° and B = 65°; the missing angle is 75° and the triangle is acute. Try A = 90° and B = 45°; the missing angle is 45° and the triangle is right. In radians, try 1.0472 and 0.7854; the third is about 1.3090. These quick tests help confirm you are entering the unit you intend.

1) Can I solve the triangle with only one angle?

No. A triangle needs at least two angles to compute the third using the angle‑sum rule.

2) What happens if my three angles do not add to 180°?

The calculator marks the set as not valid and shows the difference from the required total, helping you spot entry or rounding errors.

3) Should I use degrees or radians?

Use degrees for most geometry problems and drawings. Use radians for calculus, physics, and many engineering formulas. The calculator supports both.

4) Why does tolerance matter?

Rounded measurements may not sum exactly to the total. Tolerance lets you accept small differences while still checking whether inputs are reasonable.

5) How is triangle type determined?

If any angle is about 90°, it is right. If any exceeds 90°, it is obtuse. Otherwise, it is acute.

6) Does “equiangular” mean the sides are equal?

For triangles, equal angles imply equal opposite sides, so equiangular triangles are also equilateral. This tool reports the angle symmetry directly.

7) Can I export results without recalculating?

Exports appear after you click Calculate. Once results are shown, you can download CSV or PDF using the buttons in the result panel.