Triangle Degree Calculator

Convert triangle angles between degrees and radians, validate the angle sum, and classify the triangle type.

Enter Three Angles

Result

Triangle Classification
--
Angle A --
Angle B --
Angle C --
Sum --

Step-by-Step Analysis

Understanding Triangle Angles

In Euclidean geometry, the interior angles of any triangle always sum to exactly 180 degrees (or pi radians). This fundamental property allows us to classify triangles by their angles and to find a missing angle when two are known.

Triangle Classifications by Angle

Acute Triangle

All three interior angles are less than 90 degrees.

A < 90, B < 90, C < 90

Right Triangle

Exactly one interior angle is exactly 90 degrees.

One angle = 90

Obtuse Triangle

Exactly one interior angle is greater than 90 degrees.

One angle > 90

Equilateral Triangle

All three interior angles are exactly 60 degrees.

A = B = C = 60

Degrees vs. Radians

Degrees and radians are two units for measuring angles. A full circle is 360 degrees or 2pi radians. To convert between them:

  • Degrees to Radians: radians = degrees x (pi / 180)
  • Radians to Degrees: degrees = radians x (180 / pi)
  • 180 degrees = pi radians (the angle sum of a triangle)

Tips

  • If the sum of angles does not equal 180 degrees, the triangle is invalid in Euclidean geometry.
  • Each angle must be greater than 0 and less than 180 degrees.
  • An isosceles triangle has at least two equal angles; an equilateral has all three equal.