Radians to Degrees

Radians and degrees are two different ways to measure the same angle, so this formula converts between the two scales. The key fact behind it is that a full turn is 360° and also 2π radians, so 1 radian equals 180/π degrees. Multiplying by 180/π rescales the angle from radian units into degree units.

Use this when a problem gives an angle in radians but you need the answer in degrees, such as in trigonometry, geometry, physics, or calculator settings. It is especially useful when comparing angles to familiar degree values like 30°, 45°, or 90°.

• Multiplying by π/180 instead of 180/π
• Forgetting to keep the angle unit clear and writing only the number
• Rounding too early and losing accuracy in the final answer