Radians to Degrees
Convert radians to degrees.
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Example
π rad = 180°
How it works
Radians and degrees are two different ways to measure the same angle, so this formula converts between the two scales. A full turn around a circle is 360° and also 2π radians, so dividing both by 2 shows that 1 radian equals 180/π degrees. That is why you multiply radians by 180/π to get the angle in degrees.
When to use it
Use this when a math, physics, or engineering problem gives an angle in radians but you need the answer in degrees. It is especially common in trigonometry, circular motion, and calculator work where results may be reported in different angle units.
Worked example, step by step
Convert 2.5 rad to degrees Use the formula: deg = rad × 180/π Substitute: deg = 2.5 × 180/π Calculate: deg ≈ 2.5 × 57.2958 Result: deg ≈ 143.24°
Common mistakes to avoid
- Multiplying by π/180 instead of 180/π when converting radians to degrees
- Forgetting that the answer should include the degree symbol (°)
- Using 3.14 too early and rounding too aggressively, which can reduce accuracy
Did You Know?
A full circle is 2π radians or 360 degrees, the latter inherited from ancient Babylonian base-60 counting.
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