Convert Angle From Degrees to Radians

Degrees Angle System
Radian Angle System

To convert an angle from degrees to radians, multiply the multiply by the ratio of (tau) over . For example, to convert the angle to radians multiply the conversion ratio and simplify the fraction.

Note: This website uses the constant (tau) instead of (pi) as the default circle constant[1]. The substitution can be used to translate between the two constants.

Explanation

The converstion factor can be calculated by observing that a full rotation in degrees is and a full rotation in radians is (tau) radians, where the circle constant is a naturally occurring number approximately equal to .

Examples

Convert 30 Degrees to Radians

30 Degrees 1 over 12 tau radians

This examples demonstrates how to convert the angle degrees to radians. Generally, to convert an angle from degrees to radians multiply by the ratio of (tau) over .

Steps

  1. Set up the conversion.

  2. Multiply by the conversion factor.

  3. Simplify the expression. In this case, degree unit cancels and the fraction simplifies.

    The angle is equal to radians.

Convert 45 Degrees to Radians

45 Degrees 1 over 8 tau radians

This examples demonstrates how to convert the angle degrees to radians. Generally, to convert an angle from degrees to radians multiply by the ratio of (tau) over .

Steps

  1. Set up the conversion.

  2. Multiply by the conversion factor.

  3. Simplify the expression. In this case, degree unit cancels and the fraction simplifies.

    The angle is equal to radians.

Convert 60 Degrees to Radians

60 Degrees 1 over 6 tau radians

This examples demonstrates how to convert the angle degrees to radians. Generally, to convert an angle from degrees to radians multiply by the ratio of (tau) over .

Steps

  1. Set up the conversion.

  2. Multiply by the conversion factor.

  3. Simplify the expression. In this case, degree unit cancels and the fraction simplifies.

    The angle is equal to radians.

Common Conversions

The tables below show common conversions formed from dividing a full rotation into equal parts.

Fractions of 4

The charts below show the angles formed from dividing a full rotation into equal parts.

One Fourth Rotation in Degrees One Fourth Rotation in Radians

The measure angles shown on the charts are listed in the table below.

Degrees Radians

Fractions of 8

The charts below show the angles formed from dividing a full rotation into equal parts.

One-eigth rotation in degrees One-eigth rotation in radians

The measure angles shown on the charts are listed in the table below.

Degrees Radians

References

  1. No, really, pi is wrong: The Tau Manifesto
    Michael Hartl