Degrees to Radians Calculator

Radians measure angles by arc length: one full turn is 2π radians, which equals 360°. This calculator converts degrees to radians by multiplying by π/180 and simplifying the fraction, so you get an exact answer such as 3π/4, along with the decimal value and a diagram of the angle.

Try:

How to use the degrees to radians calculator

  1. Enter the angle in degrees.
  2. Press Calculate.
  3. Read the exact answer in terms of π and the decimal.

Formula

rad=deg×π180\text{rad} = \text{deg} \times \frac{\pi}{180}

Worked example: 135°

  • Degrees: 135

✓ Answer checked

135∘=3π4 rad135^\circ = \frac{3\pi}{4}\text{ rad}
Decimal
≈2.35619449 rad\approx 2.35619449\text{ rad}
(cos θ, sin θ) = (-0.707, 0.707) 11
135° measured anticlockwise from the positive x-axis.
Step-by-step working (2 steps)

  1. Multiply by π/180 π rad = 180°

    There are π radians in 180°, so multiply the degrees by π/180.

    135×π180135 \times \frac{\pi}{180}

  2. Simplify the fraction

    135/180 simplifies to 3/4.

    =3π4= \frac{3\pi}{4}
Formulas used
rad=deg×π180\text{rad} = \text{deg} \times \frac{\pi}{180}
How this was checked
  • ✓ Converting 3/4π back with × 180/π gives 135°.

Frequently asked questions

How do I convert degrees to radians?

Multiply by π/180 and simplify. For example, 60° × π/180 = π/3.

How many radians are in a full circle?

2π radians, because 360° × π/180 = 2π.

How big is one radian?

About 57.3°. It is the angle where the arc length equals the radius.

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