Degrees to Radians Converter

What is a degrees to radians converter?

A degrees to radians converter turns an angle written in degrees into the equivalent angle measured in radians. Degrees split a full turn into 360 equal parts, a convention inherited from ancient astronomy. Radians, by contrast, measure an angle by the length of the arc it sweeps on a unit circle, which makes them the natural unit for trigonometry and calculus. This tool lets you move between the two without doing the arithmetic by hand, and it also accepts gradians if you prefer that base.

Formula

A full circle equals 360 degrees and also equals $2\pi$ radians, so the conversion factor follows directly:

$\text{radians} = \text{degrees} \times \frac{\pi}{180}$

How to convert degrees to radians

1. Take the angle you have in degrees.
2. Multiply it by $\pi / 180$.
3. The result is the same angle expressed in radians.

The base factor is the key number to remember: 1 degree = 0.0174533 radians. Any larger angle is just a multiple of this value. Working the other way, 1 radian = 57.29578 degrees, which is the same relationship inverted.

Worked examples

Example 1 — 1 degree to radians

$1 \times \frac{\pi}{180} \approx 0.0174533 \text{ radians}$

Example 2 — 1 radian back to degrees

$1 \times \frac{180}{\pi} \approx 57.29578 \text{ degrees}$

Example 3 — 90 degrees to radians

$90 \times \frac{\pi}{180} = \frac{\pi}{2} \approx 1.570796 \text{ radians}$

FAQ

Why are radians preferred in mathematics?

Radians tie an angle directly to arc length on a unit circle, which keeps trigonometric formulas, derivatives, and series simple. Using degrees would force extra conversion constants into nearly every calculus expression.

How do I convert radians back to degrees?

Multiply the radian value by $180 / \pi$, or about 57.29578. For the reverse direction you can also use the radians to degrees converter. If you are working with arcs and angles, the circle sector area calculator is a useful companion.