Radian To Degree Converter

What this converter does

Radians are the natural unit for angles in higher maths, but they are hard to picture. Is 2 radians a small nudge or most of the way round? Turning a radian value back into degrees puts it on the scale we all read by eye, where 90 is a corner and 360 is a full circle.

Type the angle in radians, and the tool returns it in degrees.

Using the converter

1. Enter the angle in radians.
2. Press Calculate.

The result is the same angle written in degrees.

The two units, briefly

Degrees divide a circle into 360, radians into 2π. A full turn is 360° or 2π radians, which means π radians equals 180°. Radians show up in calculus, physics, and anywhere maths reaches past plain geometry, and often you will want to bring such a value back into the more familiar degrees.

The conversion | multiply by 180 ÷ π

To turn radians into degrees, multiply by 180 ÷ π, the exact reverse of the degrees-to-radians factor. So π radians becomes 180°, π ÷ 2 becomes 90°, and a single radian works out to about 57.3°. That last figure is a slightly awkward one, which is part of why degrees feel more natural for everyday angles.

What one radian actually is

So what is one radian? It is the angle you sweep out when the arc along the circle's edge is exactly as long as the radius. Because a full circle's edge, its circumference, measures 2π radii around, a complete turn comes to 2π radians. That clean geometric definition is what makes radians so tidy in the mathematics of circles.

A worked example | π radians

Convert π radians, about 3.14.

1. Multiply by 180 ÷ π.
2. The π cancels, leaving 180°.

And a single radian on its own comes to about 57.30°.

Questions people ask

How do you convert radians to degrees?

Multiply the radians by 180 ÷ π.

What is π radians in degrees?

180°, since a half circle is π radians.

What is one radian?

About 57.3°. It is the angle whose arc along the circle equals the radius.

How do I go the other way?

Use the degree to radian converter, which multiplies by π ÷ 180.

References

A note on the idea behind it. Converting from radians to degrees multiplies by 180 ÷ π, so that π radians equals 180°. One radian is defined as the angle whose arc length equals the radius, making a full turn of 2π radians. For further reading, see Radian.

1. Converting radians to degrees by multiplying by 180 ÷ π, with π radians equal to 180°.
2. The radian, defined as the angle whose arc length equals the circle's radius.