Enter the angle in radians below to get the value converted to circles. The calculator supports values containing decimals, fractions, and π: (π/2, 1/2π, etc)

Results in Circles: Do you want to convert circles to radians?

## How to Convert Radians to Circles

To convert a measurement in radians to a measurement in circles, multiply the angle by the following conversion ratio: 0.159155 circles/radian.

Since one radian is equal to 0.159155 circles, you can use this simple formula to convert:

The angle in circles is equal to the angle in radians multiplied by 0.159155.

For example, here's how to convert 5 radians to circles using the formula above.
circles = (5 rad × 0.159155) = 0.795775 cir

### How Many Circles Are in a Radian?

There are 0.159155 circles in a radian, which is why we use this value in the formula above.

A radian is the measurement of angle equal to the length of an arc divided by the radius of the circle or arc. 1 radian is equal to 180/π degrees, or about 57.29578°. There are about 6.28318 radians in a circle.

The radian is the SI derived unit for angle in the metric system. Radians can be abbreviated as rad, and are also sometimes abbreviated as c, r, or R. For example, 1 radian can be written as 1 rad, 1 c, 1 r, or 1 R.

Radians are often expressed using their definition. The formula to find an angle in radians is θ = s/r, where the angle in radians θ is equal to the arc length s divided by the radius r. Thus, radians may also be expressed as the formula of arc length over the radius.

Radians are also considered to be a "unitless" unit. That is, when multiplying or dividing by radians, the result does not include radians as part of the final units.

For example, when determining the length of an arc for a given angle, we use the formula above, rearranged to be s = θr. If θ is in radians and r is in meters, then the units of s will be meters, not radian-meters. If θ were in degrees, however, then s would have units of degree-meters.

## What Is a Circle?

A circle is the equivalent of 1 revolution around a circle, or 360°.

A circle is sometimes also referred to as a revolution. Circles can be abbreviated as cir; for example, 1 circle can be written as 1 cir.

A circle is more commonly used to describe a round, symmetrical shape with no corners or edges than it is to describe plane angle. The shape is described by its radius and circumference.

## Radian to Circle Conversion Table

Table showing various radian measurements converted to circles.