Minutes of Arc to Radians Converter

What Is a Minute of Arc?

The minute of arc is a unit of angle equal to 1/60th of one degree, or 1/21,600 of a circle. The minute of arc is also equal to π/10,800 radians.

A minute of arc is sometimes also referred to as an arc minute, arcminute, or minute arc. Minutes of arc can be abbreviated as arcmin, and are also sometimes abbreviated as MOA or amin. For example, 1 minute of arc can be written as 1 arcmin, 1 MOA, or 1 amin.

The minute of arc is most commonly represented using the prime (′), although the single-quote is commonly used. For instance, 1 minute of is most commonly expressed as 1′.

Learn more about minutes of arc.

What Is a Radian?

A radian is the measurement of angle equal to the length of an arc divided by the radius of the circle or arc.^[1] 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.

Learn more about radians.