Convert Minutes Of Arc to Radians

Enter the angle in minutes of arc below to get the value converted to radians.

Results in Radians:
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1 arcmin = 0.000291 rad

How to Convert Minutes Of Arc to Radians

Protractors are often used to measure angle

To convert a minute of arc measurement to a radian measurement, multiply the angle by the conversion ratio. One minute of arc is equal to 0.000291 radians, so use this simple formula to convert:

radians = minutes of arc × 0.000291

The angle in radians is equal to the minutes of arc multiplied by 0.000291.

For example, here's how to convert 5 minutes of arc to radians using the formula above.
5' = (5 × 0.000291) = 0.001454 rad

Minutes of arc and radians are both units used to measure angle. Keep reading to learn more about each unit of measure.

Minutes 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′.


A radian is the measurement of angle equal to the start to the end of an arc divided by the radius of the circle or arc. 1 radian is equal to 180/π, 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 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.

Minute Of Arc Measurements and Equivalent Radian Conversions

Common minute of arc values converted to the equivalent radian value
Minutes Of Arc Radians
1' 0.000291 rad
2' 0.000582 rad
3' 0.000873 rad
4' 0.001164 rad
5' 0.001454 rad
6' 0.001745 rad
7' 0.002036 rad
8' 0.002327 rad
9' 0.002618 rad
10' 0.002909 rad
11' 0.0032 rad
12' 0.003491 rad
13' 0.003782 rad
14' 0.004072 rad
15' 0.004363 rad
16' 0.004654 rad
17' 0.004945 rad
18' 0.005236 rad
19' 0.005527 rad
20' 0.005818 rad
21' 0.006109 rad
22' 0.0064 rad
23' 0.00669 rad
24' 0.006981 rad
25' 0.007272 rad
26' 0.007563 rad
27' 0.007854 rad
28' 0.008145 rad
29' 0.008436 rad
30' 0.008727 rad
31' 0.009018 rad
32' 0.009308 rad
33' 0.009599 rad
34' 0.00989 rad
35' 0.010181 rad
36' 0.010472 rad
37' 0.010763 rad
38' 0.011054 rad
39' 0.011345 rad
40' 0.011636 rad

More Minute Of Arc Angle Conversions

Convert to Milliradians
1' is equal to 0.290888 milliradians
Convert to Degrees
1' is equal to 0.016667 degrees
Convert to Seconds Of Arc
1' is equal to 60 seconds of arc
Convert to Gradians
1' is equal to 0.018519 gradians
Convert to Revolutions
1' is equal to 4.6296E-5 revolutions
Convert to Circles
1' is equal to 4.6296E-5 circles
Convert to Mils (NATO)
1' is equal to 0.296296 mils (NATO)

Unit of Measurement Conversion Made Easy!

There are thousands of units of measure in use across the globe, and converting from one to another can be very difficult since each conversion requires a different formula to derive the result. Our unit of measurement conversion tools are meant to be dead easy. We break the mold of the typical dry and complicated experience. In addition to converting from one measurement to another, we provide the formula so you can see how the conversion is done, use it on you’re own calculator if you need to!

Convert units of length, weight, volume, and area between imperial and metric measures

Understanding the Metric System

The metric system makes it relatively easy to convert from one metric unit to another metric unit. The metric system uses a base unit, think meters or grams, and a prefix such as kilo or milli. The prefixes differ from the base units by differing powers of 10. So to convert within the metric system it’s usually a matter of multiplying or dividing by one of the powers of 10.

Here is a list of some of the common metric prefixes:

  • “kilo” – 1,000x larger
  • “hecto” – 100x larger
  • “deca” – 10x larger
  • “deci” – 10x smaller
  • “centi” – 100x smaller
  • “milli” – 1,000x smaller

There is a helpful mnemonic for remembering the prefixes: “King Henry Died Until Drinking Chocolate Milk.”
The u in Until refers to the base unit.