Minutes of Arc to Radians Converter
Enter the angle in minutes of arc below to convert it to radians.
Result in Radians:
Do you want to convert radians to minutes of arc?
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How to Convert Minutes of Arc to Radians
To convert a measurement in minutes of arc to a measurement in radians, multiply the angle by the following conversion ratio: 0.000291 radians/minute of arc.
Since one minute of arc is equal to 0.000291 radians, you can use this simple formula to convert:
radians = minutes of arc × 0.000291
The angle in radians is equal to the angle in minutes of arc multiplied by 0.000291.
For example, here's how to convert 5,000 minutes of arc to radians using the formula above.
radians = (5,000' × 0.000291) = 1.454441 rad
Minutes of arc and radians are both units used to measure angle. Keep reading to learn more about each unit of measure.
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.
Minute of Arc to Radian Conversion Table
| 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 |
| 20' | 0.005818 rad |
| 30' | 0.008727 rad |
| 40' | 0.011636 rad |
| 50' | 0.014544 rad |
| 60' | 0.017453 rad |
| 70' | 0.020362 rad |
| 80' | 0.023271 rad |
| 90' | 0.02618 rad |
| 100' | 0.029089 rad |
| 200' | 0.058178 rad |
| 300' | 0.087266 rad |
| 400' | 0.116355 rad |
| 500' | 0.145444 rad |
| 600' | 0.174533 rad |
| 700' | 0.203622 rad |
| 800' | 0.232711 rad |
| 900' | 0.261799 rad |
| 1,000' | 0.290888 rad |
| 2,000' | 0.581776 rad |
| 3,000' | 0.872665 rad |
| 4,000' | 1.1636 rad |
| 5,000' | 1.4544 rad |
| 6,000' | 1.7453 rad |
| 7,000' | 2.0362 rad |
| 8,000' | 2.3271 rad |
| 9,000' | 2.618 rad |
| 10,000' | 2.9089 rad |
References
- International Bureau of Weights and Measures, The International System of Units, 9th Edition, 2019, https://www.bipm.org/documents/20126/41483022/SI-Brochure-9-EN.pdf