Radians to Minutes of Arc Converter

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

Result in Minutes of Arc:

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1 rad = 3,437.746771 arcmin
Learn how we calculate this below

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How to Convert Radians to Minutes of Arc

To convert a measurement in radians to a measurement in minutes of arc, multiply the angle by the following conversion ratio: 3,437.746771 minutes of arc/radian.

Since one radian is equal to 3,437.746771 minutes of arc, you can use this simple formula to convert:

minutes of arc = radians × 3,437.746771

The angle in minutes of arc is equal to the angle in radians multiplied by 3,437.746771.

For example, here's how to convert 5 radians to minutes of arc using the formula above.

minutes of arc = (5 rad × 3,437.746771) = 17,188.733854'

How Many Minutes of Arc Are in a Radian?

There are 3,437.746771 minutes of arc in a radian, which is why we use this value in the formula above.

1 rad = 3,437.746771'

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

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.

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.

Radian to Minute of Arc Conversion Table

Table showing various radian measurements converted to minutes of arc.
Radians Minutes Of Arc
0.001 rad 3.4377'
0.002 rad 6.8755'
0.003 rad 10.31'
0.004 rad 13.75'
0.005 rad 17.19'
0.006 rad 20.63'
0.007 rad 24.06'
0.008 rad 27.5'
0.009 rad 30.94'
0.01 rad 34.38'
0.02 rad 68.75'
0.03 rad 103.13'
0.04 rad 137.51'
0.05 rad 171.89'
0.06 rad 206.26'
0.07 rad 240.64'
0.08 rad 275.02'
0.09 rad 309.4'
0.1 rad 343.77'
0.2 rad 687.55'
0.3 rad 1,031'
0.4 rad 1,375'
0.5 rad 1,719'
0.6 rad 2,063'
0.7 rad 2,406'
0.8 rad 2,750'
0.9 rad 3,094'
1 rad 3,438'

References

  1. 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

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