Convert Arc Minutes (') to Radians (rad)

1 arc minute equals 0.000290888 radians.

Formula: rad = ' × 0.000290888

Arc Minute to Radian Converter

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How to Convert Arc Minute to Radian

1 arc minute = 0.000290888 radians

Radian = Arc Minute × 0.000290888

Example: 1' × 0.000290888 = 0.000290888 rad

Reverse Conversion

To convert radians back to arc minutes:

  • Remember, 1 radian equals 3437.75 arc minutes.
  • To convert 0.000290888 rad to', multiply 0.000290888 x 3437.75, resulting in 1'.

Common Arc Minute to Radian Conversions

Arc Minute to Radian (Part 1)
Arc Minute to Radian common conversions part 1
Arc Minute Radian Actions
1 arc minute 0.000290888 radians
5 arc minutes 0.00145444 radians
10 arc minutes 0.00290888 radians
25 arc minutes 0.00727221 radians
Arc Minute to Radian (Part 2)
Arc Minute to Radian common conversions part 2
Arc Minute Radian Actions
50 arc minutes 0.0145444 radians
100 arc minutes 0.0290888 radians
500 arc minutes 0.145444 radians
1000 arc minutes 0.290888 radians

Arc minutes to radians Conversion Table

Reference table with common arc minutes to radians conversions. All values calculated with high precision.

Arc Minutes to Radians Table
1 to 5000

Arc minutes Radians Actions
1 ' 0.000290888 rad
2 12 ' 0.000727221 rad
5 ' 0.00145444 rad
10 ' 0.00290888 rad
25 ' 0.00727221 rad
50 ' 0.0145444 rad
100 ' 0.0290888 rad
250 ' 0.0727221 rad
500 ' 0.145444 rad
1000 ' 0.290888 rad
2500 ' 0.727221 rad
5000 ' 1.45444 rad

Arc Minutes to Radians Table
10000 to 1 × 109

Arc minutes Radians Actions
10000 ' 2.90888 rad
25000 ' 7.27221 rad
50000 ' 14.5444 rad
100000 ' 29.0888 rad
250000 ' 72.7221 rad
500000 ' 145.444 rad
1000000 ' 290.888 rad
2500000 ' 727.221 rad
5000000 ' 1454.44 rad
10000000 ' 2908.88 rad
2.5 × 107 ' 7272.21 rad
5 × 107 ' 14544.4 rad
1 × 108 ' 29088.8 rad
2.5 × 108 ' 72722.1 rad
5 × 108 ' 145444 rad
1 × 109 ' 290888 rad

Radians to Arc Minutes Table
0.0001 to 12

Radians Arc minutes Actions
0.0001 rad 0.343775 '
0.00025 rad 0.859437 '
0.0005 rad 1.71887 '
0.001 rad 3.43775 '
0.0025 rad 8.59437 '
0.005 rad 17.1887 '
0.01 rad 34.3775 '
0.025 rad 85.9437 '
0.05 rad 171.887 '
0.1 rad 343.775 '
14 rad 859.437 '
12 rad 1718.87 '

Radians to Arc Minutes Table
1 to 100000

Radians Arc minutes Actions
1 rad 3437.75 '
2 12 rad 8594.37 '
5 rad 17188.7 '
10 rad 34377.5 '
25 rad 85943.7 '
50 rad 171887 '
100 rad 343775 '
250 rad 859437 '
500 rad 1718870 '
1000 rad 3437750 '
2500 rad 8594370 '
5000 rad 1.71887 × 107 '
10000 rad 3.43775 × 107 '
25000 rad 8.59437 × 107 '
50000 rad 1.71887 × 108 '
100000 rad 3.43775 × 108 '

Definition of Radian

Definition

The radian (rad) is the SI derived unit of plane angle. It is defined as the angle subtended at the center of a circle by an arc equal in length to the radius.

Although mathematically dimensionless, the radian is retained as a named unit in the SI to preserve clarity in scientific, engineering, physics, trigonometry, and calculus contexts.

Exact factor
Base unit: 1 rad = 1 rad; full circle: 2π rad = 360°
Examples
  • π rad = 180°
  • 1 rad ≈ 57.2958°
  • 2π rad = 1 turn

About the Radian

Facts & Uses

  • SI coherent unit of plane angle: 1 rad = the angle subtended at a circle's center by an arc equal in length to the radius. 1 full circle = 2π rad ≈ 6.283 rad.
  • Universal in mathematics, physics, engineering, and computer graphics — wherever calculus or trigonometric derivatives are involved.
  • Standard for angular velocity (rad/s), angular acceleration (rad/s²), and phase angles in electrical engineering and signal processing.
  • Common reference: π/6 rad = 30°, π/4 = 45°, π/3 = 60°, π/2 = 90°, π = 180°, 2π = 360°.

Curiosities

  • The radian was first proposed by Roger Cotes in 1714, but the name "radian" wasn't coined until 1873 by James Thomson (brother of Lord Kelvin).
  • Programming functions like Math.sin() and Math.cos() in JavaScript, Python, C, and most languages take radians as input — a frequent source of bugs for developers expecting degrees.
  • The reason calculus prefers radians: the derivative of sin(x) is cos(x) only when x is in radians. With degrees, you'd need a π/180 factor everywhere.
  • Approximate equivalents: 1 rad ≈ 57.2958° ≈ 63.66 grad ≈ 3437.75 arcminutes.

Sources

Frequently Asked Questions

How many radians are in one arc minute?

One arc minute equals 0.000290888 radians. To convert, multiply the arc minute value by 0.000290888. For the reverse, divide the radian value by 0.000290888 (or multiply by 3437.75).

What is 100 arc minutes in radians?

100 arc minutes = 0.029089 radians. This is one of the most commonly searched conversions for this pair.

How precise is the arc minute-to-radian conversion?

The factor 0.000290888 is accurate to 6 significant figures, derived from international measurement standards. Our calculator uses full precision internally.

Looking for the reverse? Convert Radian to Arc Minute

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Conversion factors verified against BIPM, ISO 80000-3 1 turn = 2π rad = 360° (exact, ISO 80000-3). Last reviewed: March 2026
Adilson Fernandes By Adilson Fernandes
Tiago Fernandes Reviewed by Tiago Fernandes

All unit conversions on CoolConversion use conversion factors defined or documented by internationally recognised standards bodies (such as ISO and NIST), including both SI and non-SI units.