Convert Radians (rad) to Arc Minutes (')

1 radian equals 3437.75 arc minutes.

Formula: ' = rad × 3437.75

Radian to Arc Minute Converter

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How to Convert Radian to Arc Minute

1 radian = 3437.75 arc minutes

Arc Minute = Radian × 3437.75

Example: 1 rad × 3437.75 = 3437.75'

Reverse Conversion

To convert arc minutes back to radians:

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

Common Radian to Arc Minute Conversions

Radian to Arc Minute (Part 1)
Radian Arc Minute Actions
1 radian 3437.75 arc minutes
5 radians 17188.7 arc minutes
10 radians 34377.5 arc minutes
25 radians 85943.7 arc minutes
Radian to Arc Minute (Part 2)
Radian Arc Minute Actions
50 radians 171887 arc minutes
100 radians 343775 arc minutes
500 radians 1718870 arc minutes
1000 radians 3437750 arc minutes

Radians to arc minutes Conversion Table

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

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 '

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

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 arc minutes are in one radian?

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

What is 10 radians in arc minutes?

10 radians = 34377 arc minutes. This is one of the most commonly searched conversions for this pair.

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

The factor 3437.75 is accurate to 6 significant figures, derived from international measurement standards. Our calculator uses full precision internally.

Looking for the reverse? Convert Arc Minute to Radian

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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.