One arcminute is 1/60 degree.
Arcminutes to Radians Converter — arcmin to rad
Convert Arcminute (arcmin) to Radian (rad) using the exact conversion factor (1 arcminute = 0.0002908882 radian). See the formula, worked examples, conversion table, history, and common uses.
Arcminutes to Radians converter
Converter
Angle Converter
Convert radians, degrees, gradians, turns, arcminutes, arcseconds, and milliradians.
Context values
Some unit families need one extra value for a physically accurate result.
The radian is the SI angle unit.
Result = input x 0.0002908882087 / 1.
Angle uses radians as the base unit.
Reserved above the conversion cards and below the converter.
About Converting Arcminutes to Radians
Arcminute and Radian are the two standard ways to measure angles — degrees for everyday and navigational use, radians for calculus and physics — so converting between them comes up constantly in math, engineering, and programming. Specifically: One arcminute is 1/60 degree, and the radian is the SI angle unit.
Formula
radians = arcminutes × 0.000290888208666
This factor comes from each unit's defined relationship to the category's base unit: 1 arcminute equals 0.000290888208666 base units, and 1 radian equals 1 base unit, so dividing one by the other gives the direct arcminute-to-radian factor of 0.000290888208666.
Simple example
1 arcmin × 0.0002908882087 = 0.0002908882 rad
1 arcminute = 0.0002908882 radians.
Real-world example
90 arcmin × 0.0002908882087 = 0.0261799388 rad
90 arcminutes = 0.0261799388 radians.
Conversion table
| Arcminute (arcmin) | Radian (rad) |
|---|---|
| 0 arcmin | 0 rad |
| 30 arcmin | 0.0087266463 rad |
| 45 arcmin | 0.0130899694 rad |
| 90 arcmin | 0.0261799388 rad |
| 180 arcmin | 0.0523598776 rad |
| 360 arcmin | 0.1047197551 rad |
Reverse conversion: Radian to Arcminute
0.0002908882 rad × 3437.746771 = 0.9999999702 arcmin
0.0002908882 radians = 0.9999999702 arcminutes.
arcminutes = radians × 3437.74677078
For a page dedicated to this direction, see Radian to Arcminute.
Understanding the Arcminute (arcmin)
One arcminute is 1/60 degree.
Understanding the Radian
Radian (rad) measures angle. A radian is the angle subtended when the arc length equals the radius; a full circle is 2π radians. It is classified as a SI derived unit.
Where it's used: Standard angle unit in mathematics, physics, and engineering worldwide.
Uses of the Radian today
- Calculus and trigonometry (derivatives of trig functions are simplest in radians)
- Physics and engineering (angular velocity, rotational mechanics)
- Computer graphics and robotics
History of the Radian
The radian was developed in the 1870s, with the term itself coined by James Thomson (brother of Lord Kelvin) around 1873, formalizing a ratio-based angle measure that mathematicians had used implicitly for calculus since Newton and Leibniz.
It was adopted as the SI derived unit of angle because it makes many physics and calculus formulas simpler than using degrees.
Historical origin. Radian was not the invention of a single named person; it developed through the process described above.
Radian — sources
- BIPM SI Brochure — Coherent derived units — Defines the radian as the SI unit of plane angle.
Reserved between the cards and the FAQ so the page stays balanced.
Frequently asked questions
How many radians are in 1 arcminute?
1 arcminute equals 0.0002908882 radians, using the exact defined conversion factor rather than an estimate.
How do I convert arcminute to radian?
Multiply the arcminute value by 0.0002908882087. The converter above does this instantly to whatever precision you set.
How do I convert radian back to arcminute?
Use the reverse factor: 1 radian equals 3,437.746771 arcminutes. You can also use the swap control in the converter above to flip the direction instantly.
What is a arcminute?
Arcminute (arcmin) is a unit of angle.
What is a radian?
Radian (rad) measures angle. A radian is the angle subtended when the arc length equals the radius; a full circle is 2π radians. It is classified as a SI derived unit.
Is the arcminute to radian conversion exact?
Yes. Both arcminute and radian are defined by fixed standards rather than physical artifacts, so the factor of 0.0002908882087 used above is exact to as many digits as you choose to display.