The radian is the SI angle unit.
Radians to Arcminutes Converter — rad to arcmin
Convert Radian (rad) to Arcminute (arcmin) using the exact conversion factor (1 radian = 3,437.746771 arcminute). See the formula, worked examples, conversion table, history, and common uses.
Radians to Arcminutes 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.
One arcminute is 1/60 degree.
Result = input x 1 / 0.0002908882087.
Angle uses radians as the base unit.
Reserved above the conversion cards and below the converter.
About Converting Radians to Arcminutes
Radian and Arcminute 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. Radian is most often used for calculus and trigonometry (derivatives of trig functions are simplest in radians).
Formula
arcminutes = radians × 3437.74677078
This factor comes from each unit's defined relationship to the category's base unit: 1 radian equals 1 base unit, and 1 arcminute equals 0.000290888208666 base units, so dividing one by the other gives the direct radian-to-arcminute factor of 3437.74677078.
Simple example
1 rad × 3437.746771 = 3,437.746771 arcmin
1 radian = 3,437.746771 arcminutes.
Real-world example
90 rad × 3437.746771 = 309,397.2094 arcmin
90 radians = 309,397.2094 arcminutes.
Conversion table
| Radian (rad) | Arcminute (arcmin) |
|---|---|
| 0 rad | 0 arcmin |
| 30 rad | 103,132.4031 arcmin |
| 45 rad | 154,698.6047 arcmin |
| 90 rad | 309,397.2094 arcmin |
| 180 rad | 618,794.4187 arcmin |
| 360 rad | 1,237,588.837 arcmin |
Reverse conversion: Arcminute to Radian
1 arcmin × 0.0002908882087 = 0.0002908882 rad
1 arcminute = 0.0002908882 radians.
radians = arcminutes × 0.000290888208666
For a page dedicated to this direction, see Arcminute to Radian.
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.
Understanding the Arcminute (arcmin)
One arcminute is 1/60 degree.
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 arcminutes are in 1 radian?
1 radian equals 3,437.746771 arcminutes, using the exact defined conversion factor rather than an estimate.
How do I convert radian to arcminute?
Multiply the radian value by 3437.746771. The converter above does this instantly to whatever precision you set.
How do I convert arcminute back to radian?
Use the reverse factor: 1 arcminute equals 0.0002908882 radians. You can also use the swap control in the converter above to flip the direction instantly.
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.
What is a arcminute?
Arcminute (arcmin) is a unit of angle.
Is the radian to arcminute conversion exact?
Yes. Both radian and arcminute are defined by fixed standards rather than physical artifacts, so the factor of 3437.746771 used above is exact to as many digits as you choose to display.
Where is the radian still used today?
Standard angle unit in mathematics, physics, and engineering worldwide.