Convert Radians to Arcminutes (rad to ′)
1 radian (rad) = 3437.746771 minutes of arc (′). 1 ′ = 0.0002908882087 rad. Example: 15 rad = 15 × 3437.746771 = 51566.20156 ′.
Also searched as radians to ′, radians in ′, radians into minutes of arc, rad to ′, rad in minutes of arc, rad into minute of arc, radian to minute of arc, rad to minutes of arc converter and how many minutes of arc in a radian.
1 rad = 3437.746771 ′
Type in either box. Scientific notation works: 1.5e-3.
Converting a list? Use the bulk radian to minute of arc converter to paste a column from Excel.
How to Convert Radian to Arcminute
- 1 rad = 3437.746771 ′
- 1 ′ = 0.0002908882087 rad
- Example: convert 15 rad to ′: 15 rad = 15 × 3437.746771 ′ = 51566.20156 ′
Formula
′ = rad × 3437.746770785
Derivation from SI units:
- The SI unit of plane angle: the angle subtended at the centre of a circle by an arc equal in length to the radius (1 rad = 1 m/m).
- 1′ = (1/60)° = π/10 800 rad.
Both units are defined exactly, so the factor is exact. Radian definition: radian; Arcminute definition: minute of arc.
Worked examples
- A reading of 2 rad converts to 6875.493542 ′.
2 rad × 3437.746771 = 6875.493542 ′ - A value of 4 rad is 13750.98708 ′.
4 rad × 3437.746771 = 13750.98708 ′
Radian to Arcminute conversion table
| Radians (rad) | Arcminutes (′) |
|---|---|
| 0.5 rad | 1718.873385 ′ |
| 1 rad | 3437.746771 ′ |
| 1.5 rad | 5156.620156 ′ |
| 2 rad | 6875.493542 ′ |
| 3 rad | 10313.24031 ′ |
| 3.14159 rad | 10799.99088 ′ |
| 4 rad | 13750.98708 ′ |
| 5 rad | 17188.73385 ′ |
| 6 rad | 20626.48062 ′ |
| 6.28318 rad | 21599.98176 ′ |
Where it's used
Radians are used for trigonometry and calculus (derivatives of sin and cos assume radians), while minutes of arc appear in latitude and longitude (degrees, minutes, seconds). Both measure plane angle, so the conversion is a fixed factor.
Radian to other angle units
| Conversion | 1 rad equals |
|---|---|
| radian to minute of arc | 3437.746771 ′ |
| radian to degree | 57.29577951 ° |
| radian to gradian | 63.66197724 gon |
| radian to revolution | 0.1591549431 rev |
| radian to second of arc | 206264.8062 ″ |
Frequently asked questions
How many minutes of arc are in 1 radian?
1 rad = 3437.746771 ′.
How do I convert radians to minutes of arc?
Multiply the value in rad by 3437.746771. For example, 15 rad × 3437.746771 = 51566.20156 ′.
Is the rad to ′ conversion exact?
Yes. Both units are defined exactly, so the ratio is exact; its decimal form does not terminate and is shown here to 10 significant figures (more with the precision selector).
Sources
- The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures , Table 4 (radian) and Table 8 (non-SI units accepted for use with the SI).
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
Cite this page
APA
Scientific Converters. (2026, October 15). Convert Radians to Arcminutes (rad to ′). Retrieved October 25, 2026, from https://scientificconverters.com/angle/radians-to-arcminutes/
IEEE
Scientific Converters, "Convert Radians to Arcminutes (rad to ′)," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/angle/radians-to-arcminutes/