Convert Arcminutes to Radians (′ to rad)
1 minute of arc (′) = 0.0002908882087 radians (rad). 1 rad = 3437.746771 ′. Example: 15 ′ = 15 × 0.0002908882087 = 0.00436332313 rad.
Also searched as minutes of arc to rad, minutes of arc in rad, minutes of arc into radians, ′ to rad, ′ in radians, ′ into radian, minute of arc to radian, ′ to radians converter and how many radians in a minute of arc.
1 ′ = 0.0002908882087 rad
Type in either box. Scientific notation works: 1.5e-3.
Converting a list? Use the bulk minute of arc to radian converter to paste a column from Excel.
How to Convert Arcminute to Radian
- 1 ′ = 0.0002908882087 rad
- 1 rad = 3437.746771 ′
- Example: convert 15 ′ to rad: 15 ′ = 15 × 0.0002908882087 rad = 0.00436332313 rad
Formula
rad = ′ × 0.0002908882086657
or rad = ′ ÷ 3437.746770785
Derivation from SI units:
- 1′ = (1/60)° = π/10 800 rad.
- 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).
Both units are defined exactly, so the factor is exact. Arcminute definition: minute of arc; Radian definition: radian.
Worked examples
- A reading of 15 ′ converts to 0.00436332313 rad.
15 ′ × 0.0002908882087 = 0.00436332313 rad - A value of 45 ′ is 0.01308996939 rad.
45 ′ × 0.0002908882087 = 0.01308996939 rad
Arcminute to Radian conversion table
| Arcminutes (′) | Radians (rad) |
|---|---|
| 1 ′ | 0.0002908882087 rad |
| 5 ′ | 0.001454441043 rad |
| 10 ′ | 0.002908882087 rad |
| 15 ′ | 0.00436332313 rad |
| 20 ′ | 0.005817764173 rad |
| 30 ′ | 0.00872664626 rad |
| 45 ′ | 0.01308996939 rad |
| 60 ′ | 0.01745329252 rad |
| 90 ′ | 0.02617993878 rad |
| 120 ′ | 0.03490658504 rad |
Where it's used
Arcminutes are used for latitude and longitude (degrees, minutes, seconds), while radians appear in trigonometry and calculus (derivatives of sin and cos assume radians). Both measure plane angle, so the conversion is a fixed factor.
Arcminute to other angle units
| Conversion | 1 ′ equals |
|---|---|
| minute of arc to radian | 0.0002908882087 rad |
| minute of arc to degree | 0.01666666667 ° |
| minute of arc to gradian | 0.01851851852 gon |
| minute of arc to revolution | 0.0000462962963 rev |
| minute of arc to second of arc | 60 ″ |
Frequently asked questions
How many radians are in 1 minute of arc?
1 ′ = 0.0002908882087 rad.
How do I convert minutes of arc to radians?
Multiply the value in ′ by 0.0002908882087, or divide it by 3437.746771. For example, 15 ′ × 0.0002908882087 = 0.00436332313 rad.
Is the ′ to rad 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 Arcminutes to Radians (′ to rad). Retrieved October 25, 2026, from https://scientificconverters.com/angle/arcminutes-to-radians/
IEEE
Scientific Converters, "Convert Arcminutes to Radians (′ to rad)," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/angle/arcminutes-to-radians/