Convert Arcminutes to Degrees (′ to °)
1 minute of arc (′) = 0.01666666667 degrees (°). 1 ° = 60 ′. Example: 30 ′ = 30 × 0.01666666667 = 0.5 °.
Also searched as minutes of arc to °, minutes of arc in °, minutes of arc into degrees, ′ to °, ′ in degrees, ′ into degree, minute of arc to degree, ′ to degrees converter and how many degrees in a minute of arc.
1 ′ = 0.01666666667 °
Type in either box. Scientific notation works: 1.5e-3.
Converting a list? Use the bulk minute of arc to degree converter to paste a column from Excel.
How to Convert Arcminute to Degree
- 1 ′ = 0.01666666667 °
- 1 ° = 60 ′
- Example: convert 30 ′ to °: 30 ′ = 30 × 0.01666666667 ° = 0.5 °
Formula
° = ′ × 0.01666666666667
or ° = ′ ÷ 60
Derivation from SI units:
- 1′ = (1/60)° = π/10 800 rad.
- 1° = π/180 rad exactly; a full turn is 360°.
- 1 ′ = 0.0002908882086657 rad ÷ 0.01745329251994 rad per ° = 0.01666666666667 °
Both units are defined exactly, so the factor is exact. Arcminute definition: minute of arc; Degree definition: degree.
Worked examples
- An angle of 30 ′ is 0.5 °.
30 ′ × 0.01666666667 = 0.5 ° - A latitude fraction of 45 ′ is 0.75 °.
45 ′ × 0.01666666667 = 0.75 °
Arcminute to Degree conversion table
| Arcminutes (′) | Degrees (°) |
|---|---|
| 1 ′ | 0.01666666667 ° |
| 5 ′ | 0.08333333333 ° |
| 10 ′ | 0.1666666667 ° |
| 15 ′ | 0.25 ° |
| 20 ′ | 0.3333333333 ° |
| 30 ′ | 0.5 ° |
| 45 ′ | 0.75 ° |
| 60 ′ | 1 ° |
| 90 ′ | 1.5 ° |
| 120 ′ | 2 ° |
Where it's used
Coordinates and optical measurements in minutes of arc are converted to decimal degrees for maps, GPS software and calculations. Divide by 60.
Arcminute to other angle units
| Conversion | 1 ′ equals |
|---|---|
| minute of arc to degree | 0.01666666667 ° |
| minute of arc to radian | 0.0002908882087 rad |
| 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 do I convert degrees, minutes and seconds to decimal degrees?
Add degrees + minutes/60 + seconds/3600: 40° 26′ 46″ = 40.4461°.
How many degrees are in 1 minute of arc?
1 ′ = 0.01666666667 °.
How do I convert minutes of arc to degrees?
Multiply the value in ′ by 0.01666666667, or divide it by 60. For example, 30 ′ × 0.01666666667 = 0.5 °.
Is the ′ 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 Arcminutes to Degrees (′ to °). Retrieved October 25, 2026, from https://scientificconverters.com/angle/arcminutes-to-degrees/
IEEE
Scientific Converters, "Convert Arcminutes to Degrees (′ to °)," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/angle/arcminutes-to-degrees/