Degree to Minute of Arc Conversion Chart
| Degree (deg) | Minute of arc (arcmin) | Reference Benchmark | Formula Step |
|---|---|---|---|
| 0.0167 deg | 1.002 arcmin | One Arcminute Navigational Latitude Nautical Mile Equivalence | 0.0167 × 60 = 1.002 arcmin |
| 0.05 deg | 3 arcmin | Three Arcminutes Typical Human Eye Visual Acuity Limit | 0.05 × 60 = 3 arcmin |
| 0.1 deg | 6 arcmin | Six Arcminutes Small Celestial Target Angular Diameter | 0.1 × 60 = 6 arcmin |
| 0.25 deg | 15 arcmin | Quarter Degree Marine Radar Beamwidth Aperture Threshold | 0.25 × 60 = 15 arcmin |
| 0.5 deg | 30 arcmin | Apparent Angular Diameter of Full Moon Viewed from Earth | 0.5 × 60 = 30 arcmin |
| 1 deg | 60 arcmin | Exact International Definition of Sixty Arcminutes in Degree | 1 × 60 = 60 arcmin |
| 2 deg | 120 arcmin | Two Degrees Geodetic Survey Triangulation Displacement | 2 × 60 = 120 arcmin |
| 5 deg | 300 arcmin | Five Degrees Binocular Standard Field of View Diameter | 5 × 60 = 300 arcmin |
| 10 deg | 600 arcmin | Ten Degrees Clenched Fist Angular Span at Arm Length | 10 × 60 = 600 arcmin |
| 15 deg | 900 arcmin | One Hour Earth Axial Rotational Angle in Arcminutes | 15 × 60 = 900 arcmin |
| 30 deg | 1800 arcmin | Thirty Degrees Zodiac Constellation Sign Span Sector | 30 × 60 = 1800 arcmin |
| 45 deg | 2700 arcmin | Forty-Five Degrees Octant Celestial Sector Coverage | 45 × 60 = 2700 arcmin |
| 60 deg | 3600 arcmin | Sixty Degrees Sextant Navigation Measurement Ceiling | 60 × 60 = 3600 arcmin |
| 90 deg | 5400 arcmin | Ninety Degrees Quadrant Right Angle Zenith Elevation | 90 × 60 = 5400 arcmin |
| 180 deg | 10800 arcmin | One Hundred Eighty Degrees Horizon to Horizon Diameter | 180 × 60 = 10800 arcmin |
Degree to Minute of arc Formula & Unit Definitions
The conversion from degrees to minutes of arc is governed by the exact integer ratio of 60 (1° = 60 arcmin). To convert degrees into minutes of arc, multiply the degree value by 60. Conversely, to convert minutes of arc back into degrees, divide the arcminute value by 60 (or multiply by ~0.0166667).
Quick Estimation: Multiply the degree figure by 6, then append a zero (or multiply by 60). For instance, 0.5° × 60 = 30 arcmin (apparent lunar diameter); 1.5° × 60 = 90 arcmin; 6° × 60 = 360 arcmin.
Degree Angle (°)
Sexagesimal Base Unit- Creator & Origin: Inherited from ancient Babylonian sexagesimal base-60 astronomy and circular geometry.
- Standard Definition: Defined as exactly 1/360 of a complete circular turn or revolution (360° = 1 circle).
- Everyday Focus: Compass bearings, mechanical drafting, road curve design, and general trigonometry.
Minute of Arc (arcmin / ′)
Sexagesimal Sub-Division (1/60°)- Creator & Origin: Formalized in Hellenistic astronomy by Ptolemy as the 'pars minuta prima' (first small part).
- Standard Definition: Defined as exactly 1/60 of an angular degree, equivalent to π/10,800 radians.
- Everyday Focus: Celestial coordinates, maritime nautical miles, firearm MOA accuracy, and optical resolution.
Frequently Asked Questions
Q.How many minutes of arc are in one degree?
There are exactly 60 minutes of arc (arcminutes) in one degree (1° = 60′ = 60 arcmin).
Q.What is the reverse conversion from arcminutes to degrees?
To convert back, use the Minute of Arc to Degree Converter where 1 arcmin equals 1/60 degree.
Q.How many arcminutes is 0.5 degrees?
0.5 degrees equals exactly 30 arcminutes (the apparent angular diameter of the Moon).
Q.How many arcminutes is a full circle?
A full circle (360°) equals exactly 21,600 arcminutes (360 × 60).
Q.How do you convert degrees to arcminutes without a calculator?
Multiply the degree value by 60 (e.g. 2.5° × 60 = 150 arcmin).