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The Minutes of Arc to Degrees Converter converts angular measurements from arc minutes to degrees, arc seconds, and radians. An arc minute (also written as MOA or denoted by the prime symbol ') is 1/60 of a degree, providing finer angular resolution for applications that require precise angle specification.
Arc minutes are extensively used in astronomy, navigation, geodesy, and optics. In astronomy, the apparent sizes of celestial objects are measured in arc minutes: the Moon and Sun each subtend about 31 arc minutes (roughly half a degree) in the sky. The resolution of the human eye is approximately 1 arc minute, which defines the standard for 20/20 vision.
In navigation and geography, latitude and longitude coordinates are often expressed in degrees-minutes-seconds (DMS) format. One arc minute of latitude corresponds to approximately 1.852 kilometers (one nautical mile) on Earth's surface, a relationship that gave rise to the nautical mile as a unit of distance.
Our converter provides outputs in decimal degrees (for mathematical calculations), arc seconds (for astronomy and fine positioning), and radians (for scientific computation). This makes it a versatile tool for professionals working across disciplines that use different angular units.
The formula: degrees = arc minutes / 60, because by definition 1° = 60'. For arc seconds: arcsec = arcmin × 60 (since 1' = 60"). For radians: radians = (arcmin / 60) × pi/180.
One arc minute at Earth's surface ≈ 1.852 km (1 nautical mile) along a meridian. For practical reference: 60' = 1°, 30' = 0.5°, 1' = 0.0167°. A typical telescope resolves objects separated by 1-2 arc seconds (1/60 to 1/30 of an arc minute).
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60' = 1°
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The Moon subtends ~31'
1 arc minute = 1/60 of a degree = 0.01667 degrees. This is a small but measurable angle.
1 arc minute of latitude = 1 nautical mile = 1.852 km. This elegant relationship is the basis for the nautical mile and is used extensively in maritime and aviation navigation.
At arm's length (~60 cm), 1 arc minute corresponds to about 0.17 mm — roughly the thickness of a human hair. The human eye can just barely resolve 1 arc minute, which defines 20/20 vision.
Apparent sizes of celestial objects: Moon ≈ 31', Sun ≈ 32', Venus at closest ≈ 1', Jupiter ≈ 0.5-0.8'. Deep-sky objects range from arcminutes to degrees.
Degrees-Minutes-Seconds: an angle expressed as whole degrees, whole arc minutes, and decimal arc seconds. Example: 40° 26' 46" N is a latitude in DMS format.
Decimal degrees = degrees + minutes/60 + seconds/3600. Example: 40° 26' 46" = 40 + 26/60 + 46/3600 = 40.4461°.
MOA (Minute of Angle) in firearms means 1 arc minute. At 100 yards, 1 MOA ≈ 1.047 inches. Rifle accuracy is often measured in MOA: a 1 MOA rifle groups shots within a 1-inch circle at 100 yards.
A full circle = 360° × 60'/° = 21,600 arc minutes.
Consumer GPS is accurate to about 0.1 arc seconds (0.0017 arc minutes), which corresponds to approximately 3 meters on the ground.
1 arc minute = pi/10800 radians ≈ 0.000290888 radians. This is a very small angle in radian measure.
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