Convert degrees to arc-minutes, arc-seconds, radians, and gradians with ground distance equivalents and a comprehensive reference table.
This converter turns degrees into arc-minutes, arc-seconds, radians, gradians, and turns. It is useful any time an angle starts in plain degrees but needs to be expressed in the finer subdivisions used in navigation, astronomy, surveying, mapping, and optics. A single degree can look simple on paper, but many field tools and reference tables need the same value in a more granular format before it is useful.
One degree equals 60 arc-minutes and 3,600 arc-seconds, so the page is especially helpful when a decimal-degree value needs to become a more precise angular format. The ground-distance reference at the equator also helps connect angle units with geographic distance. That is handy when you want to understand how a tiny angular change relates to real-world map movement or instrument pointing.
Use it when you need an angle in the more detailed formats that charts, instruments, or scientific references prefer. The result shows several equivalent forms at once, which makes cross-checking easier.
Arc-minutes and arc-seconds are the practical units for fine angular measurements, while degrees remain the easier starting format for most people. This page bridges those formats and keeps the related angular units together for quick reference, especially when one tool or document expects decimal degrees and another expects DMS-style detail.
Arc-Minutes = Degrees × 60. Arc-Seconds = Degrees × 3600. Radians = Degrees × π / 180. Gradians = Degrees × 200 / 180. Turns = Degrees / 360.
Result: 45° = 2,700 arc-minutes = 162,000 arc-seconds = 0.785398 radians
Multiplying 45 degrees by 60 gives 2,700 arc-minutes. Multiplying by 3,600 gives 162,000 arc-seconds. In radians, 45° = π/4 ≈ 0.785398.
The division of degrees into 60 minutes and 3,600 seconds comes from ancient Babylonian mathematics, which used a base-60 number system. This system was adopted by Greek astronomers and has persisted for over 2,000 years in angle measurement and timekeeping.
The nautical mile was originally defined as one arc-minute of latitude along any meridian. This made chart calculations intuitive: a distance of 10 nautical miles corresponds to roughly 10 arc-minutes of latitude change. Modern navigators still use this relationship daily.
Telescope resolution is measured in arc-seconds. The Hubble Space Telescope resolves about 0.05 arc-seconds. Ground-based telescopes achieve 0.5-2 arc-seconds depending on atmospheric conditions. Satellite positioning uses fractional arc-seconds for centimeter-level accuracy.
There are exactly 60 arc-minutes in one degree. This is a fixed relationship defined by the sexagesimal, or base-60, system and is the reason degrees split so neatly into smaller parts.
There are 3,600 arc-seconds in one degree because 60 minutes times 60 seconds per minute equals 3,600. That fixed ratio makes fine-angle work much easier to convert by hand or in software.
Arc-minutes measure angles, where one arc-minute is 1/60 of a degree. Time minutes measure duration, where one minute is 1/60 of an hour, so the names are similar but the meanings are different.
Gradians, also called gons, divide a right angle into 100 parts instead of 90. A full circle is 400 gradians, which is why they sometimes appear in European surveying and engineering work.
One arc-minute of latitude equals approximately 1.852 km, or one nautical mile. At the equator, one arc-minute of longitude is also about 1.852 km, but the distance decreases as you move toward the poles.
Arc-minutes provide a natural subdivision for navigation, astronomy, and precision work. A value like 0.5° can be written as 30 arc-minutes, which is often easier to read in those fields.