Degrees to Arcminutes

How Many Arcminutes in a Degree?

One degree equals exactly 60 arcminutes. To convert degrees to arcminutes, multiply the degree value by 60. Arcminutes (symbol ′) are a subdivision of the degree used for precision in astronomy, navigation, cartography, and optics. Geographic coordinates are often expressed in degrees and arcminutes (e.g., 40° 26′ N for New York City). Telescopic field of view, the apparent size of celestial objects, and optical resolution are measured in arcminutes. This conversion is essential for anyone working with celestial navigation, GPS coordinates in DMS (degrees-minutes-seconds) format, or precision angular measurements where a whole degree is too coarse a unit. It is especially useful when you need human-readable precision without jumping all the way to decimal degrees or radians. Map readers, astronomers, shooters, and mariners often think in minutes of angle because the unit is fine enough to be practical but still easy to visualize. It is the standard language of latitude, telescope resolution, and many sight adjustments where a decimal degree would be harder to picture quickly. That is why it remains common in charts, manuals, and star maps.

How to Convert Degree to Arcminute

1. Start with your angle in degrees (can include decimals).
2. Multiply the degree value by 60 to get arcminutes.
3. The result is your angle in arcminutes.
4. For mixed notation (e.g., 45.75°), separate the whole degrees from the decimal: 45° plus 0.75 x 60 = 45° 45′.
5. To further convert arcminute fractions to arcseconds, multiply the fractional arcminutes by 60.

Real-World Examples

History of Degree and Arcminute

The division of the degree into 60 minutes (and the minute into 60 seconds) comes from Babylonian mathematics, which used a base-60 number system. The Babylonians divided the zodiac circle into 360 degrees, each degree into 60 minutes, and each minute into 60 seconds. Greek astronomers including Ptolemy adopted this system in the 2nd century AD, and it has been the standard for celestial and geographic coordinates ever since. The term "minute" comes from the Latin "pars minuta prima" (first small part), and "second" from "pars minuta secunda" (second small part).

Common Mistakes to Avoid

• Confusing arcminutes (angle) with minutes (time). While they share the Babylonian base-60 origin, arcminutes measure angle and minutes measure time. In navigation, "5 minutes of latitude" means 5 arcminutes of angular measure, which equals about 5.56 nautical miles.
• Forgetting to separate whole degrees from decimal degrees before converting. If you multiply 40.5° by 60, you get 2,430 total arcminutes. Usually you want 40° 30′ instead. Only multiply the fractional part by 60.
• Using 100 instead of 60 as the conversion factor (thinking decimally). Degrees divide into 60 arcminutes, not 100. This is a sexagesimal system, not decimal.
• Mixing decimal arcminutes with arcseconds notation. A coordinate written as 26.77′ does not mean 26′ 77″; the 0.77 minute fraction must still be multiplied by 60 to become arcseconds.

Frequently Asked Questions