How to Convert Degrees to Minutes
Angles are measured in degrees, and each degree can be split into smaller units called minutes of arc (arcminutes) and seconds of arc (arcseconds), using the same base-60 system as time. One degree equals 60 minutes of arc, and one minute of arc equals 60 seconds of arc. This means one degree equals 3,600 seconds of arc in total.
To convert a decimal degree value to minutes, take the whole number of degrees, then multiply the remaining decimal fraction by 60. For example, to convert 47.835 degrees: the whole number is 47 degrees. The decimal part, 0.835, multiplied by 60 gives 50.1 minutes. So 47.835 degrees converts to 47 degrees and 50.1 minutes, written as 47° 50.1'. If you want the remainder split further into seconds, multiply the leftover 0.1 minutes by 60 to get 6 seconds, giving 47° 50' 06".
Degrees, Minutes and Seconds Conversion Table
| Unit | Equals | Symbol |
|---|
| 1 degree | 60 minutes of arc | 1° = 60' |
| 1 minute of arc | 60 seconds of arc | 1' = 60" |
| 1 degree | 3,600 seconds of arc | 1° = 3,600" |
| 1 minute of arc | 0.01667 degrees | 1' = 1/60° |
| 1 second of arc | 0.000278 degrees | 1" = 1/3,600° |
The Reverse Conversion: Minutes to Decimal Degrees
To convert minutes of arc back to decimal degrees, divide the total minutes by 60. For example, 2,870.1 minutes of arc divided by 60 equals 47.835 decimal degrees. This is useful when you have a GPS reading or survey bearing given in degrees and minutes and need a single decimal number for use in mapping software or trigonometric calculations.
Why This Matters for GPS and Navigation
Latitude and longitude coordinates are sometimes given in decimal degrees (for example, -36.8485°) and sometimes in degrees, minutes, seconds (for example, 36° 50' 54.6" S). Mapping tools, GPS devices, and land survey plans in New Zealand use both formats depending on the application. LINZ (Land Information New Zealand) survey data and marine charts commonly use DMS notation, while most consumer GPS apps default to decimal degrees. Converting between the two accurately matters because a small error in minutes or seconds can represent a real distance on the ground. At New Zealand's latitude, one minute of arc of latitude is approximately 1.852 km (one nautical mile), so an error of even a few minutes can shift a location by several kilometres.
Worked Example
Convert 47.835 decimal degrees to degrees, minutes and seconds:
- Whole degrees: 47°
- Decimal remainder: 0.835
- Minutes: 0.835 × 60 = 50.1'
- Whole minutes: 50'
- Decimal remainder of minutes: 0.1
- Seconds: 0.1 × 60 = 6.0"
- Result: 47° 50' 06", or 2,870.1 total minutes of arc
Frequently Asked Questions
How many minutes are in a degree? There are 60 minutes of arc in one degree, and 60 seconds of arc in one minute, following the same base-60 system used for time. So 1 degree equals 60 arcminutes, which equals 3,600 arcseconds.
How do I convert decimal degrees to degrees and minutes? Take the whole number part as the degrees. Multiply the remaining decimal fraction by 60 to get the minutes. For 47.835 degrees, the whole number 47 becomes the degrees, and 0.835 x 60 = 50.1 minutes, giving 47° 50.1'.
Where are arcminutes used in New Zealand? Arcminutes and arcseconds appear in GPS coordinates, LINZ survey plans, marine navigation charts, and older topographic maps that use degrees, minutes, seconds notation for latitude and longitude, rather than decimal degrees.
Related Calculators
Sources: International System of Units (SI) definitions for plane angle subunits (bipm.org). NIST Guide to the SI, Section 8.7 on units for angles (nist.gov). LINZ geodetic datum and coordinate conventions (linz.govt.nz).
This is a standard mathematical unit conversion (1 degree = 60 minutes of arc = 3,600 seconds of arc) and does not change over time. Results are rounded to the precision you select.
