Degrees Minutes Seconds (DMS) Calculator
Convert angles between decimal degrees and degrees–minutes–seconds (DMS) notation — the format used in GPS coordinates, maps, navigation and astronomy. Also outputs radians and gradians.
Conversion direction
°
45° 30′ 0.000″
- 1
Fractional degrees
|45.5| − 45 = 0.5 - 2
Total arcminutes
0.5 × 60 = 30 - 3
Whole minutes
⌊30⌋ = 30 - 4
Seconds
(30 − 30) × 60 = 0
How does this calculator work?
One degree = 60 arcminutes = 3600 arcseconds. Decimal → DMS: whole degrees = floor(dec), minutes = floor(frac × 60), seconds = (frac × 60 mod 1) × 60. DMS → Decimal: dec = d + m/60 + s/3600. Also converts to radians (× π/180) and gradians (× 400/360).
Formula
How this is calculated
Angles in degrees can be written as a single decimal number (e.g. 45.5°) or in the sexagesimal degrees–minutes–seconds format (e.g. 45° 30′ 0″), historically used in navigation, astronomy and geodesy. One degree divides into 60 arcminutes (′) and one arcminute divides into 60 arcseconds (″), mirroring the way hours are split into minutes and seconds.
To convert a decimal angle to DMS: take the integer part as the whole degrees; multiply the fractional remainder by 60 to get the total minutes, take the integer part of that as the minutes; multiply the remaining fraction by 60 again to get the seconds. To go the other way: decimal = degrees + minutes ÷ 60 + seconds ÷ 3600. Negative angles (south latitudes, west longitudes) carry through as a sign on the degree component.
The calculator also converts to radians (multiply decimal degrees by π/180) and gradians (multiply by 400/360). GPS coordinates, Google Maps, and most geographic databases store coordinates in decimal degrees; DMS is commonly required for printed charts, nautical navigation instruments and some surveying formats.
Frequently asked questions
Both express an angle in degrees, but decimal degrees use a single decimal number (e.g. 51.5074° N) while DMS breaks the fractional part into arcminutes and arcseconds (e.g. 51° 30′ 26.64″ N). DMS is traditional in navigation; decimal degrees are standard in modern GIS and GPS systems.
Add degrees + minutes ÷ 60 + seconds ÷ 3600. For southern latitudes or western longitudes, make the result negative. Example: 40° 26′ 46.8″ N = 40 + 26/60 + 46.8/3600 = 40.4463°.
A gradian (also called gon or grade) divides a full circle into 400 equal parts instead of 360 degrees. A right angle is 100 gradians. Gradians are used in some European surveying traditions but are uncommon elsewhere.
Also known as
TG we-Calculate Editorial Team. (2026). Degrees Minutes Seconds (DMS) Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/degrees-minutes-seconds-calculator
TG we-Calculate Editorial Team. "Degrees Minutes Seconds (DMS) Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/degrees-minutes-seconds-calculator.
TG we-Calculate Editorial Team, "Degrees Minutes Seconds (DMS) Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/degrees-minutes-seconds-calculator
@misc{wecalculate_degrees_minutes_seconds_calculator, title = {Degrees Minutes Seconds (DMS) Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/degrees-minutes-seconds-calculator}}, year = {2026}, note = {TG we-Calculate} }
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