Minutes to Decimal Degrees — DMS to Decimal Degree Converter
Convert an angle from degrees-minutes-seconds (DMS) format to decimal degrees — the standard used by GPS receivers, GIS software and digital maps.
°
′
″
Angle in decimal degree format — used in GPS, mapping and navigation
- 1
Arc minutes → degrees
26 ÷ 60 = 0.433333 - 2
Arc seconds → degrees
46 ÷ 3600 = 0.012778 - 3
Decimal degrees = ° + ′÷60 + ″÷3600
40 + 0.433333 + 0.012778 = 40.446111
How does this calculator work?
Decimal degrees = degrees + arc_minutes ÷ 60 + arc_seconds ÷ 3,600. Example: 40° 26′ 46″ = 40 + 26/60 + 46/3,600 = 40.446111°. Used for GPS coordinates, Google Maps, OpenStreetMap and astronomy. Negate the result for south/west coordinates.
Formula
How this is calculated
Angles in navigation and geography are traditionally expressed in degrees, arc minutes (1° = 60′) and arc seconds (1′ = 60″) — the sexagesimal system inherited from ancient Babylonian astronomy. GPS receivers, GIS platforms (Google Maps, QGIS, ArcGIS) and most modern mapping tools use decimal degrees instead, because a single number is easier to store, transmit and compute with.
The conversion is a simple weighted sum: degrees contribute directly; arc minutes contribute degrees/60 (since there are 60 arc minutes per degree); and arc seconds contribute degrees/3,600 (60 arc minutes × 60 arc seconds). For example, the Eiffel Tower is at 48° 51′ 30″ N = 48 + 51/60 + 30/3,600 = 48.858333°.
Negative degrees are supported for south latitudes and west longitudes (the sign is applied to the whole result). Arc minutes and arc seconds must each be between 0 and 59. The calculator also gives the radians equivalent (decimal degrees × π/180) and normalises the result to 0–360° for the number-line visualisation.
Frequently asked questions
A decimal degree expresses an angle as a single floating-point number rather than the degrees-minutes-seconds triplet. For example, 48° 51′ 30″ = 48.858333° in decimal form. Decimal degrees are the default format for GPS, Google Maps and most geographic information systems.
Divide arc minutes by 60: 1′ = 1/60° ≈ 0.016667°. For example, 30′ = 0.5°. The full DMS formula is: decimal° = degrees + minutes/60 + seconds/3,600.
Both use the word "minute" but measure different things. A time minute is 1/60 of an hour. An arc minute is 1/60 of a degree of angle. They share the word because both inherited the sexagesimal (base-60) system from ancient Babylonian mathematics, but they are physically unrelated units.
Also known as
TG we-Calculate Editorial Team. (2026). Minutes to Decimal Degrees — DMS to Decimal Degree Converter [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/minutes-to-decimals-degrees-calculator
TG we-Calculate Editorial Team. "Minutes to Decimal Degrees — DMS to Decimal Degree Converter." TG we-Calculate. 2026. https://we-calculate.com/calculator/minutes-to-decimals-degrees-calculator.
TG we-Calculate Editorial Team, "Minutes to Decimal Degrees — DMS to Decimal Degree Converter," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/minutes-to-decimals-degrees-calculator
@misc{wecalculate_minutes_to_decimals_degrees_calculator, title = {Minutes to Decimal Degrees — DMS to Decimal Degree Converter}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/minutes-to-decimals-degrees-calculator}}, year = {2026}, note = {TG we-Calculate} }
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