Degrees Minutes Seconds to Decimal Degrees Converter

Enter a coordinate in degrees, minutes, and seconds (DMS) to convert it to decimal degrees using DD = D + M/60 + S/3600, with sign handling for North/South and East/West.

Quick Facts

DMS to decimal
DD = D + M/60 + S/3600
Minutes and seconds are fractions of a degree (60 minutes = 1 degree, 60 seconds = 1 minute).
Sign convention
N and E are positive; S and W are negative
A single signed decimal replaces the DMS value plus a compass letter.
Precision guide
5 decimal places ≈ 1.1 m
Each extra decimal digit shrinks positional error by about 10x.

Your Results

Calculated
Decimal Degrees
-
D + M/60 + S/3600, signed
Degrees + Decimal Minutes
-
DDM format, e.g. 40° 26.7667′
Radians
-
Decimal degrees × π/180
Hemisphere
-
Sign interpretation

Ready

Enter degrees, minutes, seconds, and a hemisphere, then press Calculate.

How the Degrees Minutes Seconds to Decimal Degrees Converter works

Geographic coordinates and angles are traditionally written as degrees, minutes, and seconds (DMS) — for example, 40° 26′ 46″ N. Since a minute is 1/60 of a degree and a second is 1/60 of a minute (1/3600 of a degree), a DMS value converts to a single decimal number with DD = D + M/60 + S/3600. Decimal degrees are easier to plot, compare, and feed into mapping software, GPS devices, and spreadsheets than the sexagesimal DMS format.

Formula and method

Enter the whole-number degrees, minutes (0-59.99), and seconds (0-59.99) portions of the coordinate. The calculator adds M/60 and S/3600 to D to get the unsigned decimal degrees. It then applies the sign from your hemisphere choice: North and East stay positive, while South and West become negative — for example, 40° 26′ 46″ S converts to −40.446111°. The tool also reports the value in degrees-plus-decimal-minutes (DDM) format and in radians (decimal degrees × π/180), since some tools and formulas expect angles in radians.

Converting back to DMS

To reverse the process, take the whole-number part of the decimal degrees as D. Multiply the remaining fractional part by 60 — the whole-number part of that result is M. Multiply the new remaining fraction by 60 again to get S. For 40.446111°: 0.446111 × 60 = 26.7667 minutes, then 0.7667 × 60 ≈ 46.0 seconds, recovering 40° 26′ 46″.

Common sources of error

  • Treating minutes/seconds as decimals of a degree directly: 40° 30′ is not 40.30° — it is 40 + 30/60 = 40.5°, since minutes are base-60, not base-10.
  • Dropping the hemisphere sign: a longitude of 73° 59′ W must be entered (or recorded) as −73.98333°, not +73.98333°, or the point lands on the wrong side of the Prime Meridian.
  • Out-of-range minutes or seconds: minutes and seconds must stay below 60 — a value like 40° 65′ should be normalized to 41° 5′ before converting.

Applications

Decimal degrees are the standard input format for GPS devices, Google Maps, GIS software, and most mapping APIs, while DMS remains common on paper charts, surveying documents, and older navigation equipment. Converting between the two lets you move a coordinate from a nautical chart or legal land description into a digital map, or read a GPS decimal coordinate back into the DMS form used in a survey report.

Frequently Asked Questions

What is the formula to convert degrees, minutes, seconds to decimal degrees?
Decimal Degrees = D + M/60 + S/3600, where D is whole degrees, M is minutes (0-59), and S is seconds (0-59.999). For example, 40 degrees 26 minutes 46 seconds equals 40 + 26/60 + 46/3600 = 40.446111 degrees.
How do I convert decimal degrees back to degrees, minutes, and seconds?
Take the whole-number part as degrees. Multiply the remaining decimal fraction by 60; the whole-number part of that result is minutes. Multiply the new remaining fraction by 60 to get seconds. For 40.446111 degrees: 0.446111 × 60 = 26.7667 minutes, then 0.7667 × 60 = 46.0 seconds.
Why are North and East positive while South and West are negative?
By standard geographic convention, latitudes north of the equator and longitudes east of the Prime Meridian are positive, while latitudes south of the equator and longitudes west of the Prime Meridian are negative. This lets a single signed decimal number replace a degrees-minutes-seconds value plus a compass letter.
How many decimal places do I need for GPS-level accuracy?
Four decimal places (about 11 meters of precision) is enough for most mapping uses, and five decimal places (about 1.1 meters) matches typical consumer GPS accuracy. Each additional decimal digit divides the positional error by roughly 10.

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