Convert decimal degrees to degrees-minutes-seconds (and back). Free with steps.
GPS gives decimal degrees (40.7128° N); charts, deeds, and sextants speak degrees-minutes-seconds (40° 42′ 46″ N). The two notations describe identical angles — one in base-10 fractions, one in base-60 subdivisions inherited from Babylon. Our free Decimal Degrees to DMS Converter translates both directions, showing the 60-and-3600 arithmetic so every digit is traceable.
The sexagesimal split: 1 degree = 60 minutes (′), 1 minute = 60 seconds (″), so 1 second = 1/3600 degree. On Earth’s surface, one second of latitude is ~101 feet — the precision of a street address — while 0.0001 decimal degrees is ~36 feet. Choosing the notation is choosing the precision language your tools expect.
Surveyors, navigators, pilots, and GIS analysts convert daily: GPS waypoints into chart plotters, deed calls into mapping software, telescope coordinates into mount controllers. One notation in, the other out, zero transcription risk.
Decimal degrees write angles as plain decimals: 40.7128°. Computers love them — mapping APIs, GPS chips, and spreadsheets all compute in decimal. DMS writes the same angle as 40° 42′ 46″ — humans navigating with charts love it, because minutes and seconds map to physical distances (1′ of latitude = 1 nautical mile).
The systems’ bases differ: decimal is base-10 throughout; DMS is sexagesimal (base-60) below the degree. Converting multiplies or divides by 60 and 3,600 — the same arithmetic as hours-minutes-seconds, which is no coincidence: time and angle share Babylon’s base-60.
Precision translates too: 4 decimal places (±0.0001°) ≈ 0.36″ — roughly DMS to the nearest half-second. Survey-grade work keeps 6+ decimals or tenths of a second; hiking GPS is happy with 4 decimals or whole seconds.
Key terms:
Watch the carry: 59.999″ rounds to 60″, which carries into the minutes — the widget handles the cascade automatically.
Convert 40.7128° to DMS.
Check: 40 + 42/60 + 46.08/3600 = 40.7128° — the round trip closes.
A property corner is recorded as 34° 15′ 30″ W longitude. Express decimal for GIS.
The six decimals preserve the deed’s half-second precision — rounding to two decimals would move the corner ~150 feet.
A hiker’s paper map marks the trailhead at 44° 31′ 12″ N, 110° 50′ 05″ W; her phone’s GPS app wants decimal. Convert: 44 + 31/60 + 12/3600 = 44.520000°; −(110 + 50/60 + 5/3600) = −110.834722°. Typed into the app, the pin lands on the parking loop — but she double-checks the hemisphere signs, because a missing minus would send her to the wrong side of the planet (44.52° N, 110.83° E is in China).
The precision check: the map’s whole seconds (±0.5″ ≈ ±50 ft) versus the phone’s display of 6 decimals (±0.36 ft implied). The honest precision is the map’s — the extra decimals are noise. She navigates to the loop, not to a 4-inch pin.
A second scenario: the survey crew. Their total station reads 87° 14′ 33.5″; the CAD file needs decimal: 87 + 14/60 + 33.5/3600 = 87.242639°. Six decimals preserve the 0.1″ instrument precision (~10 ft at a mile — no, 0.1″ at one mile is ~0.03 ft; the crew knows their error budget in seconds, not decimals).
A third scenario: astronomy. A telescope mount wants M31’s declination +41° 16′ 08″ as decimal: 41.268889°. The mount’s 0.001° resolution needs 3 decimals; the catalog’s arcsecond precision supplies 6. Convert fully, then round to the instrument — never the reverse.
The sexagesimal system is 4,000 years old: Babylonian astronomers divided the circle into 360 degrees and each degree into 60 minutes because 60 has twelve divisors — the most divisible small number. Ptolemy’s Almagest carried it into Greek astronomy, medieval Islam preserved it, and it still rules angles, time, and navigation.
The nautical mile is DMS made physical: 1′ of latitude = 1 nautical mile = 1,852 m exactly. Navigators read latitude directly as distance — “we are 30 miles south” is “30 minutes of latitude.” Decimal degrees sever this link; DMS preserves it, which is why mariners and aviators never switched.
Geodesy’s modern frame, WGS 84, computes in decimal degrees (and radians internally), but survey monuments are still described in DMS on datasheets — the human-readable face of a decimal database. The converter is the daily translator between the monument’s brass plaque and the GIS.
The second’s precision frontier: 0.01″ of latitude is ~1 foot — the realm of tectonic monitoring, where stations drift centimeters per year and coordinates are quoted to milliarcseconds. At that level, even the ÷3600 must be done in double precision; single-precision floats quantize at ~0.06″.
Time shares the empire: 1 hour = 60 minutes = 3,600 seconds, and Earth turns 15° per hour — so 1 second of time = 15 seconds of arc. Astronomers convert between them constantly (right ascension is in time units), making the DMS↔decimal skill do double duty across the sky.
Keep the widget’s verification line in your workflow: every conversion displays the round-trip check, so a transposed digit surfaces immediately. In coordinates, a single wrong digit is a wrong continent — the check costs nothing and has saved more navigators than any other feature on this page.
Decimal↔DMS: to DMS: D=floor(|dec|), M=floor(frac×60), S=(frac×60−M)×60; to decimal: D+M/60+S/3600 (negative for S/W). 1′=1/60°, 1″=1/3600°. 1′ latitude = 1 nautical mile. Watch 60-carries and hemisphere signs. Source: Sigma Calculator, Decimal Degrees to DMS Converter, https://sigmacalculator.net/math-calculators/decimal-degrees-to-dms-converter/
Cite this page as: Decimal Degrees to DMS Converter, Sigma Calculator, https://sigmacalculator.net/math-calculators/decimal-degrees-to-dms-converter/
Last updated: October 12, 2026