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How to Convert Decimal Degrees to DMS Coordinates

Learn how to convert GPS coordinates from decimal degrees to degrees-minutes-seconds format step by step, with a worked example and formula.

Updated 2026-07-03

Free calculators used in this guide

Coordinates Converter — Decimal Degrees & DMSAngle Converter

Overview

Converting a coordinate from decimal degrees to degrees-minutes-seconds (DMS) format means splitting a single decimal number into three components — whole degrees, minutes, and seconds — plus a hemisphere direction. This article walks through the manual calculation and how to do it instantly with a converter.

What You Need

  • A latitude or longitude value in decimal degrees (e.g., 28.6139)
  • Knowledge of whether the value is latitude (needs N/S) or longitude (needs E/W)

Steps

  1. Note the sign of your decimal degree value. A positive value becomes N (latitude) or E (longitude); a negative value becomes S (latitude) or W (longitude).

  2. Take the absolute value and separate the whole-number part. This whole number becomes your degrees value.

  3. Multiply the remaining decimal fraction by 60. The whole-number part of this result becomes your minutes value.

  4. Take the new remaining fraction and multiply by 60 again. This result becomes your seconds value (keep 1–2 decimal places for typical precision).

  5. Combine the parts with the hemisphere letter. Format as degrees° minutes' seconds" hemisphere.

  6. Use the Coordinates Converter to skip manual calculation. The Coordinates Converter performs all of the above instantly and keeps the decimal and DMS fields in sync as you edit either one.

Common Mistakes to Avoid

  • Forgetting to convert the hemisphere sign correctly — a common error is applying N/S logic to a longitude value (which needs E/W) or vice versa.
  • Rounding too early in the calculation — rounding the minutes value before calculating seconds compounds small errors; carry full precision through all three steps.
  • Confusing DMS notation with plain decimal minutes — some GPS devices display a hybrid "degrees and decimal minutes" format (e.g., 28° 36.834'), which is different from full DMS with separate seconds.

Formula & Methodology

Degrees = whole-number part of the absolute decimal value Minutes = whole-number part of (remaining decimal fraction × 60) Seconds = (remaining fraction after minutes) × 60

Worked example — converting 28.6139° (New Delhi's latitude) to DMS:

  • Degrees = 28
  • Remaining 0.6139 × 60 = 36.834 → Minutes = 36
  • Remaining 0.834 × 60 = 50.04 → Seconds = 50.04

Result: 28° 36' 50.04" N (positive value, so N for latitude).

For a fuller definition, see our glossary entry on DMS.

Frequently Asked Questions

Most modern GPS devices and mapping apps like Google Maps use decimal degrees by default, but older survey documents, nautical charts, and aviation references often use degrees-minutes-seconds (DMS) instead, so converting between the two is necessary whenever you're combining data from both types of sources. The [Coordinates Converter](/coordinates-converter/) handles this instantly for both latitude and longitude.
The hemisphere letter indicates direction — N or S for latitude (north or south of the equator), E or W for longitude (east or west of the prime meridian) — and replaces the negative sign used in decimal degree notation. A decimal value of -33.8688 becomes 33.8688° S in DMS.
One second of arc corresponds to roughly 30 metres of distance at the equator, so seconds are usually given to one or two decimal places for typical navigation or mapping precision. Fewer decimal places are fine for general reference; survey-grade work may need more precision.
Yes — the [Coordinates Converter](/coordinates-converter/) includes separate fields for latitude and longitude that convert simultaneously, so you can process a complete GPS coordinate pair without running the conversion twice.
Some GPS devices display a hybrid format showing whole degrees and decimal minutes (like 28° 36.834') without splitting further into seconds, which is different from full DMS notation that separates minutes and seconds into two distinct values. Check which format your source device or document actually uses before converting, since treating one as the other will produce an incorrect result.
Latitude measures angular distance from the equator toward either pole, and the poles are 90° away in each direction, while longitude measures angular distance around the Earth's full circumference from the prime meridian, giving it double the range. This is why the [Coordinates Converter](/coordinates-converter/) enforces different valid ranges for each.
Yes — the Coordinates Converter is fully bidirectional, so editing the Deg/Min/Sec/Hemisphere fields updates the Decimal Degrees field automatically, and vice versa. You don't need a separate tool or reversed formula for the opposite direction.
DMS predates GPS and digital mapping by centuries, originating from angular measurement conventions in astronomy and navigation, and many official survey, aviation, and maritime standards have continued using it for consistency with historical records and international conventions in those fields. Decimal degrees became more common only after digital GPS devices made the simpler single-number format more practical.
Rounding degrees or minutes too early in the calculation compounds error into the final seconds value, potentially shifting the represented location by a meaningful distance — one second of arc alone represents about 30 metres at the equator. Carry full decimal precision through each step (degrees, then minutes, then seconds) rather than rounding intermediate results.
Convert your DMS result back to decimal degrees using the formula in reverse (degrees + minutes/60 + seconds/3600) and confirm it matches your original decimal value — this is exactly what the bidirectional [Coordinates Converter](/coordinates-converter/) does automatically as you edit either field.

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