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.

Free calculators used in this guide

Coordinates Converter — Decimal Degrees & DMS Angle Converter

Overview

Converting a coordinate from decimal degrees to degrees-minutes-seconds (DMS) format means splitting a single decimal number into three parts: 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

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).
Take the absolute value and separate the whole-number part. This whole number becomes your degrees value.
Multiply the remaining decimal fraction by 60. The whole-number part of this result becomes your minutes value.
Take the new remaining fraction and multiply by 60 again. This result becomes your seconds value (keep 1-2 decimal places for typical precision).
Combine the parts with the hemisphere letter. Format as degrees° minutes' seconds" hemisphere.
Use the Coordinates Converter to skip manual calculation. The Coordinates Converter does all of the above instantly and keeps the decimal and DMS fields in sync as you edit either one.

Common Mistakes to Avoid

Getting the hemisphere sign wrong. A common error is applying N/S logic to a longitude value, which needs E/W, or the reverse.
Rounding too early in the calculation. Rounding the minutes value before calculating seconds compounds small errors, so 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'), and that's 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

Why do I need to convert decimal degrees to DMS at all?

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. Converting between the two matters whenever you're combining data from both kinds of sources. The [Coordinates Converter](/coordinates-converter/) handles this instantly for both latitude and longitude.

What does the hemisphere letter (N, S, E, W) tell me in a DMS coordinate?

It tells you direction: N or S for latitude (north or south of the equator), E or W for longitude (east or west of the prime meridian). It replaces the negative sign used in decimal degree notation, so a decimal value of -33.8688 becomes 33.8688° S in DMS.

How precise do seconds need to be for an accurate location?

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 work fine for general reference, though survey-grade work may call for more.

Can I convert a full coordinate pair (both latitude and longitude) at once?

You can. The [Coordinates Converter](/coordinates-converter/) has separate fields for latitude and longitude that convert at the same time, so you can process a complete GPS coordinate pair without running the conversion twice.

What's the difference between DMS and 'degrees and decimal minutes'?

Some GPS devices display a hybrid format showing whole degrees and decimal minutes, like 28° 36.834', without splitting further into seconds. That's different from full DMS notation, which 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 produces the wrong result.

Why does latitude range from -90 to 90 while longitude ranges from -180 to 180?

Latitude measures angular distance from the equator toward either pole, and the poles sit 90° away in each direction. Longitude measures angular distance around the Earth's full circumference from the prime meridian, which gives it double the range. That's why the [Coordinates Converter](/coordinates-converter/) enforces different valid ranges for each.

Can I convert DMS back to decimal degrees using the same tool?

Yes. The Coordinates Converter works both directions, so editing the Deg/Min/Sec/Hemisphere fields updates the Decimal Degrees field automatically, and the reverse works too. There's no separate tool or reversed formula needed.

Why do old maps and nautical charts still use DMS instead of decimal degrees?

DMS predates GPS and digital mapping by centuries, coming out of angular measurement conventions in astronomy and navigation. Many official survey, aviation, and maritime standards kept using it for consistency with historical records and international conventions in those fields. Decimal degrees only became common once digital GPS devices made the simpler single-number format practical.

What happens if I round a DMS conversion too aggressively?

Rounding degrees or minutes too early compounds error into the final seconds value, and that can shift the represented location by a meaningful distance since one second of arc alone represents about 30 metres at the equator. Carry full decimal precision through each step (degrees, then minutes, then seconds) instead of rounding along the way.

Is there a quick way to sanity-check a DMS-to-decimal conversion?

Convert your DMS result back to decimal degrees using the formula in reverse (degrees + minutes/60 + seconds/3600) and check it against 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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