Degrees Minutes Seconds (DMS) Calculator

This calculator converts between decimal degrees and degrees, minutes and seconds (DMS), the two main ways latitude and longitude are written for GPS devices, surveying, marine charts and aviation. Toggle between Decimal to DMS or DMS to Decimal, enter either a decimal degree value (for example -36.8485) or separate degrees, minutes and seconds figures, then choose whether the coordinate is positive (north or east) or negative (south or west). Four NZ reference points, the latitudes of Auckland, Wellington, Christchurch and Queenstown, are built in so you can load a real example instantly. It returns the decimal degrees, the DMS equivalent, and the degrees decimal minutes (DM) format used on marine and outdoor GPS units, alongside a step by step breakdown of how the degrees, minutes and seconds are derived, plus a reverse check that adds them back together to confirm the total matches your original value. Use it whenever you need to move a coordinate between systems, such as reading a DMS value off a survey plan or nautical chart before entering it into Google Maps. The conversion is exact base 60 arithmetic, so there is no rounding error beyond the decimal places you keep, though the tool does not perform coordinate datum transformations, so check your source data uses the same datum, such as NZGD2000 or WGS84, before relying on the result.

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Verified formula  Standard sexagesimal degree conversion (base 60 minutes and seconds).

1. Choose Conversion Direction

2. Quick NZ Reference Points

Loading a preset switches to Decimal → DMS mode and fills the decimal degrees field with that location's latitude, so you can see the DMS equivalent used on marine charts and survey plans.

Conversion Result

Decimal Degrees
41.123400°
Used by GPS and web maps
DMS
41° 7’ 24.24”
Used by surveying and charts
DM (Degrees, Decimal Minutes)
41° 7.4040’
Common on marine GPS units

Step by Step Breakdown

Input value41.1234 deg
Whole degrees41 deg
Remaining fraction × 60 (minutes)7.4040 min
Whole minutes7 min
Remaining fraction × 60 (seconds)24.2400 sec
Final DMS41° 7’ 24.24”

Reverse Check

Degrees41 deg
Minutes ÷ 600.116667 deg
Seconds ÷ 36000.006733 deg
Sum (decimal degrees)41.123400 deg
Summary: Enter a value above.

How Degrees, Minutes and Seconds Work

A degree of angle or latitude/longitude can be split into smaller units the same way an hour is split into minutes and seconds. One degree equals 60 arcminutes, and one arcminute equals 60 arcseconds, so one degree equals 3,600 arcseconds. This base 60 (sexagesimal) system dates back to Babylonian astronomy and is still the standard for expressing latitude and longitude on marine charts, survey plans, and aviation documents.

Converting Decimal Degrees to DMS

To convert a decimal degree value to degrees, minutes and seconds, follow three steps:

  1. The whole number part of the value is the degrees.
  2. Multiply the remaining decimal fraction by 60. The whole number part of that result is the minutes.
  3. Multiply the remaining decimal fraction of the minutes by 60. The result is the seconds.

For example, 41.1234 degrees: 41 is the degrees. The fraction 0.1234 times 60 equals 7.404, so 7 is the minutes. The fraction 0.404 times 60 equals 24.24, giving 24.24 seconds. The result is written as 41 degrees 7 minutes 24.24 seconds, or 41 deg 7 min 24.24 sec.

Converting DMS to Decimal Degrees

To reverse the process, divide the minutes by 60 and the seconds by 3,600, then add both to the degrees:

FormulaDescription
Decimal degrees = D + M/60 + S/3600D is degrees, M is minutes, S is seconds

Using the same example: 41 + 7/60 (0.1167) + 24.24/3600 (0.00673) equals 41.1234 decimal degrees, matching the original value.

Handling Hemisphere and Sign

Latitude and longitude use a hemisphere letter (N, S, E, W) alongside DMS, but decimal degree values use a positive or negative sign instead. Northern latitudes and eastern longitudes are positive. Southern latitudes and western longitudes are negative. Auckland's latitude, for example, is written as either 36 degrees 50 minutes 54.6 seconds S or as -36.8485 in decimal form. Always convert the unsigned DMS value first, then apply the sign or hemisphere letter afterward.

Where DMS and Decimal Degrees Are Used

All three formats describe the exact same angle or location. Converting between them is purely arithmetic and introduces no loss of accuracy provided enough decimal places are used.

Related Calculators

Sources: Standard sexagesimal (base 60) degree, minute, second conversion used in geodesy, surveying and navigation (International Hydrographic Organization chart conventions; Land Information New Zealand survey standards, linz.govt.nz).

This calculator performs a standard mathematical conversion between decimal degrees and degrees, minutes, seconds notation. It does not perform coordinate datum transformations (for example between NZGD2000 and WGS84). Always round to an appropriate number of decimal places for your application.

Frequently asked questions

How do you convert decimal degrees to degrees, minutes and seconds?

Take the whole number part as the degrees. Multiply the remaining decimal part by 60 to get minutes, taking the whole number part of that result as the minutes. Multiply the remaining decimal part of the minutes by 60 to get seconds. For example, 41.1234 degrees: the whole number 41 is the degrees. 0.1234 times 60 equals 7.404, so 7 is the minutes. 0.404 times 60 equals 24.24, so the seconds are approximately 24.24. The result is 41 degrees, 7 minutes, 24.24 seconds.

How do you convert degrees, minutes and seconds to decimal degrees?

Divide the minutes by 60 and the seconds by 3600, then add both to the degrees. The formula is decimal degrees equals degrees plus minutes divided by 60 plus seconds divided by 3600. For example, 41 degrees, 7 minutes, 24.24 seconds becomes 41 plus 7/60 (0.1167) plus 24.24/3600 (0.00673), which equals 41.1234 decimal degrees. If the coordinate is in the southern or western hemisphere, the final decimal value is expressed as negative.

Why do GPS coordinates use both decimal degrees and DMS?

Decimal degrees (for example -36.8485, 174.7633 for Auckland) are the format most mapping software, GPS devices and web maps like Google Maps use internally, because they are easier to store and calculate with. Degrees, minutes and seconds (for example 36 degrees 50 minutes 54.6 seconds S) are the traditional format used in surveying, marine navigation, aviation charts and some older GPS units. Both describe exactly the same location, just in different notations, so converting between them is often needed when moving data between systems.

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