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

Decimal degrees equal degrees plus minutes divided by 60, plus seconds divided by 3600. For example, 41 degrees, 17 minutes, 11.4 seconds converts to 41 + (17/60) + (11.4/3600) = 41.2865 decimal degrees. If the coordinate is in the southern or western hemisphere (S or W), the result is expressed as a negative number.

Why are New Zealand coordinates negative in decimal degrees?

New Zealand sits in the southern hemisphere, so latitudes convert to negative decimal degrees, for example -41.2865 for Wellington. Longitude stays positive because New Zealand is east of the prime meridian, typically between 166 and 179 degrees. Mapping tools like Google Maps and GPS devices use this signed decimal format by default.

How accurate is a decimal degree conversion?

Each decimal place in a decimal degree represents roughly 11.1 km at the equator for the first decimal place, dropping to about 1.11 cm by the seventh decimal place. Four decimal places (about 11 metres of precision) is normally accurate enough for maps and navigation, while six or more decimal places is used for surveying and precise GPS work.

Degrees Minutes Seconds to Decimal Degrees Converter

Convert a coordinate given in degrees, minutes and seconds (DMS) into decimal degrees (DD), the format used by Google Maps, GPS devices and most mapping software. Enter degrees, minutes, seconds and a hemisphere, and the decimal degree value updates instantly.

You can also enter a decimal degree value below to see it converted back into degrees, minutes and seconds.

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Reference standard Standard geographic coordinate conversion (60 minutes per degree, 60 seconds per minute).

1. DMS to Decimal Degrees

Degrees

Minutes

Seconds

Hemisphere

2. Decimal Degrees to DMS

Decimal degrees (reverse conversion, optional)

Enter a signed decimal degree value here (negative for south or west) to see it converted back to degrees, minutes and seconds. This field works independently of the DMS fields on the left.

Conversion Results

DMS Input as Decimal Degrees
-
-

Decimal Degrees Input as DMS

From the field on the right

Approx. Precision

At the equator, at 4 decimal places (default display precision)

DMS to Decimal Degrees Working

Degrees-

Minutes ÷ 60-

Seconds ÷ 3600-

Sum (unsigned)-

Hemisphere sign-

Decimal degrees-

Decimal Degrees to DMS Working

Input value-

Hemisphere (from sign)-

Whole degrees-

Whole minutes-

Seconds (remainder)-

Summary: Enter a DMS coordinate above.

How to Convert Degrees, Minutes and Seconds to Decimal Degrees

Geographic coordinates can be written in two common formats. Degrees, minutes and seconds (DMS) splits a coordinate into three parts, for example 41 degrees, 17 minutes, 11.4 seconds south. Decimal degrees (DD) writes the same location as a single signed number, for example -41.2865. Decimal degrees are the format used by Google Maps, most GPS units and almost all web mapping and spatial software, which is why converting from DMS is such a common task.

The formula for converting DMS to decimal degrees is:

Step	Calculation
1. Convert minutes to a fraction of a degree	Minutes ÷ 60
2. Convert seconds to a fraction of a degree	Seconds ÷ 3600
3. Add degrees, minutes fraction and seconds fraction	Degrees + (Minutes ÷ 60) + (Seconds ÷ 3600)
4. Apply the sign	Negative for South or West, positive for North or East

Worked Example

Take a coordinate of 41 degrees, 17 minutes, 11.4 seconds south. First, divide the minutes by 60: 17 ÷ 60 = 0.283333. Next, divide the seconds by 3600: 11.4 ÷ 3600 = 0.003167. Add these to the degrees: 41 + 0.283333 + 0.003167 = 41.2865. Since the hemisphere is south, the result is written as a negative number: -41.2865 decimal degrees. This is close to the latitude of Wellington, New Zealand.

Converting Decimal Degrees Back to DMS

To reverse the conversion, start with the decimal degree value and drop the sign to work out the hemisphere separately (negative latitude is South, negative longitude is West). The whole number part is the degrees. Multiply the remaining decimal fraction by 60 to get the minutes; the whole number part of that result is the minutes value. Multiply the new remaining fraction by 60 again to get the seconds. For example, -41.2865 becomes 41 degrees (whole number), then 0.2865 × 60 = 17.19 minutes (17 whole minutes), then 0.19 × 60 = 11.4 seconds, giving 41 degrees, 17 minutes, 11.4 seconds south.

Why Decimal Places Matter for Accuracy

Decimal Places	Approx. Precision at Equator	Typical Use
1	~11.1 km	Country or large region
2	~1.11 km	City or town
3	~111 m	Suburb or large landmark
4	~11.1 m	Street address, general navigation
5	~1.11 m	Individual building or property
6	~11.1 cm	Precise survey or vehicle tracking

For most everyday mapping purposes, four to five decimal places is more than enough precision. Surveyors and engineers working with legal boundaries or high-accuracy GPS equipment may use six or more decimal places.

New Zealand Coordinates

New Zealand sits entirely in the southern hemisphere and mostly east of the prime meridian, so New Zealand latitudes convert to negative decimal degrees (roughly -34 in the far north to -47 in Stewart Island and the subantarctic islands) while longitudes stay positive (roughly 166 to 179 degrees east, with the Chatham Islands further east again). Keeping the correct sign is essential, since mixing up North/South or East/West will place a coordinate on the opposite side of the world.

Related Calculators

Essential Calculators: the full hub of everyday conversion and reference tools.
Coordinates Converter: convert latitude and longitude both ways between DMS and decimal degrees.
Angle Converter: convert between degrees, radians, gradians and more.
Degrees to Radians Calculator: convert angles to radians for maths and physics.
Radians to Degrees Calculator: convert radians back to degrees.

Sources: Standard geographic coordinate conversion formulae (degrees, minutes and seconds to decimal degrees), as used by national mapping agencies including Land Information New Zealand (linz.govt.nz) and the US National Geodetic Survey.

This converter uses the standard sexagesimal (base 60) definition of minutes and seconds within a degree. Results are shown to four decimal places by default for readability; copy the underlying calculation if you need additional precision for survey work.