Degrees Minutes Seconds to Decimal Degrees Converter
This tool converts geographic coordinates between degrees, minutes and seconds (DMS) and decimal degrees (DD), the two formats used for latitude and longitude worldwide. Decimal degrees are what Google Maps, GPS devices and most mapping software expect, so converting from DMS is a common step whenever you copy a coordinate off a map, survey plan or GPS unit. Enter the degrees, minutes and seconds of your coordinate along with its hemisphere (north, south, east or west), and the calculator instantly returns the equivalent decimal degree value, alongside a full working breakdown showing how the minutes and seconds portions were divided down and summed, with the correct sign applied for southern and western coordinates. A second field lets you work the conversion the other way: type in a signed decimal degree value and see it broken back down into whole degrees, minutes and seconds. The results panel also shows the approximate precision, in metres, represented by the number of decimal places displayed, helping you judge whether four decimal places is enough for everyday navigation or whether you need more for survey-grade work. Because New Zealand sits in the southern hemisphere and east of the prime meridian, local latitudes convert to negative decimal degrees while longitudes stay positive, so keep hemisphere and sign consistent to avoid placing a point on the wrong side of the globe.
1. DMS to Decimal Degrees
2. Decimal Degrees to DMS
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.
DMS to Decimal Degrees Working
Decimal Degrees to DMS Working
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.