Coordinates are written in two main ways. Mapping software and spreadsheets use decimal degrees (40.689247, −74.044503), while nautical charts, aviation, surveying and many printed documents use degrees, minutes and seconds (40° 41′ 21.29″ N, 74° 2′ 40.21″ W). Handheld GPS units often use a hybrid, degrees and decimal minutes. This converter goes in either direction, adds the correct hemisphere letter for latitude and longitude, and produces a plain-text version you can paste into a map search box.
How to use the converter
- Choose the direction: Decimal → DMS or DMS → Decimal.
- For decimal input, type the value, say whether it is a latitude, longitude or plain angle, and pick how many decimal places the seconds should show.
- For DMS input, enter degrees, minutes and seconds as positive numbers and choose the direction letter (N, S, E or W), or + / − for a plain angle.
- The tape shows the result in DMS, degrees-decimal-minutes, signed decimal degrees and radians. Invalid values, such as 75 minutes or a latitude above 90°, are flagged.
Conversion formulas
A degree has 60 minutes (′) and a minute has 60 seconds (″), so a degree has 3,600 seconds.
Going the other way:
The sign carries the hemisphere: positive for north and east, negative for south and west. When seconds round up to 60, the converter carries one into the minutes (and minutes into degrees), so you never see 59′ 60″.
Worked example: the Statue of Liberty
The statue’s latitude is about 40.689247°. Converting to DMS:
Degrees: 40°
Minutes: 0.689247 × 60 = 41.35482 → 41′
Seconds: 0.35482 × 60 = 21.2892 → 21.29″
Result: 40° 41′ 21.29″ N (degrees-decimal-minutes: 40° 41.3548′ N)
Its longitude, written as 74° 2′ 40.21″ W, converts back as 74 + 2/60 + 40.21/3,600 = 74.044503, which becomes −74.044503 because it is west of Greenwich.
Three coordinate formats
| Format | Example | Common uses |
|---|---|---|
| Decimal degrees (DD) | 40.689247, −74.044503 | Web maps, GIS, spreadsheets, APIs |
| Degrees decimal minutes (DDM) | 40° 41.3548′ N, 74° 2.6702′ W | Marine and aviation GPS, geocaching |
| Degrees minutes seconds (DMS) | 40° 41′ 21.29″ N, 74° 2′ 40.21″ W | Charts, surveys, legal descriptions |
How precise should you be?
| Decimal places (DD) | DMS equivalent | Ground distance (latitude) |
|---|---|---|
| 0.1° | 6′ | about 11 km |
| 0.01° | 36″ | about 1.1 km |
| 0.001° | 3.6″ | about 111 m |
| 0.0001° | 0.36″ | about 11 m |
| 0.00001° | 0.036″ | about 1.1 m |
| 0.000001° | 0.0036″ | about 11 cm |
Longitude distances shrink toward the poles by the cosine of the latitude; at 40° N, one second of longitude is about 23.7 m instead of 30.9 m.
Common mistakes
- Dropping the minus sign. A west longitude entered as positive lands in Asia instead of North America.
- Treating minutes as decimals. 40° 30′ is 40.5°, not 40.30°.
- Mixing formats. In 40° 41.3548′ the minutes are already decimal; don’t add a seconds value as well.
- Swapping latitude and longitude. Most systems list latitude first, but some GIS formats (and GeoJSON) put longitude first.
For general angle units such as radians and gradians, use the angle converter. To measure the straight-line distance between two points on a grid, try the distance calculator.
Frequently asked questions
How do I convert decimal degrees to degrees, minutes and seconds?
Keep the whole number as degrees. Multiply the decimal part by 60; the whole number of that is the minutes. Multiply the remaining decimal by 60 again to get seconds. For 40.689247°: 0.689247 × 60 = 41.35482′, and 0.35482 × 60 = 21.29″, so 40° 41′ 21.29″.
How do I convert DMS to decimal degrees?
Use degrees + minutes/60 + seconds/3,600, then make the result negative for south latitudes and west longitudes. 74° 2′ 40.21″ W = 74 + 2/60 + 40.21/3,600 = 74.044503, written −74.044503.
Which coordinates are negative in decimal degrees?
Latitudes south of the equator and longitudes west of the prime meridian. All of the contiguous United States has a negative longitude, between about −67° and −125°.
How precise is a second of latitude?
One second of latitude is about 30.9 m (101 ft). Six decimal places in decimal degrees (0.000001°) correspond to about 11 cm, which is more precise than most consumer GPS receivers.