Degrees Minutes Seconds Converter
Convert decimal degrees to degrees, minutes and seconds (DMS), or DMS back to decimal degrees. Paste a single angle or a full latitude and longitude, with or without symbols and N, S, E, W letters.
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One angle, or a latitude, longitude pair. Negative = south or west. N/S/E/W letters also work.
Symbols are optional: 40 41 21.29 N 74 2 40.21 W also works. Use a minus sign or S/W for negative.
How to use the Degrees Minutes Seconds Converter
- Choose a direction: decimal to DMS or DMS to decimal.
- Type or paste the value: one angle, or latitude and longitude separated by a comma.
- Set how many decimals you want on the seconds.
- Read the result plus the other formats (decimal, DMS, degrees and decimal minutes).
- Copy the results or download the table of all formats.
DMS and decimal degree formulas
| Conversion | Formula | Example |
|---|---|---|
| DMS → decimal | DD = D + M/60 + S/3600 | 40° 41′ 21.29″ = 40.689247° |
| Decimal → degrees | D = whole part of |DD| | 74.044502 → 74° |
| Decimal → minutes | M = whole part of (|DD| − D) × 60 | 0.044502 × 60 = 2.67012 → 2′ |
| Decimal → seconds | S = ((|DD| − D) × 60 − M) × 60 | 0.67012 × 60 = 40.21″ |
| Degrees + decimal minutes | M′ = (|DD| − D) × 60 | 74° 2.6701′ W |
| Sign | S and W are negative | 74° 2′ 40.21″ W = −74.044502 |
What each unit means on the ground
Distances for latitude (north–south). Longitude distances shrink with the cosine of the latitude: at 40° they are about 77% of these, and at the poles they reach zero.
| Unit | Approximate distance |
|---|---|
| 1 degree (1°) | 111 km (69 mi) |
| 1 minute (1′) | 1.85 km, one nautical mile |
| 1 second (1″) | 30.9 m (101 ft) |
| 0.1 second | 3.1 m |
| 0.01 second | 0.31 m |
| 0.0001° (4 decimals) | 11.1 m |
| 0.000001° (6 decimals) | 0.11 m |
Frequently asked questions
How do I convert DMS to decimal degrees?
Add the parts: decimal = degrees + minutes ÷ 60 + seconds ÷ 3600. For 40° 41′ 21.29″ that is 40 + 0.683333 + 0.005914 = 40.689247. Make it negative if the direction is S or W.
How do I convert decimal degrees to DMS?
Keep the whole number as degrees. Multiply the remaining fraction by 60: the whole part is the minutes. Multiply the new fraction by 60 again for the seconds. For 74.044502: 0.044502 × 60 = 2.67012, so 2′, and 0.67012 × 60 = 40.21″, giving 74° 2′ 40.21″.
Which is positive, north or south?
In decimal degrees, north latitudes and east longitudes are positive; south latitudes and west longitudes are negative. So 33.8568° S, 151.2150° E becomes −33.8568, 151.2150.
What is the range of latitude and longitude?
Latitude runs from −90° (South Pole) to +90° (North Pole). Longitude runs from −180° to +180°, measured east or west from the prime meridian through Greenwich.
How accurate is one second of latitude?
One degree of latitude is about 111 km, so one minute is about 1.85 km (one nautical mile) and one second is about 30.9 m. Six decimal places in decimal degrees resolve about 0.11 m.
What is degrees decimal minutes (DDM)?
DDM writes whole degrees plus minutes with a decimal, such as 40° 41.3548′ N. It is common on marine charts and many GPS receivers. Convert it to decimal degrees with degrees + minutes ÷ 60.
Do I have to type the ° ′ ″ symbols?
No. The converter accepts plain spaces (40 41 21.29 N), apostrophes and quotes (40°41'21.29"N), or letters (40d 41m 21.29s). Separate a latitude and longitude with a comma or by their N/S and E/W letters.
Are all the tools on FreeToolCabin tested for quality and accuracy?
Yes! Every tool on our site undergoes automated Q/A testing in real browser environments to ensure high precision, correct output, and zero errors. If you happen to spot a bug or have a suggestion, please contact us at [email protected] and our team will review it right away.