DMS Converter
Convert latitude, longitude or any angle between degrees, minutes and seconds and decimal degrees, with degrees and decimal minutes as well.
Result
Decimal degrees: 40.446111
Seconds are shown to hundredths and decimal minutes to ten-thousandths, rounded once so a carry never shows 60″.
- Degrees, minutes and seconds
- 40° 26′ 46″ N
- Degrees and decimal minutes
- 40° 26.7667′ N
https://calcgallery.com/notation-conversions/dms-converter-calculator/
Unit conversions follow from exact definitions and published notation rules. Sizes follow published standards and are approximate: makers grade their own, so check their chart. Figures are rounded only for display. Read the full disclaimer
How to use the DMS Converter
- Choose the direction, and say whether the angle is a latitude, a longitude or some other angle, so the right letter is added.
- Enter degrees, minutes and seconds with north or east as positive and south or west as negative, or enter decimal degrees with a minus sign for south or west.
- Read decimal degrees, degrees minutes and seconds, and degrees with decimal minutes, the three forms coordinates are usually written in.
Sixty minutes to the degree
Minutes and seconds of arc divide a degree the way minutes and seconds divide an hour: 60 minutes to the degree and 60 seconds to the minute. The SI Brochure lists them as units accepted for use with the SI, defined exactly that way.
decimal degrees = degrees + minutes ÷ 60 + seconds ÷ 3600minutes = (decimal degrees − whole degrees) × 60seconds = (minutes − whole minutes) × 60The sign is handled separately. A negative decimal becomes a positive angle with S or W, and the arithmetic runs on the size of the angle, so −73.985656 does not turn into −74° plus some positive minutes.
Rounding without 60 seconds
Seconds are shown to the hundredth and decimal minutes to the ten-thousandth. The whole angle is rounded once to that precision before it is split, so a value just under a whole minute becomes the next minute rather than printing 60″. Decimal degrees are shown to six places.
Limits
Latitude runs from 90° south to 90° north and longitude from 180° west to 180° east, and for anything beyond those the page gives no result and a note naming the limit. For an angle that is not a coordinate, such as a bearing or a surveyor’s measurement, choose any other angle, which accepts up to a full turn either way and uses a minus sign instead of a letter. To go on to radians, use the degrees and radians converter.
With your numbers
- 40 + 26 ÷ 60 + 46 ÷ 3600
- Decimal degrees = 40.446111
Quick reference
Seconds are shown to hundredths and decimal minutes to ten-thousandths, rounded once so a carry never shows 60″.
| Example | Result |
|---|---|
| 40° 26′ 46″ N | Decimal degrees: 40.446111 |
| 33° 51′ 35.9″ S | Decimal degrees: -33.859972 |
| 151° 12′ 40″ E | Decimal degrees: 151.211111 |
| −73.985656, a longitude | Degrees, minutes and seconds: 73° 59′ 8.36″ W |
| 51.5007, a latitude | Degrees, minutes and seconds: 51° 30′ 2.52″ N |
| 0.5 degrees | Degrees, minutes and seconds: 0° 30′ 0″ |
| 90° N, the pole | Degrees, minutes and seconds: 90° 0′ 0″ N |
Common questions about the DMS Converter
- How do I convert degrees, minutes and seconds to decimal?
- Divide the minutes by 60 and the seconds by 3,600, and add both to the degrees. 40° 26′ 46″ is 40 + 26 ÷ 60 + 46 ÷ 3,600 = 40.446111°. Make the result negative for a southern latitude or a western longitude.
- How do I convert decimal degrees to degrees, minutes and seconds?
- The whole number is the degrees. Multiply what is left by 60: the whole part of that is the minutes. Multiply what is left again by 60 for the seconds. 73.985656° is 73°, then 0.985656 × 60 = 59.13936′, then 0.13936 × 60 = 8.36″.
- Why does my GPS show a different format?
- Some devices use a third form, degrees and decimal minutes, such as 40° 26.7667′. It is the same position written with the seconds folded into the minutes. The page shows all three, so you can copy whichever one the other device or map expects.
- Is a minus sign the same as S or W?
- Yes. In decimal degrees, south latitudes and west longitudes are negative. In degrees, minutes and seconds the letter is used instead, so a coordinate never carries both. Mixing them up moves the point to another hemisphere.