Coordinate converter — DMS and decimal degrees
Convert coordinates between degrees-minutes-seconds and decimal degrees.
Fill in the fields and the result will appear here automatically.
Converts a geographic coordinate from degrees, minutes and seconds into decimal degrees and back. Maps and devices disagree on the notation: paper charts and aviation data keep minutes and seconds, while browser maps and GPX files use signed decimal degrees. In that pair the sign carries the hemisphere — this form accepts unsigned DMS components and a separate direction — so the direction lives in its own field here rather than inside the number.
How it works
Formula and logic
Decimal degrees = degrees + minutes ÷ 60 + seconds ÷ 3600. Back again: the integer part gives degrees, the fraction times 60 gives minutes, and the remainder times 60 gives seconds. Degrees and minutes must be whole numbers: 0 ≤ degrees ≤ 180, 0 ≤ minutes < 60 and 0 ≤ seconds < 60. Seconds may be fractional. N supplies a positive sign and S a negative sign. At 180°, minutes and seconds must be zero. The reverse mode accepts one angle from −180° to 180°; seconds round to four decimal places with 60 carried into the next minute. There is no axis selector: check latitude separately against ±90°. This does not validate a coordinate pair or GPX file. Very small nonzero angles use scientific notation with four significant digits. Positive seconds below 0.00005″ remain in scientific notation when ordinary rounding would erase them. A nonzero angle below the numerical range produces an explicit error.
Example
55° 45′30″ north is 55.7583 decimal degrees.
Fields and units
- Direction — list option
- Degrees — °
- Minutes — ′
- Seconds — ″
- Hemisphere — list option
- Decimal degrees — °
How to use
- — Choose the direction of the conversion.
- — From DMS, enter degrees, minutes and seconds and pick the hemisphere.
- — The other way, enter signed decimal degrees: a minus means south or west.
- — Mind the range: latitude stays within 90°, longitude within 180°.
Method and limitations
- Calculation method
- Formula and logic
- Data or methodology source
- Topografix GPX1.1: schema latitude/longitude bounds; this converter does not validate GPX export
- Limitation
- There is no axis selector: check latitude separately against ±90°. This does not validate a coordinate pair or GPX file.
FAQ
Why is the hemisphere a separate field?
This form uses a separate direction control: north or east is positive, south or west negative. Enter non-negative DMS components and a signed decimal angle.
How many decimals are enough?
Four decimal places are this page’s angular display rule. They do not certify measurement accuracy or a location on a map. Check the receiving system’s format and permitted range.
Why are seconds shown with a fraction?
Fractional seconds are accepted, including 59.5″;60″ requires a carry into minutes. DMS output rounds to four decimal places. This rounds the angle notation and does not guarantee geographic accuracy.
Latitude or longitude?
The conversion formula is the same, but this page handles one angular component up to ±180°. Enforce ±90° for latitude yourself. GPX 1.1 specifies latitude from −90° to 90° and longitude from −180° inclusive to 180° exclusive; this page does not check export validity.