This coordinate converter translates geographic coordinates between decimal degrees (40.748817°) and degrees-minutes-seconds (40° 44′ 55.74″) in both directions, with hemisphere letters handled properly.
Same Point, Two Notations — Maps Speak Decimal, Charts Speak DMS
GPS chips and Google Maps use decimal degrees; nautical charts, surveying and aviation keep degrees-minutes-seconds (a Babylonian inheritance, base-60 and proud). Distances between two such points are our Distance Calculator. Part of our Conversion Calculators collection.
Worked Example (Verified)
- 40.748817° (Empire State Building latitude) → 40° 44′ 55.74″ N: 0.748817 × 60 = 44.93′ → 44′, remainder 0.93 × 60 = 55.74″
- Reverse: 40 + 44/60 + 55.74/3600 = 40.748817° — the round trip closes exactly, the mark of a honest converter
- Precision sense: 0.00001° of latitude ≈ 1.1 m; one second of arc (1″) ≈ 30.9 m; the second decimal of seconds is ~30 cm — surveying territory
- Longitude shrinks with latitude: 1° of longitude = 111.32 × cos(latitude) km — at 40.7° that’s 84.4 km, not 111
Notation Rules
- Sign does hemisphere duty in decimal (− = South/West); DMS carries letters instead — never mix a minus with a letter.
- Minutes and seconds must stay < 60; inputs at 60+ are a rounding smell in your source data.
- DD° MM.MMM′ (degrees + decimal minutes) is the marine/aviation hybrid — convert by treating the decimal minutes as minutes + seconds/60.
- Copy-paste trap: the ″ and ′ primes in text are often mangled by encodings; the numbers underneath remain what matter.
Related Tools
- Distance Calculator — between two points
- Time Zone Converter — longitude’s clock cousin
- Conversion Calculators — the full collection
Frequently Asked Questions
How do you convert decimal degrees to DMS?
Keep the integer degrees; multiply the fraction by 60 for minutes (integer part), then the new fraction by 60 for seconds. 40.748817° → 40°, 0.748817 × 60 = 44.93′ → 44′, 0.93 × 60 = 55.74″ → 40° 44′ 55.74″. This converter runs both directions.
How do you convert DMS back to decimal?
Degrees + minutes/60 + seconds/3600: 40 + 44/60 + 55.74/3600 = 40.748817°. Apply the sign from the hemisphere (S/W negative) at the end.
What do the hemisphere letters mean?
N/S for latitude (north/south of the equator), E/W for longitude (east/west of Greenwich). In signed decimal form, north and east are positive; south and west negative — a single convention that lets software skip the letters.
How precise is the sixth decimal place?
0.000001° of latitude ≈ 0.11 m (about 11 cm) — handheld-GPS territory. Five decimals ≈ 1.1 m; four ≈ 11 m. Seconds to two decimals (0.01″) carry similar ~0.3 m resolution.
Why is a degree of longitude shorter than a degree of latitude?
Meridians converge at the poles: the east-west circle at latitude φ has radius R·cos φ, so 1° of longitude = 111.32·cos φ km (84.4 km at New York, 0 at the pole), while latitude degrees stay ≈ 111 km everywhere (Earth’s slight bulge aside).
Is this coordinate converter free?
Yes — free, instant, no sign-up.