Degrees, minutes and seconds to decimal degrees converter (and back)
Type an angle or paste a list: the calculator understands decimal degrees and degrees, minutes and seconds (with or without ° ' ") and returns every format at once.
With a letter (S or W), the value becomes negative. A pair on the same line (lat, lon) also works.
Result
Type an angle above.
How to convert by hand
DMS → decimal: degrees + minutes ÷ 60 + seconds ÷ 3600. E.g. 25°05'40" = 25 + 5/60 + 40/3600 = 25.094444°. South latitudes and west longitudes take a negative sign: −25.094444.
Decimal → DMS: the integer part is the degrees; multiply the fraction by 60 to get the minutes; the fraction of the minutes × 60 gives the seconds. E.g. 50.1633° → 0.1633 × 60 = 9.798' → 0.798 × 60 = 47.9" → 50°09'47.9".
Precision: on the ground, 1 second of latitude ≈ 30.9 m, 0.1" ≈ 3 m and 0.0001" ≈ 3 mm. For survey-grade GNSS coordinates, use 4 or 5 decimals in the seconds.
FAQ
How many decimal places do I need in coordinates?
In decimal degrees: 5 decimals ≈ 1 m, 6 decimals ≈ 10 cm, 8 decimals ≈ 1 mm (in latitude). In seconds: 1" ≈ 31 m, 0.01" ≈ 31 cm, 0.0001" ≈ 3 mm. For boundary and cadastral surveys, keep at least 4 decimals in the seconds or 8 in decimal degrees.
Which sign do south and west take?
In decimal degrees, south latitudes and west longitudes are negative; north and east are positive. So 40.7580, −73.9855 (New York) is 40°45'28.8"N, 73°59'07.8"W, and −33.8688, 151.2093 (Sydney) is 33°52'07.7"S, 151°12'33.5"E. A missing minus sign moves the point to the other side of the equator or of Greenwich.
What is a gon (grad)?
A full circle has 400 gons (grads) instead of 360°. Many total stations and levels, especially in continental Europe, are set to gons; 1 gon = 0.9°. A wrong angle unit is a classic cause of a skewed survey.
What about the calculator format 25.0540 (degrees.minutes seconds)?
Some HP calculators and field books use "DDD.MMSS" (25.0540 = 25°05'40"). Here, a number with a decimal point is always decimal degrees. To type DMS, separate with spaces (25 05 40) or use the symbols.