Degrees, minutes, seconds converter
Enter coordinates, get decimal degrees or DMS.
How do I convert degrees, minutes and seconds to decimal degrees?
Decimal degrees = degrees + minutes ÷ 60 + seconds ÷ 3600. 38° 53′ 23″ is 38 + 53/60 + 23/3600 = 38.889722°.
How do I convert decimal degrees to DMS?
The whole part is degrees; multiply the rest by 60 for minutes, and the remainder by 60 again for seconds. 77.00861° is 77° 0′ 31″.
What do N, S, E and W mean for the sign?
South latitudes and west longitudes are negative in decimal form: 77° 0′ 31″ W is −77.00861.
How precise is a second of latitude?
One second of latitude is about 101 feet (31 m) on the ground, so seconds with two decimals locate a point within about a foot.
Where are DMS coordinates used?
On paper maps, in surveying and on many GPS units, while web maps usually use decimal degrees.
How many decimal places of a degree do I need?
USGS puts one second of latitude at about 101 feet, and a degree has 3,600 seconds. So 0.00001° is 0.036″, about 3.6 feet, and the six decimals this calculator shows (0.000001°) are about 0.4 feet.
Why is a second of longitude shorter than a second of latitude?
Meridians meet at the poles, so a degree of longitude shrinks toward them in proportion to the cosine of the latitude. At 38° N USGS gives 101 feet for one second of latitude but only 80 feet for one second of longitude (101 × cos 38° ≈ 80).
Is an arcminute the same as a minute of time?
No. NIST SP 811 defines the angle minute (′) as 1/60 of a degree and the angle second (″) as 1/60 of a minute, π/648,000 radian, and writes the time units min and s. They share names and the base-60 pattern, nothing else.
The formulas and what they assume
The units are defined by 1° = π/180 rad, 1′ = 1/60° and 1″ = 1/60′ (NIST SP 811, Table 6), so decimal degrees = D + M ÷ 60 + S ÷ 3600. Going back, the whole part is D, the fraction times 60 gives M, and the fraction left in M times 60 gives S. The sign belongs to the whole angle: south latitudes and west longitudes are negative. Minutes and seconds must lie between 0 and 59. Seconds are shown to two decimals, and if rounding makes them 60 the calculator carries into the minute, so 10.9999999° prints as 11° 0′ 0″ rather than 10° 59′ 60″.
Worked example, both directions
To convert 40° 26′ 46.3″: 26 ÷ 60 = 0.433333 and 46.3 ÷ 3600 = 0.012861, so the angle is 40 + 0.433333 + 0.012861 = 40.446194°. To go back with 122.4194° W: the whole part is 122; 0.4194 × 60 = 25.164, so 25′; 0.164 × 60 = 9.84, so 9.84″. The answer is 122° 25′ 9.84″ W.
Common mistakes
Reading minutes as decimals: 38° 53′ is 38.8833°, not 38.53°, because 53′ is 53/60 of a degree. Putting the minus on the degrees only: −77° 30′ means −(77 + 30/60) = −77.5°, not −77 + 0.5 = −76.5°. Typing 60 minutes or 60 seconds, which the calculator rejects because 60′ is the next whole degree. And the wrong hemisphere letter, which puts the point on the other side of the equator or the prime meridian.
Sources: NIST Special Publication 811, chapter 5 “Units outside the SI”, Table 6 (degree, minute and second of plane angle); USGS, “How much distance does a degree, minute, and second cover on your maps?” (distances at 38° N). Related tools: angle converter, degrees to radians, coordinate distance calculator and sun angle calculator. How we check our calculators.