Degrees Minutes Seconds Calculator

What degrees, minutes and seconds mean

Degrees minutes seconds is a sexagesimal notation: each degree divides into 60 minutes, and each minute into 60 seconds. It is the same base-60 structure as hours, minutes and seconds of time, inherited from Babylonian astronomy, and the shared vocabulary is why the two are so often confused.

The symbols matter. A degree uses °, a minute uses a prime ′ (usually typed as an apostrophe), and a second uses a double prime ″ (usually typed as a straight double quote). So 40° 26′ 46″ reads as forty degrees, twenty-six minutes, forty-six seconds. Written out in decimal that is 40.446111 degrees — the same angle, different notation.

One degree of latitude is about 111 kilometres anywhere on Earth, so one minute is roughly 1.85 km and one second about 31 metres. That relationship is worth internalising because it tells you immediately how much precision a given notation carries, which is the subject of the ground-distance section below.

Converting DMS to decimal degrees

Divide the minutes by 60, divide the seconds by 3600, and add both to the degrees. Apply the sign at the end, after the arithmetic — applying it first and then adding positive minutes is a classic error that produces a point on the wrong side of the equator.

1. Take the degrees as they are.
2. Divide the minutes by 60.
3. Divide the seconds by 3,600.
4. Add all three together.
5. If the coordinate is south or west, negate the whole result — not just the degrees.

Worked example: 40° 26′ 46″. The minutes give 26 ÷ 60 = 0.433333. The seconds give 46 ÷ 3600 = 0.012778. Adding: 40 + 0.433333 + 0.012778 = 40.446111°. For a southern coordinate such as 33° 51′ 24.4″ S, do the same arithmetic to get 33.856778 and then negate it to −33.856778.

Converting decimal degrees to DMS

Work with the absolute value and split it apart in stages. The whole-number part is the degrees. Multiply what is left by 60 — the whole-number part of that is the minutes. Multiply what remains by 60 again and that is the seconds.

Worked example: 40.446111°. The degrees are 40, leaving 0.446111. Multiplied by 60 that is 26.76666, so the minutes are 26, leaving 0.76666. Multiplied by 60 that is 46.0, so the seconds are 46. The answer is 40° 26′ 46″.

One trap is worth naming because it produces visibly wrong output. If you round seconds to one decimal place and the result lands on 60.0, you must carry: 12.999999° should display as 13° 0′ 0.0″, never as 12° 59′ 60.0″. The same applies if carrying pushes minutes to 60. Several tools get this wrong at the boundary.

The third format: degrees and decimal minutes

There is a third notation that trips people up because it looks like DMS with a piece missing. Degrees and decimal minutes, or DDM, keeps the degrees and minutes but writes the seconds as a fraction of a minute instead: 40° 26.767′ rather than 40° 26′ 46″.

It exists because marine and aviation GPS standardised on it. NMEA sentences — the data format almost every GPS receiver emits — carry position in DDM, so chart plotters, autopilots and handheld marine units display it that way. If a coordinate has exactly two parts and the minutes have a decimal point, it is DDM, and reading it as DMS will put you roughly a mile out.

Converting is straightforward: decimal minutes are just minutes plus seconds ÷ 60. So 26′ 46″ becomes 26 + 46÷60 = 26.767′. The calculator above shows all three notations simultaneously so the distinction is visible rather than something to remember.

Signs, hemispheres and the N/S/E/W problem

A coordinate can carry its hemisphere in two mutually exclusive ways: a letter (N, S, E, W) or a sign on the number. Mixing the two is the single most common cause of a point landing in the wrong hemisphere, and no calculator on this SERP addresses it.

The convention is that north and east are positive, south and west negative. So 33° 51′ 24.4″ S is −33.856778 in decimal, and 74° 2′ 40.2″ W is −74.044500. Writing −33.856778 S is redundant but harmless; writing −33.856778 N is contradictory, and different software resolves that contradiction differently. The calculator above always shows the sign and the letter together for exactly this reason.

Doing arithmetic in DMS

Adding and subtracting angles in DMS is base-60 arithmetic, and it is genuinely useful — surveyors average repeated observations, astronomers stack offsets, and navigators add bearings. Every tool on this SERP makes you convert to decimal, do the sum, and convert back.

Adding works right to left with carrying at 60. Take 45° 30′ 45″ plus 20° 45′ 30″. The seconds give 75, which is 1′ 15″, so write 15″ and carry one minute. The minutes give 30 + 45 + 1 = 76, which is 1° 16′, so write 16′ and carry one degree. The degrees give 45 + 20 + 1 = 66. The answer is 66° 16′ 15″.

Subtraction borrows the same way: if the seconds you are subtracting are larger, borrow a minute as 60 seconds. The arithmetic panel in the calculator above does this directly, including a mode for summing and averaging a list of values, which is the form the task actually takes in survey work.

How much ground a second covers

Precision in coordinates is not abstract — each decimal place or each arcsecond corresponds to a real distance, and knowing which is which tells you how many digits to keep.

One degree of latitude is about 111.32 km everywhere, because meridians are great circles. One minute is therefore about 1.852 km, which is exactly where the nautical mile comes from — it was defined as one minute of latitude. One second is about 31 metres.

Longitude behaves differently. A degree of longitude is 111 km at the equator but narrows toward the poles as the meridians converge, reaching zero at the pole itself. At 60° north or south it is exactly half the equatorial value. This is why a fixed decimal precision means different real-world accuracy depending on where you are, and why survey work states a datum and a projection rather than relying on raw degrees.

Where DMS is actually used

This notation serves two largely separate audiences who rarely read each other’s material, and no page currently ranking for this term addresses both. Knowing which one you are in tells you which parts of this page matter.

Who uses this and why