How this instrument works
Degrees Minutes Seconds to Decimal Degrees Converter runs one identity in a single direction: decimal = D + M⁄60 + S⁄3600. Minutes are sixtieths of a degree and seconds are sixtieths of a minute — so 1⁄3600 of a degree — the same base-60 subdivision that splits an hour into minutes and seconds. Multiply each part by the fraction it represents and add the three together; nothing more elaborate sits underneath the D° M′ S″ notation.
The reason a single decimal figure matters is arithmetic. Two angles written as D° M′ S″ triples cannot be added, averaged, or interpolated without first aligning three separate bases — 30′ plus 45′ does not simply read as 75 minutes, because 75′ overflows into another whole degree. Collapsed into one continuous decimal, ordinary addition and subtraction work directly, which is exactly why GPS receivers, spreadsheets, and mapping libraries store coordinates this way rather than as three linked fields.
One genuine trap sits in the sign. The formula adds M⁄60 and S⁄3600 onto whatever D already is, so a negative degrees value needs care: −1° 30′ 0″ is meant to read as −1.5°, a point a degree and a half south of the equator, yet D + M⁄60 alone gives −1 + 0.5 = −0.5 if the fraction is simply added rather than treated as widening the negative magnitude. Converting the unsigned reading first and reattaching the sign afterward avoids the mistake — the same fix this site's decimal-to-minutes-degrees sheet recommends for the reverse conversion.
- Enter the whole-number part of your angle into Degrees — positive for north or east, negative for south or west.
- Enter Minutes, the arcminute count from 0 to 59, sixtieths of one degree.
- Enter Seconds, from 0 up to 59.999, sixtieths of one minute — 60 would already be the next whole minute.
- Read Decimal degrees for the combined figure; its unit dropdown defaults to deg, with rad and turn sitting alongside it.
- For a negative angle, enter Degrees as the negative number and keep Minutes and Seconds positive, then check that the returned sign matches what a chart or GPS reading would show.
Worked example — 40° 30′ 0″ becomes 40.5°
Set Degrees to 40, Minutes to 30, and Seconds to 0 — a reading straight off a sextant or an older handheld GPS unit. Minutes contributes 30⁄60 = 0.5 and Seconds contributes 0⁄3600 = 0, so Decimal degrees returns 40 + 0.5 + 0 = 40.5, read directly in its default deg unit.
Flip the unit dropdown on Decimal degrees to rad and the identical angle reads 0.7068583470577035 — still the same 40.5°, expressed after a separate multiplication by π⁄180 layered on top of, not inside, the base-60 combination above. Carried to full double-precision, that radian figure is the exact conversion, not a rounded stand-in.
Questions
Why does 30 minutes turn into 0.5, not 0.30, in the decimal result?
Because minutes are sixtieths of a degree, not hundredths. Dividing 30 by 60 gives 0.5, so 40° 30′ becomes 40.5° once combined — reading the minutes digits as if they were decimal places straight after the degree, giving 40.30° instead, is the single most common slip with D° M′ S″ notation.
How is combining D° M′ S″ different from converting degrees to radians?
They are two separate steps stacked on top of each other. Combining Degrees, Minutes, and Seconds only changes the base an angle is written in — sexagesimal to decimal — and stays measured in degrees throughout. Converting to radians is an unrelated multiplication by π⁄180 that this sheet performs afterward, only once the Decimal degrees unit dropdown is switched to rad.
What happens with a negative degrees value, such as a southern latitude?
Enter Degrees as the negative whole number with Minutes and Seconds left positive, then check the sign of the result. The formula decimal = D + M⁄60 + S⁄3600 adds the fractional part rather than widening a negative magnitude, so −1° 30′ 0″ computes to −0.5, not the −1.5 a chart intends — converting the unsigned reading first and reattaching the sign afterward avoids the error.
Why does the Seconds field stop at 59.999 instead of 60?
Because 60 arcseconds already equal one whole arcminute — a reading of 40° 30′ 60″ is really 40° 31′ 0″, just written before that carry has happened. Capping Seconds below 60 keeps each field a genuine remainder, the same rule that keeps a clock from ever showing 61 seconds.
Is this the exact reverse of splitting a decimal angle into degrees, minutes, and seconds?
Yes. This site's decimal-to-minutes-degrees sheet peels a single decimal apart with floor and multiply steps to produce D, M, and S; this page runs the identical base-60 relationship backward, folding three sexagesimal numbers into the one continuous decimal those floor steps started from.
Where does dividing a degree into 60 minutes and 3600 seconds come from?
Babylonian sexagesimal counting, a base-60 number system already thousands of years old when Ptolemy adopted it for a circle's 360°. It survives today in three unrelated places at once — clock time, geographic coordinates, and angle notation — each dividing a unit into 60 smaller parts, and every one of those into 60 smaller still.