DMS to Decimal Degrees Converter

Enter the values to get the decimal degrees.

Result

-33.865000°

How it is calculated

The tool adds the minutes and seconds to the degrees as fractions of a degree: decimal = sign × (|degrees| + minutes ÷ 60 + seconds ÷ 3600). Minutes and seconds are optional and default to 0; the degrees box is required. The sign comes from the degrees box only: type a minus sign there for south latitudes and west longitudes, and the whole value, not just the degrees, becomes negative. A typed -0 also counts as negative, so −0° 30′ gives −0.500000°. Minutes and seconds themselves must not be negative, or no result is shown. The result has six decimals and a degree sign, about 0.1 metre on the ground. The tool does not check that minutes and seconds are below 60: 40° 90′ is accepted and gives 41.500000°. A hemisphere letter (N, S, E, W) cannot be typed; use the sign instead.

Worked example

A point at 33° 51′ 54″ south, entered as degrees −33, minutes 51, seconds 54. Minutes as degrees: 51 ÷ 60 = 0.85. Seconds as degrees: 54 ÷ 3600 = 0.015. Sum with the absolute degrees: 33 + 0.85 + 0.015 = 33.865. The minus sign from the degrees field applies to the whole value, so the result is -33.865000°. This is the format map and GPS software expect.

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Common mistakes

  • Applying the minus sign only to the degrees part by hand, as in −33 + 0.865 = −32.135. The tool applies the sign to the whole value, which is correct: the minutes and seconds also move the point further south or west.
  • Entering south or west as positive numbers. Without a minus sign the result lands in the opposite hemisphere, in a different part of the map.
  • Typing a hemisphere letter or a full string such as 33°51′54″S into the degrees box. Degrees, minutes and seconds go in separate boxes, as plain numbers.
  • Typing decimal minutes (such as 51.9) in the minutes box and also filling seconds. Use either decimal minutes with seconds empty, or whole minutes with seconds.
  • Typing minutes or seconds of 60 or more. The tool will not warn you, and the result will be a different point from the one you meant.

About this calculator

Geographic coordinates are traditionally written in degrees-minutes-seconds (DMS) notation, such as 40°44′54″N, where each minute is 1/60 of a degree and each second is 1/60 of a minute. Converting to decimal degrees uses the formula decimal = degrees + minutes/60 + seconds/3600, with the result made negative for southern latitudes or western longitudes so a single signed number can represent the full globe.

Decimal degrees are the format required by GPS devices, mapping APIs (Google Maps, GIS software), and most modern navigation systems, while DMS is still the format used in surveying documents, nautical charts, and older reference material. Surveyors, pilots, sailors, and developers building location-based apps regularly need to move between the two when combining data from different sources.

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