Decimal Degrees to Degrees Minutes Seconds

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Decimal Degrees to Degrees Minutes Seconds Calculation:

  • DD =

    Degrees of latitude, longitude or other units in a single number decimal form.

  •  D =

    Degrees of latitude or longitude as entered.

  •  M =

    Minutes of latitude or longitude as entered. Each minute is 1/60 of a degree.

  •  S =

    Seconds of latitude or longitude as entered. Each second is 1/60 of a minute or 1/3600 of a degree.

  •     

    Choose the number of decimals to show in your answer. This is also known as significant figures. Select an appropriate amount of significant figures based on the precision of the input numbers.

Decimal Degrees to Degrees Minutes Seconds Formula

Decimal degrees of latitude or longitude can be expressed in degrees with minutes and seconds. Each minute is 1/60 of a degree and each second is 1/60 of a minute or 1/3600 of a degree.

Multiply the decimal portion of degrees by 60 to get decimal minutes.

Multiply the decimal portion of minutes by 60 to get seconds.

Degrees and minutes are the remaining non-decimal portion.

Converting decimal degrees to degrees minutes seconds is more easily expressed by this pseudo-coded algorithm than by a formula. Take a look at this example below to see how decimal degrees (DD) are converter to degrees, minutes, seconds (D,M,S):

  • DECIMAL DEGREES = 51.4811
  • Write the whole number part as the degrees
  • DEGREES = 51
  • Multiply the leftover decimal by 60
  • DECIMAL MINUTES = 0.4811 * 60 = 28.866
  • Write the whole number part as the minutes
  • MINUTES = 28
  • Multiply the leftover decimal by 60
  • SECONDS = 0.866 * 60
  • Seconds are expressed with the decimal
  • SECONDS = 51.96
Decimal Degrees to Degrees Minutes Seconds Example
Formula for DD to DMS Conversion

Decimal Degrees to Degrees Minutes Seconds Variables

Only the latitude or longitude reported in decimal degrees is required to calculate the degrees minutes and seconds of the same location. The conversion works on the know information that there are 60 minutes in a degree and 60 seconds in a minutes (or arcminutes and arcseconds). The conversion is identifcal for latitude or longitude values, don't forget to include the north/south and east/west indicator in you answer.

Decimal Degrees (DD)
The input latitude or longitude measured in degrees with the decimal portion (or without if exactly on whole degrees).
Degrees (D)
Degrees of latitude or longitude without the decimal portion. There are 180° for each hemisphere east and west and 90° for each hemisphere north and south. Each imaginary line of latitude or longitude starts at the center of the earth and extends out to the surface of the earth. The degrees measure how far north/south or east/west the imaginary line is relative to the equator or prime meridian, two line chosen to be at zero degrees.
Minutes (M)
A whole number representing 1/60 of a degree. Along with the seconds this represents the decimal portion of the degree. Each degree can have sixty ticks in the minute possition, if further accuracy is required minutes are subdivided into seconds.
Seconds (S)
A decimal number representing 1/60 of a minutes along with a decimal representing fractions of a second.
Decimal Minutes (DM)
Decimal minutes are an alternative way of expressing the decimal portion of a degree without taking the extra step of calculating out seconds. They are most often used to shorten the notation when the required accuracy or more approximate but something more conventient than decimal degrees are desired. Decimal minutes are an easy to calculate intermediate step on the way to calculate seconds from decimal degrees.

Decimal Degrees to Degrees Minutes Seconds Solution

How can a latitude or longitude given in decimal degrees be expressed in degrees minutes and seconds? The degrees are already given as the whole number part of the decimal degrees, the decimal part can be converted to minutes and seconds on the principle that there are 60 minutes in a degree and 60 seconds in a minute:

  • DD = 51.4811
  • the degrees are already known
  • D = 51
  • take the decimal and multiply by 60 for minutes
  • DM = (DD - D) * 60 = 28.866
  • these are the decimal minutes, the whole number is the minutes
  • M = 28
  • take the fraction from the decimal minutes and multiply by 60 for seconds
  • S = (DM - M) * 60 = 51.96
  • finally write degrees, minutes, and seconds together:
  • = 51° 28' 51.96"

Decimal Degrees to Degrees Minutes Seconds Example

Sometimes a latitude or longitude can be expressed with a degative value to indicate the hemisphere. Negative latitudes range from 0 to -90° and are found south of the equator. Negative longitudes range from 0 to -180° and are found east of the prime meridian. The conversion method is identical to above, keep the negative symbol on the degrees.

  • DD = -150.589287
  • D = -150
  • DM = 35.35722
  • M = 35
  • S = 21.4332
  • DMS = -150° 35' 21.4332"

-150.589287 decimal degrees is expressed in degrees, minutes, seconds as: -150° 35' 21.4332".

Expressing Degrees Minutes Seconds

How to write a degree symbol:

  • DD = -150.589287
  • D = -150
  • DM = 35.35722
  • M = 35
  • S = 21.4332
  • DMS = -150° 35' 21.4332"

-150.589287 decimal degrees is expressed in degrees, minutes, seconds as: -150° 35' 21.4332".

Decimal Degrees to Degrees Minutes Seconds Example