How to Convert DMS to Decimal Degrees

To convert degrees, minutes and seconds to decimal degrees, divide the minutes by 60, divide the seconds by 3600, and add both to the whole degrees. Then apply a negative sign if the direction is south or west. The reverse conversion uses the same relationships in the opposite direction.

The formula

Decimal degrees = degrees + (minutes / 60) + (seconds / 3600)

This works because there are 60 minutes in a degree and 60 seconds in a minute, so 3600 seconds in a degree.

Worked example: DMS to decimal

Convert 40° 26' 46" N to decimal degrees.

1. Degrees: 40
2. Minutes: 26 / 60 = 0.43333
3. Seconds: 46 / 3600 = 0.01278
4. Sum: 40 + 0.43333 + 0.01278 = 40.44611

The direction is north, so the answer stays positive: 40.44611.

Now convert 79° 58' 56" W:

1. 79 + 58/60 + 56/3600 = 79 + 0.96667 + 0.01556 = 79.98222
2. West is negative, so the answer is -79.98222.

Together: 40.44611, -79.98222.

Worked example: decimal to DMS

Convert 40.44611 to DMS.

1. Degrees: take the whole number, 40.
2. Minutes: take the fraction 0.44611 and multiply by 60 to get 26.7666. The whole number, 26, is the minutes.
3. Seconds: take the new fraction 0.7666 and multiply by 60 to get about 46.0 seconds.

Result: 40° 26' 46". Add the letter N for a positive latitude. For a negative number, convert the absolute value and add S or W.

Rounding and precision

• Keep at least five decimal places when you convert, or you will lose roughly a metre or more. The decimal places guide explains exactly how much.
• If the seconds come out as 60 after rounding, carry one into the minutes. Do the same for minutes reaching 60.

Common errors

• Forgetting to apply the negative sign for south or west. See positive and negative coordinates.
• Dividing seconds by 60 instead of 3600.
• Treating the digits after a decimal point in a minutes value as seconds. 26.5 minutes is 26 minutes 30 seconds, not 26 minutes 50 seconds.

For an overview of why both formats exist, read decimal degrees vs degrees, minutes and seconds.