Decimal Degrees to Degrees, Minutes, Seconds Calculator

Enter decimal degrees to convert to degrees, minutes, and seconds (DMS).

How to Convert Decimal Degrees to Degrees, Minutes, and Seconds

Angular measurements are commonly expressed using degrees, minutes, and seconds, otherwise referred to as DMS. In this representation, degrees are the whole units without any decimal places.

Minutes, denoted with an apostrophe, are used to express an angular value less than one degree, and seconds, denoted with two apostrophes, are used to express an angular value less than one minute.

Minutes, so as not to be confused with the time measurement, are often referred to as arcminutes, and seconds, so as not to be confused as well, are often called arcseconds. There are 60 arcseconds in one arcminute and 60 arcminutes in one degree.

There are a few simple steps to convert decimal degrees to degrees, minutes, and seconds.

Step One: Find Whole Degrees

Since minutes and seconds are used to express the measurement of an angle less than one degree, start by setting the whole number to the left of the decimal point as the number of degrees.

Step Two: Find Minutes

The decimal point, or the remainder of the angle that is less than one degree, can be converted to minutes and seconds. Multiply this decimal value by 60 to find the number of minutes.

minutes = remaining decimal × 60

This resulting number is the minutes and seconds. The whole number to the left of the decimal point is the number of minutes. The remainder, or the values to the right of the decimal, is the number of partial minutes, which need to be converted to seconds.

Step Three: Find Seconds

Multiply the remaining decimal value by 60 again to find the number of seconds.

seconds = remaining decimal × 60

Step Four: Rewrite Decimal as Degree, Minutes, & Seconds

Finally, express the whole degrees, minutes, and seconds with their respective symbols

D° M′ S″

Decimal Degrees to DMS Example

For example, convert 47.31° to DMS.

Find the whole degrees:
47.31° = 47° + .31°
whole degrees = 47°

Find minutes:
minutes = .31 × 60 = 18.6′
minutes = 18′ + .6′
whole minutes = 18′

Find seconds:
seconds = .6′ × 60
seconds = 36″

Thus, 47.31° is equal to 47° 18′ 36″.

graphic showing how to apply the equations to convert degrees in decimal to minutes & seconds

Here’s a fun fact: there are 360 degrees in a circle, and each degree is composed of 60 minutes or 3,600 seconds. That means that there are 21,600 minutes around a circle or 1,296,000 seconds around a circle.

Frequently Asked Questions

Are decimal degrees and DMS the same thing?

Decimal degrees and DMS are just two different formats to represent the same value of an angle.

Why are minutes and seconds used with degrees?

Minutes and seconds are used to represent angles for historical reasons dating back to the sexagesimal system developed by the Babylonians.

Are minutes and seconds more precise than decimal degrees?

DMS is just as accurate as decimal degrees as long as no rounding is done when calculating the number of minutes and seconds.