Degrees Minutes Seconds Calculator

Created by Julia Żuławińska
Reviewed by Bogna Szyk and Jack Bowater
Last updated: Jan 03, 2023

This degrees minutes seconds calculator can help you convert degrees minutes seconds to decimal degrees. In the text below, we give you the DMS to decimal degrees formula. We also explain how to convert decimal degrees to DMS with a step by step guide and example. Be sure to check out our other calculators, like this lat long to utm converter!

When something takes 1 hour and 30 minutes, you usually say it took you an hour and a half. But if something takes 1 hour and 23 minutes, you wouldn't say it took you 1.38 hours. It's the same with degrees. You can use decimal degrees, but sometimes it's clearer to use degrees with minutes and seconds. You can tell them apart by the symbols after the number:

  • the degree symbol is °;
  • the symbol for minute is '; and
  • the symbol for second is ".

The DMS format is most common in geographic coordinate system. Go to the coordinates converter to learn more about this topic.

For now, let's find out how our DMS calculator does it!

How to convert degrees minutes seconds to decimal degrees? - degree converter formula

How many minutes are in a degree? Just like with hours, one degree is equal to sixty minutes. And one minute has sixty seconds, which means that one degree has three thousand six hundred seconds.

  • 1° = 60'

  • 1' = 60"

  • 1° = 3600"

To convert DMS to decimal degrees all you need to do is use this formula:

Decimal degrees = Degrees + Minutes / 60 + Seconds / 3600

Where does this DMS to decimal degrees formula come from? As you now know, 1 degree has 60 minutes. That means that 1 minute is 1/60 of a degree, and 1 second is equal to 1/3600 of a degree.

Let's look at an example: Convert 67°48'23" to decimal degrees.

This angle has 67 degrees, 48 minutes, and 25 seconds, so input these values into their correct places:

Decimal degrees = 67° + 48'/60 + 25"/3600 = 67 + 0.8 + 0.00694 = 67.80694° ≈ 67.81°

Simple, right? If you don't want to do the calculation by hand, our degrees minutes seconds calculator will do it for you! And, if you need a more precise answer, the fraction to decimal converter might be your lifesaver!

Now, let's see how to convert decimal degrees to DMS.

Decimal degrees to DMS - step by step conversion

Converting decimal degrees to degrees with minutes and seconds is slightly more challenging. Let's take it one step at a time:

  1. First, take the whole number part - these are the degrees.
  2. Then, take what's left and multiply it by sixty. Again, take the whole number from that - these are the minutes.
  3. Lastly, multiply the rest, again, by sixty. The result is the number of seconds.

To make it easier to understand, let's look at an example. What is 47.392° in DMS?

  1. The integer from 47.392° is 47, so degrees = 47°.
  2. The decimal part: 0.392 multiplied by 60 equals 23.52. Take the integer again - minutes = 23'.
  3. Take the decimal part of step 2, 0.52, and multiply it by 60. You will get the amount of seconds = 31.2".

The degree in decimals - 47.392° - is the same as 47°23'31.2".

Why are we multiplying by sixty? 47.392° is the same as 47 degrees and 0.392 of a degree. As you know, one degree equals 60 minutes. By multiplying the part of a degree by sixty, you get 23 minutes and 0.52 of a minute. One minute equals 60 seconds. So, when you multiply the part of a minute by sixty, you find the number of seconds.

You don't want to calculate it by hand? Use our degrees minutes seconds calculator! And don't forget to check out our other calculators like this scale converter.

Julia Żuławińska
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