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How to Find Degrees Minutes and Seconds on A Calculator

Reviewed by Calculator Editorial Team

Degrees, minutes, and seconds (DMS) is a way to represent angles or geographic coordinates that divides a degree into 60 minutes, and each minute into 60 seconds. This format is commonly used in navigation, astronomy, and cartography. In this guide, we'll explain how to find degrees, minutes, and seconds on a calculator.

What is Degrees, Minutes, and Seconds (DMS)?

The degrees, minutes, and seconds (DMS) system is an alternative to the decimal degree system for measuring angles. In this system:

  • 1 degree (°) = 60 minutes (')
  • 1 minute (') = 60 seconds (")

This system is particularly useful for precise measurements in navigation, astronomy, and surveying. For example, a location might be represented as 40°26'46" N, 79°58'56" W.

DMS is often used in GPS devices and older maps, while decimal degrees are more common in modern digital systems.

How to Convert Decimal Degrees to DMS

To convert decimal degrees to DMS, follow these steps:

  1. Separate the integer part of the decimal degrees as the degrees value.
  2. Multiply the decimal part by 60 to get the minutes value.
  3. Separate the integer part of the minutes as the minutes value.
  4. Multiply the remaining decimal part by 60 to get the seconds value.

Formula:

Degrees = Integer part of decimal degrees

Minutes = (Decimal part × 60) rounded to nearest integer

Seconds = (Remaining decimal part × 60) rounded to nearest integer

For example, to convert 40.446° to DMS:

  1. Degrees = 40
  2. 0.446 × 60 = 26.76 → Minutes = 26
  3. 0.76 × 60 = 45.6 → Seconds = 46

So, 40.446° = 40°26'46".

Using a Calculator to Find DMS

Most scientific calculators have a built-in function to convert decimal degrees to DMS. Here's how to use it:

  1. Enter the decimal degree value.
  2. Press the "DMS" or "DEG→DMS" function (this may vary by calculator model).
  3. The calculator will display the degrees, minutes, and seconds.

If your calculator doesn't have a DMS function, you can use the manual method described above.

For precise calculations, always use the full decimal degree value before conversion.

Examples of DMS Conversion

Here are some examples of converting decimal degrees to DMS:

Decimal Degrees DMS
35.75 35°45'0"
123.456 123°27'21.6"
47.123456 47°7'24.44"

These examples show how the conversion works for different decimal degree values.

Frequently Asked Questions

How do I convert DMS back to decimal degrees?
To convert DMS back to decimal degrees, use the formula: Decimal Degrees = Degrees + (Minutes/60) + (Seconds/3600).
Why is DMS used instead of decimal degrees?
DMS is often used in older navigation systems and maps for better readability of precise measurements. Modern digital systems typically use decimal degrees.
Can I use this method for negative angles?
Yes, the same method applies to negative angles. The negative sign applies to the entire DMS value.