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How to Find Degrees Minutes and Seconds on Calculator

Reviewed by Calculator Editorial Team

Degrees, minutes, and seconds (DMS) is a way to represent angles that's commonly used in navigation, surveying, and astronomy. This guide explains how to convert decimal degrees to DMS format using a calculator, including the formula, step-by-step instructions, and practical examples.

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

The DMS system divides an angle into three parts:

  • Degrees (°): The main unit, with 360° in a full circle
  • Minutes ('): Each degree is divided into 60 minutes
  • Seconds ("): Each minute is divided into 60 seconds

This system provides more precise angle measurements than decimal degrees, which is why it's often used in professional applications. For example, GPS coordinates are sometimes displayed in DMS format.

Conversion Formula

To convert decimal degrees to DMS, use these formulas:

Degrees = Integer part of the decimal degrees Minutes = (Decimal part × 60) without the integer part Seconds = (Remaining decimal part × 60)

For example, converting 45.765° to DMS:

  1. Degrees = 45
  2. Minutes = 0.765 × 60 = 45.9
  3. Seconds = 0.9 × 60 = 54

The result is 45°45'54".

How to Convert Decimal Degrees to DMS

Step-by-Step Instructions

  1. Identify the integer part of your decimal degree value - this is your degrees value.
  2. Subtract the integer part from the original value to get the decimal part.
  3. Multiply the decimal part by 60 to get the minutes value.
  4. Take the integer part of the minutes value and multiply the remaining decimal by 60 to get the seconds value.
  5. Combine all three values with the appropriate symbols (°, ', ")

Note: For negative angles, apply the same process to the absolute value and then add the negative sign to the degrees value.

Example Calculation

Let's convert 32.456° to DMS:

  1. Degrees = 32 (integer part)
  2. Decimal part = 0.456
  3. Minutes = 0.456 × 60 = 27.36
  4. Seconds = 0.36 × 60 = 21.6

The final DMS value is 32°27'21.6".

In practical applications, you might round the seconds to a whole number (32°27'22") depending on the required precision.

FAQ

Why convert decimal degrees to DMS?
DMS format is often preferred in professional fields like surveying and navigation because it provides more precise angle measurements than decimal degrees.
Can I convert DMS back to decimal degrees?
Yes, the reverse calculation is: Decimal degrees = Degrees + (Minutes/60) + (Seconds/3600)
What's the difference between DMS and decimal degrees?
Decimal degrees use a single decimal number (e.g., 45.765°), while DMS breaks it into degrees, minutes, and seconds (e.g., 45°45'54").
When should I use DMS instead of decimal degrees?
Use DMS when working with older maps, navigation systems, or when higher precision is needed in professional applications.
Can I use this calculator for latitude and longitude?
Yes, the same conversion principles apply to geographic coordinates, though you'll need to handle the direction (N/S/E/W) separately.