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How to Convert Decimal to Degrees in Scientific Calculator

Reviewed by Calculator Editorial Team

Converting decimal degrees to degrees, minutes, and seconds is a common task in navigation, astronomy, and geography. This guide explains how to perform this conversion using a scientific calculator and provides step-by-step instructions.

How to Convert Decimal Degrees to Degrees, Minutes, Seconds

The decimal degree format (e.g., 45.75°) is commonly used in digital systems, while the degrees-minutes-seconds (DMS) format (e.g., 45°45'0") is more traditional and often used in maps and navigation.

Step-by-Step Conversion Process

  1. Identify the decimal degrees value you want to convert.
  2. Separate the integer part (degrees) from the decimal part.
  3. Multiply the decimal part by 60 to get the minutes.
  4. Separate the integer part (minutes) from the new decimal part.
  5. Multiply the remaining decimal part by 60 to get the seconds.
  6. Combine the degrees, minutes, and seconds in the DMS format.

Important Notes

This method works for both positive and negative decimal degrees. The sign (positive or negative) should be preserved in the final DMS result.

Using a Scientific Calculator

Most scientific calculators have built-in functions for degree conversions. Here's how to use them:

Using the Calculator's Degree Conversion Function

  1. Enter the decimal degrees value in the calculator.
  2. Press the "DEG" button to ensure the calculator is in degree mode.
  3. Use the calculator's conversion function (often labeled "DMS" or "DEG→DMS").
  4. The calculator will display the converted value in degrees, minutes, and seconds.

Example

If your calculator has a dedicated DMS conversion function, simply enter 45.75 and press the conversion button to get 45°45'0".

The Conversion Formula

The mathematical formula for converting decimal degrees to DMS is:

Formula

Degrees = Integer part of decimal degrees

Minutes = (Decimal part × 60) rounded to integer

Seconds = (Remaining decimal part × 60) rounded to 2 decimal places

This formula can be implemented in any programming language or spreadsheet software.

Worked Example

Let's convert 45.75° to DMS format:

  1. Integer part (degrees): 45
  2. Decimal part: 0.75
  3. Minutes: 0.75 × 60 = 45 minutes
  4. Remaining decimal part: 0 (since 45 is an integer)
  5. Seconds: 0 × 60 = 0 seconds

The final result is 45°45'0".

Decimal Degrees DMS Format
45.75° 45°45'0"
36.5° 36°30'0"
12.375° 12°22'30"

Frequently Asked Questions

Why convert decimal degrees to DMS?

DMS format is often preferred in traditional navigation and cartography because it provides more precise fractional values for angles.

Can I convert DMS back to decimal degrees?

Yes, the reverse calculation is straightforward: degrees + (minutes/60) + (seconds/3600).

What if my calculator doesn't have a DMS conversion function?

You can perform the manual calculation using the formula provided in this guide.

Is this conversion used in GPS coordinates?

Yes, GPS coordinates are often displayed in decimal degrees, but DMS format is still used in some traditional navigation systems.