How to Calculate Decimal Degrees to Degree Minute Second

Converting decimal degrees to degrees, minutes, and seconds (DMS) is a common requirement in navigation, surveying, and cartography. This guide explains the process step-by-step and provides an interactive calculator for quick conversions.

What are decimal degrees?

Decimal degrees are a way to represent geographic coordinates where the degrees, minutes, and seconds are combined into a single decimal number. For example, 40.6892° N, 74.0445° W represents New York City's coordinates in decimal degrees.

While decimal degrees are easier to work with in calculations, degrees-minutes-seconds (DMS) format is often preferred for traditional navigation and mapping applications.

Conversion formula

The conversion from decimal degrees to DMS uses the following steps:

Separate the integer part of the decimal degree as the degrees component
Multiply the fractional part by 60 to get the minutes component
Multiply the new fractional part by 60 to get the seconds component

Degrees = floor(decimal degrees)
Minutes = floor((decimal degrees - Degrees) × 60)
Seconds = (decimal degrees - Degrees - (Minutes / 60)) × 3600

This formula works for both latitude and longitude coordinates.

How to convert decimal degrees to DMS

Step 1: Identify the decimal degree value

Start with your decimal degree value, for example, 36.789°.

Step 2: Extract the degrees component

Take the integer part of the decimal degree. For 36.789°, the degrees are 36.

Step 3: Calculate the minutes component

Subtract the degrees from the decimal value (36.789 - 36 = 0.789), then multiply by 60 to get minutes: 0.789 × 60 = 47.34 minutes.

Step 4: Calculate the seconds component

Take the fractional part of the minutes (0.34) and multiply by 60 to get seconds: 0.34 × 60 = 20.4 seconds.

Step 5: Combine the components

The final DMS format is 36° 47' 20.4".

Note: For negative coordinates (south or west), the degrees, minutes, and seconds are all negative in DMS format.

Example calculation

Let's convert 51.4778° to DMS:

Degrees: floor(51.4778) = 51°
Minutes: (51.4778 - 51) × 60 = 0.4778 × 60 = 28.668 minutes
Seconds: (0.668) × 60 = 40.08 seconds

The result is 51° 28' 40.08".

Decimal Degrees	DMS Equivalent
34.0544°	34° 3' 16.00"
-73.9876°	-73° 59' 15.40"
12.3456°	12° 20' 44.20"

When to use this conversion

Converting decimal degrees to DMS is particularly useful in these scenarios:

Traditional navigation using paper maps or compasses
Surveying and land measurement applications
Historical documents that use DMS format
When working with older GPS devices that display coordinates in DMS
Cartographic applications that require precise coordinate formatting

For most modern applications, decimal degrees are preferred due to their simplicity in calculations and computer processing.

FAQ

Why would I need to convert decimal degrees to DMS?

DMS format is often required for traditional navigation, surveying, and some older mapping systems that don't support decimal degrees. It provides a more precise way to represent coordinates in certain applications.

Is the conversion the same for latitude and longitude?

Yes, the same conversion formula applies to both latitude and longitude coordinates. The only difference is the direction (north/south for latitude, east/west for longitude).

Can I convert DMS back to decimal degrees?

Yes, you can reverse the process by calculating: Degrees + (Minutes / 60) + (Seconds / 3600). Our calculator can perform both conversions.

What if my decimal degree value is negative?

Negative values indicate south latitude or west longitude. The conversion process remains the same, but the final DMS value will be negative for all components.

Are there any rounding considerations?

For most practical purposes, you can round the seconds to two decimal places. However, for precise applications, you may want to keep more decimal places during intermediate calculations.