How to Convert Decimal to Degrees in Calculator

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

What is Decimal to Degrees Conversion?

Decimal degrees are a way to represent geographic coordinates where the whole number represents degrees, and the decimal portion represents minutes and seconds. For example, 45.75° is 45 degrees and 45 minutes (since 0.75 × 60 = 45).

Converting decimal degrees to degrees, minutes, and seconds is useful when working with older maps, navigation systems, or when precise angular measurements are needed.

How to Convert Decimal Degrees

To convert decimal degrees to degrees, minutes, and seconds:

Separate the integer part (degrees) from the decimal part.
Multiply the decimal part by 60 to get minutes.
Separate the integer part of minutes from the new decimal part.
Multiply the remaining decimal part by 60 to get seconds.

This process breaks down the decimal portion into its minutes and seconds components.

Conversion Formula

Formula

Given a decimal degree value D:

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

The formula uses basic arithmetic operations to separate the components of the decimal degree value.

Worked Example

Let's convert 45.75° to degrees, minutes, and seconds:

Degrees = floor(45.75) = 45°
Minutes = floor((45.75 - 45) × 60) = floor(0.75 × 60) = 45'
Seconds = (45.75 - 45 - (45 / 60)) × 3600 = 0"

The result is 45°45'0".

Note

In this example, the seconds component is zero because 0.75 × 60 is exactly 45 minutes with no remaining decimal.

FAQ

Why convert decimal degrees to degrees, minutes, and seconds?: Older navigation systems and some mapping applications use degrees, minutes, and seconds format. Converting allows compatibility with these systems.
Is this conversion reversible?: Yes, you can convert degrees, minutes, and seconds back to decimal degrees using the formula: D = Degrees + (Minutes / 60) + (Seconds / 3600).
What if the decimal part is very small?: The conversion will result in very small minutes and seconds values, which can be rounded to a desired precision.
Can I use this for latitude and longitude?: Yes, the same conversion process applies to both latitude and longitude values.
Are there any rounding considerations?: For most practical purposes, you can round the seconds to the nearest whole number. For higher precision, keep more decimal places.