How to Calculate Degrees From Decimal

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

What is a decimal degree?

A decimal degree is a way of expressing latitude and longitude coordinates that combines degrees and a decimal fraction. For example, 40.7128° is 40 degrees and 0.7128 of a degree north or south.

Decimal degrees are commonly used in GPS devices, mapping software, and scientific calculations because they provide a precise and easy-to-use format for working with geographic coordinates.

How to convert decimal degrees to degrees, minutes, and seconds

To convert a decimal degree to degrees, minutes, and seconds, follow these steps:

Identify the whole number of degrees. This is the integer part of the decimal degree.
Multiply the decimal part of the degree by 60 to get the minutes.
Take the decimal part of the minutes and multiply it by 60 to get the seconds.

Conversion Formula

Degrees = Integer part of decimal degree

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

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

For example, to convert 40.7128° to degrees, minutes, and seconds:

The integer part is 40°, so degrees = 40°.
0.7128 × 60 = 42.768, so minutes = 42'.
0.768 × 60 = 46.08, so seconds = 46".

The final result is 40°42'46".

Note: When converting, you may need to round the seconds to the nearest whole number, depending on the required precision.

Example calculation

Let's convert 36.9875° to degrees, minutes, and seconds:

Degrees = 36° (the integer part)
0.9875 × 60 = 59.25, so minutes = 59'
0.25 × 60 = 15, so seconds = 15"

The result is 36°59'15".

Decimal Degree Conversion Example
Decimal Degree	Degrees	Minutes	Seconds
36.9875°	36°	59'	15"

Common uses of decimal degrees

Decimal degrees are widely used in various fields:

Navigation: GPS devices and mapping applications use decimal degrees to display precise locations.
Astronomy: Astronomers use decimal degrees to specify the positions of celestial objects.
Geography: Decimal degrees are used in geographic information systems (GIS) to represent locations on maps.
Surveying: Surveyors use decimal degrees to measure and record land boundaries.

FAQ

Why do we need to convert decimal degrees to degrees, minutes, and seconds?

Converting decimal degrees to degrees, minutes, and seconds is often required for compatibility with older systems, maps, and documents that use the traditional format. It also provides a more intuitive way to understand and communicate geographic coordinates.

Can I convert degrees, minutes, and seconds back to decimal degrees?

Yes, you can convert degrees, minutes, and seconds back to decimal degrees using the reverse formula: Decimal degrees = Degrees + (Minutes / 60) + (Seconds / 3600).

What is the difference between decimal degrees and degrees, minutes, and seconds?

Decimal degrees combine degrees and a decimal fraction, while degrees, minutes, and seconds express the same angle in terms of whole numbers. Decimal degrees are more precise and easier to work with in calculations, while degrees, minutes, and seconds are often used for readability and compatibility.