How to Calculate Degrees Minutes and Seconds

Degrees, minutes, and seconds (DMS) is a system of measuring angles that divides a full circle into 360 degrees, each degree into 60 minutes, and each minute into 60 seconds. This format is commonly used in navigation, astronomy, and geography. This guide explains how to work with DMS values and provides an interactive calculator to perform conversions.

What Are Degrees, Minutes, and Seconds?

The degrees, minutes, seconds (DMS) system is an alternative to decimal degrees for measuring angles. It breaks down an angle into three parts:

Degrees (°): The largest unit, representing 1/360 of a full circle (360° = full circle)
Minutes ('): Each degree is divided into 60 minutes (1° = 60')
Seconds ("): Each minute is divided into 60 seconds (1' = 60")

For example, 45°30'15" means 45 degrees, 30 minutes, and 15 seconds. This format is particularly useful in fields like navigation where precise angle measurements are needed.

Note: DMS is often used in GPS coordinates and geographic measurements. Decimal degrees are more common in scientific calculations.

How to Convert Between DMS and Decimal Degrees

DMS to Decimal Degrees

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

Decimal Degrees = Degrees + (Minutes / 60) + (Seconds / 3600)

For example, convert 45°30'15" to decimal degrees:

45 + (30 / 60) + (15 / 3600) = 45 + 0.5 + 0.0041667 ≈ 45.5041667°

Decimal Degrees to DMS

To convert decimal degrees to DMS:

Take the integer part as degrees
Multiply the decimal part by 60 to get minutes
Take the integer part of minutes
Multiply the remaining decimal by 60 to get seconds

For example, convert 45.5041667° to DMS:

Degrees = 45 Minutes = 0.5041667 × 60 ≈ 30.25 Seconds = 0.25 × 60 ≈ 15 Result: 45°30'15"

DMS to Decimal Degrees Conversion Table
DMS	Decimal Degrees
0°0'0"	0.0000000
1°0'0"	1.0000000
45°30'0"	45.5000000
90°0'0"	90.0000000
180°0'0"	180.0000000

Worked Examples

Example 1: Convert 30°15'30" to Decimal Degrees

30 + (15 / 60) + (30 / 3600) = 30 + 0.25 + 0.0083333 ≈ 30.2583333°

Example 2: Convert 75.75° to DMS

Degrees = 75 Minutes = 0.75 × 60 = 45 Seconds = 0 × 60 = 0 Result: 75°45'0"

Example 3: Convert 12°30'45" to Decimal Degrees

12 + (30 / 60) + (45 / 3600) = 12 + 0.5 + 0.0125 ≈ 12.5125°

FAQ

Why use DMS instead of decimal degrees?

DMS is often used in navigation and geographic applications where precise angle measurements are needed. It provides a more intuitive way to represent angles compared to decimal degrees.

How accurate is the DMS system?

The DMS system can represent angles with high precision, especially when dealing with small angles. However, decimal degrees are often more convenient for calculations in scientific contexts.

Can I use negative values in DMS?

Yes, negative values can be used to represent angles in the southern hemisphere or west of the prime meridian. The conversion formulas work the same way for negative values.