Convert Degrees to Dms Calculator

Degrees, minutes, and seconds (DMS) is a format used to represent angles or coordinates. This calculator converts decimal degrees to DMS format, which is commonly used in navigation, surveying, and cartography.

What is DMS format?

DMS stands for Degrees, Minutes, and Seconds. This format divides an angle into three parts:

Degrees (°): The whole number part of the angle (0-360°)
Minutes (′): The fractional part of the degree, divided into 60 parts (0-59′)
Seconds (″): The fractional part of the minute, divided into 60 parts (0-59″)

DMS format is often used in geographic coordinates (latitude and longitude) and in navigation systems. For example, 40.6892° latitude is equivalent to 40°41′21″N in DMS format.

How to convert degrees to DMS

Converting decimal degrees to DMS format involves these steps:

Separate the whole number part (degrees)
Multiply the decimal part by 60 to get minutes
Multiply the new decimal part by 60 to get seconds
Round the seconds to the desired precision

Note: The conversion process assumes positive values. For negative angles, the same process applies to the absolute value, and the direction (N/S/E/W) is determined separately.

Conversion formula

Degrees: deg = floor(decimal)

Minutes: min = floor((decimal - deg) × 60)

Seconds: sec = ((decimal - deg) × 60 - min) × 60

The formula first extracts the whole degrees, then calculates the remaining minutes and seconds from the decimal portion.

Example conversion

Let's convert 40.6892° to DMS:

Degrees: floor(40.6892) = 40°
Minutes: floor((40.6892 - 40) × 60) = floor(0.6892 × 60) = 41′
Seconds: (0.6892 × 60 - 41) × 60 ≈ (41.352 - 41) × 60 ≈ 1.352 × 60 ≈ 81″

The result is 40°41′81″. In practical applications, you might round this to 40°41′81.2″ or 40°41′81″ depending on the required precision.

FAQ

What is the difference between decimal degrees and DMS?

Decimal degrees represent angles as a single decimal number (e.g., 40.6892°), while DMS format breaks it into degrees, minutes, and seconds (e.g., 40°41′21″). DMS is often used in navigation and cartography for better readability.

How do I convert DMS back to decimal degrees?

To convert DMS back to decimal degrees, use the formula: decimal = deg + (min/60) + (sec/3600). For example, 40°41′21″ becomes 40 + (41/60) + (21/3600) ≈ 40.6892°.

When should I use DMS format instead of decimal degrees?

DMS format is often preferred in fields like navigation, surveying, and cartography because it provides more precise fractional parts of a degree. Decimal degrees are more commonly used in calculations and digital systems.