Degrees, Minutes, Seconds to Decimal Calculator

Enter degrees, minutes, and seconds to convert them to degrees in decimal form.

How to Convert Degrees, Minutes, Seconds to Decimal

Angles can be expressed as degrees, minutes, and seconds (DMS) or in degree decimal (DD) form. One degree is equal to 60 minutes or 3,600 seconds, and one minute is equal to 60 seconds.

To convert an angle in DMS form to decimal form, convert both the minutes and seconds to fractions of a degree, and then add them to the whole number of degrees.

Step One: Convert Minutes to Decimal Degrees

Minutes are expressed using the prime symbol (′). Minutes can be converted to decimal form by dividing them by 60 since there are 60 minutes in a degree.

decimal = minutes ÷ 60

Step Two: Convert Seconds to Decimal Degrees

Seconds are expressed using the double-prime symbol (″). Seconds can be converted to decimal form by dividing them by 3,600 since there are 3,600 seconds in a degree.

decimal = seconds ÷ 3,600

Step Three: Add Degrees, Minutes, & Seconds

Once the minutes and seconds have been converted to degrees, the final step to convert to decimal form is to add them to the whole degrees. Thus, the decimal value is equal to the whole degrees plus the converted minutes plus the converted seconds.

Degrees, Minutes, Seconds to Decimal Formula

Summing it all up, the formula to convert DMS to decimal is:

decimal = degrees + (minutes ÷ 60) + (seconds ÷ 3,600)

For example, let’s convert 60° 35′ 15″ to decimal form.

decimal = 60 + (35′ ÷ 60) + (15″ ÷ 3,600)
decimal = 60 + 0.583333 + 0.004167
decimal = 60.5875°

Thus, 60° 35′ 15″ is equal to 60.5875°.

graphic showing how the equation to convert degrees, minutes, and seconds to decimal works

You might also be interested in our calculator to convert decimal degrees to degrees, minutes, and seconds.

Frequently Asked Questions

Are DMS and DD the same thing?

DMS (Degrees, Minutes, Seconds) and DD (Decimal Degrees) are just two different formats to represent the same value of an angle.

Why are degrees divided into minutes and seconds?

Degrees are divided into minutes and seconds to represent angles for historical reasons dating back to the sexagesimal system developed by the Babylonians.

Are decimal degrees more precise than minutes and seconds?

Decimal degrees are just as accurate as minutes and seconds as long as no rounding is done when calculating the number of minutes and seconds from decimal degrees or vice versa.