Degrees to Degrees Minutes Seconds Converter
This degrees to degrees minutes seconds converter works in both directions. Example: 40.7128° is 40° 42′ 46.08″, and 40° 42′ 46.08″ gives 40.7128° again.
Example: Direction: Decimal degrees → degrees, minutes, seconds · Decimal degrees 40.7128 → Result: 40.7128° = 40° 42′ 46.08″. Source: Wikipedia – Degree (angle). Updated: .
How it is calculated
Angles can be written as decimal degrees (40.7128°) or as degrees, arcminutes and arcseconds (40° 42′ 46.08″). Both mean the same thing; they are often needed for coordinates and maps.
Decimal degrees to degrees, minutes, seconds
The whole number before the decimal point is the degrees. Multiply the fractional part by 60: the whole part is the minutes. Multiply the remaining fraction by 60 again to get the seconds. Seconds are rounded to two decimals; if rounding reaches 60″, the calculator carries correctly into the next minute or degree.
Back to decimal degrees
Decimal degrees = degrees + minutes / 60 + seconds / 3600. For 40° 42′ 46.08″ this gives 40 + 0.7 + 0.0128 = 40.7128°. An example with a sign: −73.9857° is 73° 59′ 8.52″ with a negative sign, because 0.9857 · 60 = 59.142′ and 0.142 · 60 = 8.52″. And 51° 30′ 26″ is 51.507222°.
- The sign applies to the whole angle, not to each unit separately.
- Minutes and seconds are always from 0 up to below 60.
- For coordinates a negative value stands for south or west.
Frequently asked questions
How do you convert decimal degrees to degrees, minutes and seconds?
Whole number = degrees; fraction · 60 = minutes; its fraction · 60 = seconds. 40.7128° becomes 40° 42′ 46.08″.
How do you convert degrees, minutes, seconds to decimal degrees?
With degrees + minutes / 60 + seconds / 3600. For 40° 42′ 46.08″ that gives 40.7128°.
How many minutes are in a degree?
A degree has 60 arcminutes and an arcminute 60 arcseconds, so one degree is 3600 arcseconds.
Sources and legal basis
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