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Decimal Degrees Converter

Convert degrees, minutes and seconds into decimal degrees.

About Decimal Degrees Converter

Minutes and seconds are sixtieths and thirty-six-hundredths of a degree, so the conversion is two divisions and an addition. Direction supplies the sign that decimal notation encodes numerically. One arc second of latitude is about 31 metres, which sets the practical precision needed when transcribing coordinates by hand.

Formula

Decimal Degrees

Decimal degrees = degrees + minutes ÷ 60 + seconds ÷ 3,600, signed by direction

arc second
One 3,600th of a degree, about 31 metres of latitude
sign convention
South and west are negative

Worked example

With the default values below, Decimal Degrees Converter returns Decimal Degrees of 40.446200. Change any input above and every figure here is recalculated in your browser.

Inputs used

Degreesaccepts 0–180 degrees
40 degrees
Minutesaccepts 0–59 min
26 min
Secondsaccepts 0–59.999 s
46.32 s
Directionone of North, South, East, West
North

Results

Decimal Degrees
40.446200 degrees
Radians
0.70591936 rad
Total Arc Seconds
145,606.32 s
Sign Applied
Positive, north or east of the origin
Approximate Metres per Degree
110,574 m

Step by step

  1. 1Values used
  2. 2Decimal Degrees
  3. 3Decimal Degrees= 40.446200 degrees
  4. 4Radians= 0.70591936 rad
  5. 5Total Arc Seconds= 145,606.32 s
  6. 6Sign Applied= Positive, north or east of the origin
  7. 7Approximate Metres per Degree= 110,574 m

Assumptions and limits

  • The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How is Decimal Degrees calculated?

Decimal degrees = degrees + minutes ÷ 60 + seconds ÷ 3,600, signed by direction Minutes and seconds are sixtieths and thirty-six-hundredths of a degree, so the conversion is two divisions and an addition. Direction supplies the sign that decimal notation encodes numerically.

Why does Decimal Degrees matter?

One arc second of latitude is about 31 metres, which sets the practical precision needed when transcribing coordinates by hand.

What values do I need to enter?

This calculator takes 4 inputs: Degrees, Minutes, Seconds, Direction. The pre-filled defaults are a realistic starting point — replace them with figures from your own environment for a result you can act on.

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