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Degrees Minutes Seconds Converter Calculator

Work out degrees minutes seconds converter instantly with clear inputs, formula shown and shareable results.

About Degrees Minutes Seconds Converter Calculator

Degrees, minutes and seconds are a sexagesimal system: sixty seconds to the minute and sixty minutes to the degree. So 45 degrees 22 minutes 30 seconds is 45.375 degrees, or 0.79195 radians. The negative case applies the sign to the whole angle rather than to each component, which is the convention for latitude and longitude.

Formulas

Decimal degrees

DD = degrees + minutes/60 + seconds/3600

Radians

rad = degrees x pi / 180

Worked example

With the default values below, Degrees Minutes Seconds Converter Calculator returns Decimal Degrees of 45.375000. Change any input above and every figure here is recalculated in your browser.

Inputs used

Degrees
45
Minutesaccepts 0–59.999
22
Secondsaccepts 0–59.999
30

Results

Decimal Degrees
45.375000 deg
Same Angle In Radians
0.791943
Total Arc Seconds
163,350.00 arcsec
Decimal Minutes
22.5000

Step by step

  1. 1Values used
  2. 2Decimal degrees
  3. 3Radians
  4. 4Decimal Degrees= 45.375000 deg
  5. 5Same Angle In Radians= 0.791943
  6. 6Total Arc Seconds= 163,350.00 arcsec
  7. 7Decimal Minutes= 22.5000

Assumptions and limits

  • The result is derived only from the 3 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 6 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 do I handle southern latitudes?

Enter the degrees as negative. The sign is applied to the total, so -33 degrees 52 minutes reads as -33.8667 rather than -33 plus 52 minutes.

Why is the system base 60?

It descends from Babylonian mathematics, which used base 60 because it divides evenly by 2, 3, 4, 5 and 6 - convenient before decimals existed.

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