Dms To Decimal Degrees CalculatorFree online math calculator — instant results, no sign-up
Convert signed degrees, minutes and seconds to decimal degrees.
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About the Dms To Decimal Degrees Calculator
The Dms To Decimal Degrees Calculator converts an angle entered as signed whole degrees, minutes, and seconds into decimal degrees. It combines the fractional-degree contributions of minutes and seconds with the degree magnitude, then applies the sign of the degrees entry to the entire angle. With the default inputs of 40 degrees, 26 minutes, and 46 seconds, the result is 40.4461111111 decimal degrees.
- Signed whole degrees
- The whole-degree component of the angle, measured in degrees, with its sign specifying the sign of the entire angle; the default is 40.
- Minutes
- The arcminute component of the angle, normally from 0 up to but not including 60, where each arcminute equals 1/60 of a degree; the default is 26.
- Seconds
- The arcsecond component of the angle, normally from 0 up to but not including 60, where each arcsecond equals 1/3600 of a degree; the default is 46.
Formula and method
DD = s × (|D| + M/60 + S/3600), where s = −1 for a negative degrees entry and +1 otherwise. For the default inputs: DD = +1 × (|40| + 26/60 + 46/3600) = 40.4461111111, rounded to 10 decimal places.
- DDThe resulting angle in decimal degrees.
- DThe signed whole-degree input; |D| is its nonnegative magnitude.
- MThe nonnegative minutes input, measured in arcminutes.
- SThe nonnegative seconds input, measured in arcseconds.
- sThe sign applied to the entire angle, taken from the signed degrees entry.
Divide the minutes by 60 and the seconds by 3600 to express both components in degrees. Add these contributions to the absolute value of the whole degrees, then apply the degrees entry's sign to the total. For the defaults, 40 + 26/60 + 46/3600 gives 40.4461111111 when rounded to 10 decimal places.
Worked example
These are the calculator's starting values and the results it actually produces for them.
Inputs
- Signed whole degrees40
- Minutes26
- Seconds46
Results
- Result40.4461111111
How to use the Dms To Decimal Degrees Calculator
- 1Enter the signed whole-degree component in Signed whole degrees; use 40 for the worked example.
- 2Enter the nonnegative arcminute component in Minutes; use 26 for the worked example.
- 3Enter the nonnegative arcsecond component in Seconds; use 46 for the worked example.
- 4Run the calculation to combine the three components into decimal degrees.
- 5Read the Result row: the default inputs produce 40.4461111111 decimal degrees.
Reading your result
The Result row reports the complete signed angle in decimal degrees, not separate degree, minute, and second components. For the default inputs, 40.4461111111 means 40 whole degrees plus the fractional degree contributed by 26 arcminutes and 46 arcseconds. A negative result indicates a negative angle; a compass direction requires a separate coordinate convention.
Limitations
This conversion assumes whole degrees and nonnegative minutes and seconds, with each of the latter components below 60 in standard DMS notation. Do not enter negative minutes or seconds to indicate direction. A negative angle whose whole-degree magnitude is zero requires a reliably preserved negative-zero entry or a separate sign control; do not assume this calculator supports that case. Display rounding does not increase the precision of the original measurements. The conversion alone does not validate latitude or longitude ranges, assign a hemisphere, or transform a coordinate reference system.
Common questions
Why are minutes divided by 60 and seconds by 3600?+
One degree contains 60 arcminutes, and each arcminute contains 60 arcseconds, so one degree contains 3600 arcseconds. These divisions express both smaller angular units as fractions of a degree.
Does a negative degrees entry also make the minutes and seconds negative?+
Yes—the degrees entry's sign applies to the combined angle magnitude. Keep the minutes and seconds nonnegative; the calculator applies the negative sign after adding their fractional-degree contributions.
Why does 40 degrees, 26 minutes, and 46 seconds produce 40.4461111111?+
The calculator adds 26/60 and 46/3600 to 40. The exact result has a repeating decimal expansion, which rounds to 40.4461111111 at 10 decimal places.
Can I use this calculator for latitude and longitude?+
Yes, convert each coordinate separately. Under the usual geographic convention, north and east are positive, while south and west are negative. Check coordinate bounds separately, and be cautious with negative coordinates whose whole-degree component is zero because negative-zero handling is not guaranteed.
Does the calculator save my information?+
Calculations run in your browser. While signed in, inputs and results are automatically recorded in account history; saving a result creates a separate saved record.
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Results are estimates for informational purposes and are not financial, medical or legal advice.