DMS Coordinate Converter

Convert decimal degrees to degrees, minutes and seconds with rounding control.

About DMS Coordinate Converter

Each conversion step takes the fractional remainder and multiplies by sixty. Rounding the seconds introduces a small error, which the round-trip figure quantifies. Rounding seconds to whole numbers loses up to fifteen metres of precision, which matters for property boundaries but not for navigation.

Formula

DMS Coordinate

Degrees is the integer part; minutes and seconds come from successive multiplication by 60

sexagesimal: Base-60 notation inherited from Babylonian astronomy
round-trip error: Precision lost when seconds are rounded

Worked example

With the default values below, DMS Coordinate Converter returns DMS Notation of -33° 52' 2.95". Change any input above and every figure here is recalculated in your browser.

Inputs used

Decimal degreesaccepts -180–180 degrees: -33.867487 degrees
Decimal places on secondsaccepts 0–4: 2

Results

DMS Notation: -33° 52' 2.95"
Degrees: 33 degrees
Minutes: 52 min
Seconds: 2.9532 s
Round-Trip Error After Rounding: 0.000000889 degrees

Step by step

1Values used
2DMS Coordinate
3DMS Notation= -33° 52' 2.95"
4Degrees= 33 degrees
5Minutes= 52 min
6Seconds= 2.9532 s
7Round-Trip Error After Rounding= 0.000000889 degrees

Assumptions and limits

The result is derived only from the 2 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 9 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 DMS Coordinate calculated?

Degrees is the integer part; minutes and seconds come from successive multiplication by 60 Each conversion step takes the fractional remainder and multiplies by sixty. Rounding the seconds introduces a small error, which the round-trip figure quantifies.

Why does DMS Coordinate matter?

Rounding seconds to whole numbers loses up to fifteen metres of precision, which matters for property boundaries but not for navigation.

What values do I need to enter?

This calculator takes 2 inputs: Decimal degrees, Decimal places on seconds. The pre-filled defaults are a realistic starting point — replace them with figures from your own environment for a result you can act on.