Worked guide · geographic angle notation

The same pair,
written with care.

Changing decimal degrees to degrees, minutes and seconds is arithmetic on angles. A useful conversion keeps each axis separate, applies the sign to the full angle and explains when a displayed number has been rounded.

Identify latitude and longitude before entering values

Coordnote accepts one pair with latitude in its own labelled field and longitude in another. It does not guess which came first in a pasted string. Latitude magnitudes run from zero to 90 degrees, while longitude magnitudes run from zero to 180 degrees. This converter uses positive decimal latitude for north and negative for south; positive decimal longitude means east and negative means west.

The USGS Landsat data dictionary documents these latitude and longitude ranges and explicit hemisphere characters in its decimal and DMS field descriptions. That is useful format context, rather than a claim that this general-purpose tool implements a Landsat product specification. Always check the order and sign convention of the source and destination form you are using.

Degrees, minutes and seconds are angle units

There are 60 arcminutes in a degree and 60 arcseconds in an arcminute. These names describe angular subdivisions here. They are not elapsed minutes or seconds on a clock. One arcsecond is therefore 1/3600 of a degree, and 30 arcminutes are half a degree.

Apply the sign after combining all three components. A southern angle of 12 degrees, 30 minutes and zero seconds has magnitude 12.5 degrees and signed value −12.5. Subtracting only the whole-degree part would give a different and incorrect result. The same rule matters when the degree component is zero, because the minutes or seconds can still represent a nonzero southern or western angle.

Extract DMS from an exact magnitude

Take the whole-degree quotient from the nonnegative angle magnitude. Multiply the remainder by 60 and take the whole-minute quotient. Multiply that remaining fractional minute by 60 to obtain seconds. The sign never becomes a negative minute or second component; it is represented by the explicit N/S or E/W selector.

Coordnote parses entered decimals as exact rational numbers made from integer numerators and denominators. Thus 12.5 becomes 25/2 degrees, while one second becomes 1/3600 degree. The core conversion does not repeatedly approximate the fraction with binary floating-point numbers. Human-readable decimal and DMS output is rounded separately at the precision you select.

South and west within the first degree

A whole-degree component of zero does not determine hemisphere. Latitude 0° 00′ 01″ S is exactly −1/3600 degree. Longitude 0° 00′ 01″ W has the same signed angular value on the other axis. At ten decimal places both display approximately −0.0002777778°, with the minus sign intact.

What a minus sign on exact zero means

The typed strings −0 and 0 have the same numerical angle. Coordnote nevertheless preserves a lexical minus on exact DD zero as a south or west notation tag, depending on the axis. An explicit DMS S or W selection at all-zero components is preserved in the same way. This does not create a second physical equator or prime meridian.

The report distinguishes the exact magnitude, the signed representation, the hemisphere tag and original input provenance. Format-only switches retain that provenance. A direct edit establishes a new angle for the edited axis from the currently visible fields. The untouched axis retains its canonical value even if its converted display was rounded.

Round seconds, then normalize the carry

Rounding is applied to the total magnitude in arcseconds at the selected second precision. The rounded total is then split into degrees, minutes and seconds. This automatically carries a displayed 60-second boundary into the next minute and a 60-minute boundary into the next degree. Output never leaves an unnormalized 60 in either component.

Magnitude rounding is half up: a value exactly halfway between display steps rounds to the larger nonnegative magnitude, and its original sign is applied afterwards. This convention is a formatting choice. It does not change the source measurement or imply that any particular digit is accurate in the real world.

Typed 60 is a validation error

Input DMS degrees and minutes must be unsigned whole numbers. Seconds must be a nonnegative plain decimal below 60. A typed value of 60 seconds is rejected, even though normalized output can carry a rounded value across that boundary. Typed 60 minutes is also invalid. This separation helps catch an accidental unit or field mistake rather than quietly guessing the intended normalization.

Latitude at exactly 90 degrees and longitude at exactly 180 degrees require zero minutes and seconds. For example, 90° 00′ 00″ S is accepted, but 90° 00′ 00.000001″ S is outside the allowed latitude range. Decimal values 90.0001 and 180.0001 are rejected on their respective axes. The longitude +180 and −180 representations are retained explicitly and label the same antimeridian; there is no automatic wrap to another range.

Switch formats using valid active fields

The input-format selector converts only when the current active pair is valid. If a field is blank or outside its bounds, the selector returns to the current format, the problem is explained, and old results and exports remain unavailable. A previously valid hidden form cannot replace invalid active data. Correct the field first.

Converted fields use up to twelve decimal-degree places or six decimal second places. Repeating fractions may therefore need a rounded visible entry. Internally, each unchanged axis keeps its exact prior angle through repeated switches. Editing any coordinate field for that axis deliberately replaces the cache with a new angle interpreted from its currently visible format. Precision selectors change output formatting and do not change the canonical pair.

Reference conventions need to stay explicit

The NOAA NGS OPUS API documentation gives decimal-degree and explicit-hemisphere DMS examples, including negative-west longitude. Coordnote follows an explicitly stated positive-east decimal convention locally. It does not call OPUS or accept the API's packed coordinate strings; its separate fields avoid that string-format ambiguity.

A notation conversion does not transform a datum, reference frame, epoch or map projection. A source described as WGS84 is not validated by typing its numbers here, and an unspecified source remains unspecified. No UTM/grid, altitude, geodesic distance or coordinate-system transformation is performed. At a pole, longitude's representational role also needs source context; the calculator simply retains your entered angular pair without claiming a distinct ground location.

Keep useful precision and a reproducible report

Decimal-degree displays offer 6, 8, 10 or 12 places. DMS seconds offer 0, 2, 4 or 6 places. Inputs accept at most twelve decimal places with no commas, exponent notation or combined hemisphere letters. DD permits an optional leading plus or minus; DMS components permit no sign, including a typed minus on zero. The hemisphere selector supplies the complete DMS sign.

Copy, text and CSV reports are generated locally and retain exact rational degrees, explicit hemisphere tags and canonical input provenance alongside rounded representations. They are reference records, without a map link or automatic coordinate submission. Changing an input clears old results and export availability; Restore returns the illustrative pair. More output digits preserve arithmetic detail but cannot improve the accuracy, age or reference information of the source measurement.