Coordinates Converter — Decimal Degrees and DMS

Background.

Geographic coordinates are often written in two equivalent notations. Decimal degrees put the whole angle in one signed number, such as −1.286389°. Degrees-minutes-seconds, usually shortened to DMS, splits the same angle into whole degrees, arcminutes and arcseconds and replaces the sign with a cardinal hemisphere, such as 1° 17′ 11.0004″ S. This calculator converts one labelled latitude or longitude component between those forms.

The coordinate type matters. Latitude measures north or south of the equator and is limited to 90 degrees in either direction. Longitude measures east or west of the prime meridian and is limited to 180 degrees. A negative latitude maps to S, a negative longitude maps to W, while positive values map to N or E. Zero has no negative direction, so this page displays zero latitude as N and zero longitude as E.

DMS is sexagesimal. One degree contains 60 arcminutes and one arcminute contains 60 arcseconds. To convert DMS to decimal, divide minutes by 60 and seconds by 3,600, add both to the whole degrees, then apply the hemisphere sign. South and west are negative; north and east are positive.

The reverse starts with the absolute decimal value. Keep its whole-number part as degrees. Multiply the remaining fraction by 60 and keep the whole part as minutes. Multiply the remaining minute fraction by 60 to obtain seconds. The original sign and coordinate type determine the final cardinal letter.

This page is deliberately stricter than a general angle converter. DMS degrees must be non-negative because direction belongs to the hemisphere field. Minutes must be a whole number from 0 through 59, seconds must be at least zero and below 60, and a coordinate exactly at a pole or antimeridian endpoint cannot carry extra minutes or seconds. Latitude also rejects the otherwise valid angle 120° because it lies outside the geographic range.

The conversion changes notation only. It does not change the coordinate reference system, datum, map projection or axis order. A point expressed in NAD83, ETRS89 or a local datum does not become WGS 84 merely because its degrees are rearranged. Use the dedicated latitude/longitude-to-UTM calculator only when the source coordinates are explicitly WGS 84 and a projected easting and northing are needed.

Precision deserves restraint. One decimal degree covers a large ground distance; extra digits can imply metre or centimetre accuracy. This converter faithfully carries the number entered, but it cannot improve the survey, receiver or map that produced it. Seconds are rounded to ten decimal places only at the output boundary, and a value that rounds to 60 is correctly carried into the next minute.

Longitude at +180° and −180° describes the same antimeridian from opposite sign conventions. The page preserves the sign-derived E or W label rather than wrapping it. Likewise, it does not combine latitude and longitude into one text string, so it cannot silently reverse axis order—a real interoperability problem because different systems publish lat/long and long/lat.

The worked example uses a latitude near central Nairobi. −1.286389° becomes 1° 17′ 11.0004″ S and converts back exactly at the displayed precision. The focused tests repeat that round trip for coordinates in both hemispheres and test the poles and antimeridian directly.

What is coordinates converter?

A geographic coordinate component is an angular position relative to the equator or prime meridian. Decimal degrees write the angle as one signed value. DMS writes the same value as whole degrees, arcminutes and arcseconds plus N, S, E or W. Conversion preserves the angle and datum; it changes only notation.

How to use this calculator.

1. 01Choose decimal-to-DMS or DMS-to-decimal mode.
2. 02Label the component as latitude or longitude so the correct limits and hemispheres apply.
3. 03Enter either the signed decimal value or non-negative DMS components and a compatible cardinal direction.
4. 04Read both forms and retain only the precision justified by the source measurement.
5. 05Do not treat this notation conversion as a datum or map-projection transformation.

The formula.

For DMS input, add whole degrees, minutes divided by sixty, and seconds divided by 3,600. Apply a negative sign for south or west. For decimal input, operate on the absolute value: floor it for degrees, multiply its fraction by sixty for minutes, then multiply the remaining fraction by sixty for seconds. The original sign maps to a hemisphere based on whether the component is latitude or longitude.

For −1.286389° latitude, the absolute remainder after one degree is 0.286389. Multiplying by 60 gives 17.18334, so minutes are 17. The remaining 0.18334 multiplied by 60 is 11.0004 seconds. Decimal.js carries the arithmetic and outputs round once to ten decimal places.

A worked example.

Frequently asked questions.

References& sources.

1. [1]USGS/NASA Technical Methods 11-E1 §§2.33–2.35 publishes decimal-degree and DMS conversion procedures.
2. [2]FCC Degrees, Minutes, Seconds to/from Decimal Degrees independently gives D + M/60 + S/3600.
3. [3]NGA coordinate-system reference documents sexagesimal coordinate notation and hemispheres.
4. [4]ISO 6709:2022 defines standard representation of geographic point locations by coordinates.
5. [5]EPSG Guidance Note 7 explains that datum, coordinate reference system and axis order are separate from numeric notation.