GPS Coordinate Converter

Convert GPS coordinates without second-guessing the format

GPS coordinates all point to the same kind of thing: a location on Earth. The confusion usually comes from the way that location is written. A phone app may show a latitude like 40.689247, while a field note, marine chart, or handheld receiver may write the same place as 40° 41′ 21.29″ N. Both are valid. One is decimal degrees, which packs the full angle into a single number. The other is degrees, minutes, and seconds, usually shortened to DMS, which breaks the same angle into three pieces. This calculator helps you move cleanly between those notations so you can copy coordinates into the format required by a map, spreadsheet, navigation device, GIS tool, survey document, or programming workflow.

That sounds simple, but small notation mistakes can send a point far away from where you intended. A lost hemisphere letter can move a point from north to south. Treating minutes as if they were base-10 decimals instead of sixtieths shifts the position. Rounding too early can also matter when you are marking a trailhead, exporting data to software, or comparing coordinates from different sources. A converter is helpful because it keeps the place-value rules consistent and gives you a quick way to check whether the number you plan to use is plausible before you paste it somewhere else.

This page includes two practical tools. The first form converts DMS into decimal degrees. The second form does the reverse and breaks a decimal value back into degrees, minutes, and seconds. In both cases, the result also includes radians because many trigonometric formulas, geodesy routines, and mapping libraries expect angular values in radians rather than degrees. If you are moving between navigation notes and code, that extra line saves a step.

How the two coordinate styles relate

Think of decimal degrees as the compact version. A value like 51.500833° N stores the whole latitude in one number. DMS is the expanded version: 51° 30′ 3″ N. The degree is the large unit, the minute is one-sixtieth of a degree, and the second is one-sixtieth of a minute. That means one second is one 3,600th of a degree. Once you remember that base-60 structure, the conversions become straightforward.

Hemisphere matters just as much as the number itself. For latitude, use N for north of the equator and S for south of the equator. For longitude, use E for east of the prime meridian and W for west of it. In decimal form, north and east are positive; south and west are negative. So 74.044502° W corresponds to -74.044502 in signed decimal notation. This calculator uses the hemisphere menu to capture that sign choice clearly.

Ranges also help with quick sanity checks. Latitude normally runs from 0 to 90 degrees with a hemisphere of N or S. Longitude normally runs from 0 to 180 degrees with a hemisphere of E or W. Minutes and seconds should usually be between 0 and 59.999…. If you see 75 minutes or 90 seconds, the value probably needs to be carried into the next larger unit before conversion.

How to use the converter on this page

If you already have degrees, minutes, and seconds, use the first form. Enter the degree count, then the minutes and seconds, and choose the hemisphere. Press Convert to Decimal to get the decimal degree result plus the angle in radians. This is the common direction when you are copying a coordinate from a paper source into software that expects decimal numbers.

If you start with a decimal value, use the second form. Enter the decimal degrees and choose the hemisphere you want displayed in the result. Then press Convert to DMS. This is useful when a GPS app gives a decimal value but you need a more traditional DMS readout for a report, a checklist, or manual navigation notes.

• Use the correct hemisphere family: N or S for latitude, E or W for longitude.
• Keep minutes and seconds nonnegative: the direction should be carried by the hemisphere selector, not by negative minutes or seconds.
• Check the range: latitude should not exceed 90°, and longitude should not exceed 180°.
• Read the sign carefully: a west or south result should correspond to a negative decimal angle.

The copy buttons below each result make it easier to move values into another document or application after you confirm the output looks right.

What each input means in plain language

Degrees are the whole-number part of the angle. They tell you the broad position. A longitude of 74 degrees west is already in the right general neighborhood for New York Harbor even before you add minutes and seconds.

Minutes divide one degree into 60 equal parts. They are not decimal hundredths. If you add 30 minutes, you are adding half a degree, not 0.30 degrees. That distinction is one of the most common sources of conversion mistakes.

Seconds divide one minute into 60 equal parts. They fine-tune the coordinate. In DMS notation, seconds may be integers or decimals. A value such as 21.29 seconds is perfectly normal. The first form on this page accepts decimal seconds because real GPS and surveying data often use them.

Hemisphere tells the converter which side of the equator or prime meridian the coordinate sits on. It is the directional sign. North and east are positive. South and west are negative. If the magnitude looks correct but the point lands on the wrong side of the world, the hemisphere is the first thing to check.

One more practical note: this page converts one angle at a time. A full location usually needs two coordinates, one latitude and one longitude. You can run the calculator twice, once for each value. That is normal, and it often makes checking easier because you can focus on whether each coordinate uses the correct hemisphere family and range.

Formulas behind the conversion

For this calculator, the DMS-to-decimal formula is the key relationship. Start with the absolute degree count, then add the minutes divided by 60 and the seconds divided by 3,600. Finally, apply a negative sign for south or west.

If the hemisphere is S or W, the signed decimal value becomes negative. That sign is what many APIs and spreadsheets use internally.

To go the other way, take the absolute value first. The whole-number part becomes degrees. Multiply the remaining fractional part by 60 to get total minutes. The whole-number part of that result becomes minutes. Multiply the leftover fraction by 60 again to get seconds.

The page also shows radians. That conversion is simply degrees multiplied by π divided by 180. It matters in coding, geometry, and distance formulas on spheres because trigonometric functions almost always expect radians.

If you like thinking about calculators in a broader way, the converter still fits the usual pattern of inputs flowing into a consistent rule. The following MathML blocks were already part of this page and still describe that more general idea:

For GPS coordinates, the important part is that the function is deterministic. The same DMS input should always become the same decimal output, and vice versa, as long as the hemisphere and rounding rules are the same.

Worked examples you can check by hand

Suppose you have the latitude 40° 26′ 46″ N. Divide 26 by 60 to get 0.433333…, and divide 46 by 3,600 to get 0.012778…. Add those to 40 and you get 40.446111… degrees north. In signed decimal notation that stays positive because the hemisphere is north. If you also want radians, multiply 40.446111 by π/180 to get about 0.705922 radians.

Now go in the opposite direction with 79.982222° W. The whole-number part is 79 degrees. The fractional part, 0.982222, multiplied by 60 gives 58.93332. That means 58 minutes and a leftover fraction of 0.93332 minute. Multiply that remainder by 60 and you get about 55.9992 seconds, which rounds to 56 seconds. The DMS form is therefore 79° 58′ 56″ W.

These examples are worth imitating when you verify your own data. If the minutes and seconds look small, the decimal fraction should also be modest. If the decimal fraction is large, the DMS result should show substantial minutes or seconds rather than a nearly whole degree.

How to interpret the result

After conversion, read the result as a coordinate value, not just a number. The hemisphere or sign tells you direction. The decimal places tell you precision. A decimal degree rounded to four places is useful for many everyday mapping tasks, while more places keep finer detail. In latitude, each additional decimal place represents a much smaller change in position. Longitude spacing also depends on latitude, but the same general lesson holds: extra decimals are meaningful when you need more precise location data.

The radians value is not a second opinion on the coordinate. It is the same angle written in a different unit. If you are building a script, using a geospatial formula, or feeding the value into trigonometric functions, that radians line is often exactly what you need next.

If the output surprises you, do a quick sense check. A southern or western coordinate should be negative in signed decimal terms. A DMS value with 59 minutes and 59 seconds should be just shy of the next full degree. A value near zero should stay near the equator or prime meridian. These rough checks catch many copying and sign errors immediately.

Common mistakes and assumptions

The most common mistake is reading DMS as if the minute and second fields were base-10 decimals. They are not. Writing 12° 30′ as 12.30° is wrong because 30 minutes is half a degree, so the correct decimal value is 12.5°. The second common mistake is mixing up hemisphere and sign. If a source says W but you record a positive decimal value, your point shifts east. The third common mistake is using the wrong hemisphere family, such as choosing N for a longitude. That is a labeling issue rather than a math issue, but it matters just as much.

This converter also makes a few practical assumptions. It treats the input as a plain angular conversion only. It does not change map datums, transform between coordinate systems such as UTM and latitude/longitude, or correct for projection differences. So if two sources disagree because they use different datums or grids, a DMS-versus-decimal conversion alone will not solve that mismatch.

Rounding is another subtle point. When a decimal value is converted back into DMS, the seconds field may show a rounded result. That is normal. A coordinate written as 10.123456 degrees cannot always be represented with a neat whole-number second count unless you accept a tiny amount of rounding. The important question is whether the precision suits your task.

• Use this tool for format conversion, not for changing coordinate systems.
• Check hemisphere first when a result lands on the wrong side of the world.
• Check minutes and seconds next when the result is close but not quite right.
• Keep source precision in mind: a rounded input produces a rounded output.

In practice, the best workflow is simple: copy the number carefully, choose the correct hemisphere, convert, and then compare the result against your mental picture of the location. If the coordinate should be near London, you should not end up with a west longitude that belongs near the Pacific. If the coordinate came from a latitude field, it should not exceed 90 degrees. Those sanity checks are quick, and they prevent most downstream mistakes.