How to convert DMS to decimal degrees

Three ways to write the same angle

• Degrees, minutes, seconds (DMS): 36°09'57.60"N. Used on paper maps, deeds and many survey documents.
• Degrees and decimal minutes (DMM): 36°09.9600'N. Common on marine and aviation GPS units.
• Decimal degrees (DD): 36.166. Used by web maps, spreadsheets and almost every API, including every data file on this site.

DMS to decimal, step by step

Divide minutes by 60 and seconds by 3,600, then add both to the whole degrees. Apply the sign last: south and west are negative.

36° 9' 57.60" N
= 36 + 9/60 + 57.60/3600
= 36 + 0.150000 + 0.016000
= 36.1660

In Excel, with degrees in A2, minutes in B2 and seconds in C2, use =A2+B2/60+C2/3600, and multiply by -1 for a west longitude.

Decimal to DMS, step by step

Take the whole number as degrees. Multiply the remaining fraction by 60; the whole part is minutes. Multiply the new fraction by 60 again for seconds. Write the hemisphere letter instead of a minus sign.

36.166
degrees = 36
0.166 × 60 = 9.9600  → 9 minutes
0.9600 × 60 = 57.60  → seconds
result: 36°09'57.60"N

Ten capitals in all three formats

Where conversions go wrong

• Applying the minus sign to degrees only. -86° 46' means -(86 + 46/60), which is -86.7667, not -86 + 0.7667.
• Reading decimal minutes as seconds. 36° 9.95' is not 36° 9' 95". Seconds never reach 60.
• Rounding too early. Each rounded second is about 101 feet of latitude. Keep full precision until the last step.
• Losing the hemisphere. A coordinate with no sign and no letter is ambiguous. For US data, longitudes should be west.

How many decimals match a second?

One second of arc is 1/3600 of a degree, or about 0.00028°. Four decimal places in decimal degrees resolve to about 11.1 meters of latitude, close to a third of a second. The decimal places guide has the full table.

Decimal minutes to decimal degrees

Degrees and decimal minutes only need one division. Take the minutes, divide by 60, add to the degrees, and apply the sign. Nashville's latitude in this form is 36°09.9600'N:

36 + 9.9600/60
= 36 + 0.166000
= 36.1660

Many marine and handheld GPS units display this format, so a waypoint copied from a boat and pasted into a web map needs this step.

Converting a whole column

When coordinates arrive as text like 36°09'57"N, split them before converting. In Excel or Google Sheets, pull out the parts with text functions, or use find and replace to turn the symbols into spaces and then split the column on spaces into degrees, minutes, seconds and hemisphere.

Then apply =A2+B2/60+C2/3600 and multiply by -1 when the hemisphere column says S or W. Check a few rows against the GPS coordinate converter before trusting the column. A single missing minus sign sends a point to the other side of the world, which is easy to spot on a map and easy to miss in a table.

Reading coordinates off a paper map

Topographic maps mark latitude and longitude along their edges with tick marks. To read a point, measure its position between the two nearest ticks, turn that fraction into minutes and seconds, then convert to decimal. A second of latitude is about 101 feet, so reading to the nearest second on paper is already a precise result.

A quick sanity check

After converting, the decimal value should sit between the whole degree and the next one: 36° 9' must land between 36 and 37. Minutes of 30 put you at the halfway mark, .5, and 15 minutes at .25. If the result falls outside that range, a minute or second value was probably entered in the wrong column.