Convert latitude or longitude between degrees minutes seconds and decimal degrees with clear direction rules, range checks, and copy-ready outputs.
Advanced options
How to use our Degrees Minutes Seconds Calculator
- Choose Convert from and Coordinate type first so the calculator knows whether to use latitude rules or longitude rules.
- Enter either Degrees, Minutes, Seconds, and Direction, or enter Decimal degrees, depending on the mode you picked.
- If needed, open Advanced options and set Decimal places for seconds, Decimal places for decimal degrees, or Decimal-degree style.
- Click Calculate, then copy Converted coordinate or Same coordinate in the other common style based on what your map, form, or worksheet asks for.
- Sanity-check Range check and Normalized DMS before using the answer, especially if seconds rounded up or if the coordinate is near 90 degrees latitude or 180 degrees longitude.
Definitions
Degrees minutes seconds (DMS): A coordinate written in three parts, like 40 degrees, 26 minutes, 46 seconds.
Decimal degrees: A coordinate written as one decimal number, like 40.446111.
Direction: The hemisphere letter. Latitude uses N or S. Longitude uses E or W.
Signed decimal degrees: Decimal degrees where positive means North or East, and negative means South or West.
Decimal degrees with direction letter: A positive decimal number shown with N, S, E, or W instead of a negative sign.
Normalized DMS: A cleaned-up DMS result after rounding, so 60 seconds carries into the next minute and 60 minutes carries into the next degree.
Range check: A quick validity test that confirms the value fits the allowed latitude or longitude range.
Common mistakes and quick fixes
Mistake: Typing a negative number in Degrees while also choosing South or West in Direction .
Fix: In DMS mode, keep Degrees non-negative and let Direction set the sign.
Mistake: Entering 60 or more in Minutes .
Fix: Keep Minutes from 0 up to less than 60, then put any extra amount into Degrees instead.
Mistake: Entering 60 or more in Seconds .
Fix: Keep Seconds from 0 up to less than 60; the calculator only rolls over after rounding the final DMS result.
Mistake: Choosing East or West in Direction when Coordinate type is latitude, or North or South for longitude.
Fix: Match Direction to Coordinate type : latitude uses N or S, longitude uses E or W.
Mistake: Entering a latitude above 90 or a longitude above 180 in Decimal degrees or Degrees .
Fix: Check Coordinate type and stay within the valid limit shown by Range check .
Mistake: Copying the wrong output style for another app or form.
Fix: Use Signed decimal degrees when negative values are allowed, or use Decimal degrees with direction letter when a form wants N, S, E, or W.
Limitations & Key Assumptions / Boundary Conditions
- This calculator converts one coordinate at a time, either a latitude or a longitude, not a full coordinate pair or a map location.
- It checks format ranges only: latitude must stay within 0 to 90 degrees and longitude within 0 to 180 degrees by direction or sign.
- In DMS mode, Minutes and Seconds must be from 0 up to less than 60 before conversion.
- Rounding can change the displayed DMS parts, so a value near 59.9999 seconds may carry into the next minute or degree.
- The result format may still need to match the exact punctuation or spacing required by your map app, worksheet, or field form.
- Negative zero is displayed as 0 for readability, while the hemisphere still follows the entered direction or decimal sign rules.
Methodology
How the calculator converts coordinates
For DMS input, the calculator turns degrees, minutes, and seconds into one decimal-degree value, then applies the sign from Direction. North and East are positive. South and West are negative.
decimal_degrees = sign * (abs(degrees) + minutes/60 + seconds/3600)
For decimal-degree input, the calculator uses the absolute value to split the number into whole degrees, whole minutes, and remaining seconds. The sign decides the direction letter based on latitude or longitude.
abs_dd = abs(decimal_degrees)
degrees = floor(abs_dd)
rem1 = (abs_dd - degrees) * 60
minutes = floor(rem1)
seconds = (rem1 - minutes) * 60
Rollover after rounding
If rounding makes the seconds display equal to 60, the calculator carries that extra amount into minutes. If minutes then reaches 60, it carries into degrees. This keeps the final DMS output in normal form.
if rounded_seconds = 60 then rounded_seconds = 0 and minutes = minutes + 1
if minutes = 60 then minutes = 0 and degrees = degrees + 1
Mini example
Example:
40 degrees, 26 minutes, 46 seconds North becomes 40 + 26/60 + 46/3600 = 40.446111, so the signed decimal result is 40.446111. If the same DMS value were West longitude, the signed decimal result would be negative.
Validation and interpretation
The calculator blocks DMS entries with negative Degrees, or with Minutes or Seconds outside 0 to less than 60. It also checks that latitude stays within 90 degrees and longitude stays within 180 degrees. Standard tools and examples commonly use both decimal degrees and DMS formats for geographic coordinates [2][3].
Assumptions used
The calculator treats the input as a geographic latitude or longitude only. It does not convert datums, map projections, UTM, or distance and bearing values. Real apps may also require a specific coordinate order, punctuation style, or number of decimal places.