Converting Latitude and Longitude Between DMS and Decimal: Reading Exif Values and Precision by Digits

The same place has many latitude and longitude notations

Latitude and longitude express an angle in degrees. Notations differ in whether finer parts than 1 degree are shown as base-60 minutes and seconds, or as a decimal. Using the area around Tokyo Station as an example, the common notations are as follows.

All five point to the same spot. Only the notation differs, and you can convert back and forth between them.

Converting DMS to decimal

1 degree = 60 minutes and 1 minute = 60 seconds, so divide minutes by 60 and seconds by 3,600, and add them to the degrees.

1. 1

   Set up the formula

   Decimal degrees = degrees + minutes ÷ 60 + seconds ÷ 3,600

2. 2

   Enter the numbers

   For 35 degrees 40 minutes 52.45 seconds: 35 + 40 ÷ 60 + 52.45 ÷ 3,600 = 35 + 0.666667 + 0.014569 = 35.681236

3. 3

   Add a minus sign for south and west

   In decimal, north and east are positive, and south and west are negative. Forget the sign for somewhere west like New York, and you'll point to 74 degrees east in Central Asia, near the border between Kyrgyzstan and China.

Converting decimal to DMS

1. 1

   The whole number part is the degrees

   For 35.681236, it's 35 degrees.

2. 2

   The whole number part of the decimal × 60 is the minutes

   0.681236 × 60 = 40.87416, so 40 minutes.

3. 3

   The remaining decimal × 60 is the seconds

   0.87416 × 60 = 52.45, so 52.45 seconds. Together that's 35 degrees 40 minutes 52.45 seconds.

Reading GPSLatitude in Exif

In a photo's Exif, latitude and longitude are each stored as three fractions (rationals) for degrees, minutes and seconds. North or south, and east or west, are in separate fields, GPSLatitudeRef and GPSLongitudeRef, as the single letter N, S, E or W.

Divide the fractions to get degrees, minutes and seconds, then convert to decimal with the formula in the earlier section. Some devices store minutes as a decimal and seconds as 0, as in "35/1, 4087416/100000, 0/1." The same formula works here too, with the same result.

The Photo Exif & Location Checker automatically converts a photo's latitude and longitude to decimal, and gives links to Google Maps, GSI Map (from Japan's Geospatial Information Authority) and OpenStreetMap. In its lat/long conversion tab, you can convert DMS entered by hand, or pasted Exif rationals, into six notations.

Decimal places and rough precision

1 degree of latitude is about 111 km anywhere on Earth. So the number of decimal places gives a guide to how finely a value can pinpoint a location.

In DMS, 1 second is about 31 m and 0.01 seconds is about 30 cm. Smartphone photo Exif often records seconds to around two decimal places, fine enough to identify a building entrance. 1 degree of longitude is about 111 km at the equator and about 91 km near 35° north, getting shorter at higher latitudes.

Four common conversion mistakes

• Order of latitude and longitude: Google Maps uses latitude, longitude, but some formats such as GeoJSON use longitude, latitude. Near Japan, remembering that around 35 is latitude and around 135 is longitude helps you spot a swap.
• Signs for south and west: decimal uses a minus sign. Exif keeps the value itself positive and shows the direction with the one letter in Ref, so the sign is easy to forget when converting.
• Confusing minutes and seconds: a notation separated by periods like "35.40.52" means 35 degrees 40 minutes 52 seconds, not 35.4052 degrees.
• Different geodetic datums: current maps and GPS use world datums (WGS84, JGD2011). Values in the old Tokyo datum found in older Japanese documents are off by around 400 m near Tokyo.

How to check whether a photo has location data and remove it before publishing is in How to Remove Location Data from Photos, and how to remove only location data while keeping the date and time is in How to Remove Exif Without Quality Loss.

FAQ

What's the formula to convert DMS to decimal?

Decimal degrees = degrees + minutes ÷ 60 + seconds ÷ 3,600. 35 degrees 40 minutes 52.45 seconds becomes 35.681236. For south and west, add a minus sign to the result.

How do I read "35/1, 40/1, 5245/100" in Exif?

It's degrees, minutes and seconds each written as a fraction, meaning 35 degrees 40 minutes 52.45 seconds. North or south is stored as N or S in a separate field, GPSLatitudeRef. In decimal, it's 35.681236.

How many decimal places are enough for latitude and longitude?

North-south, 4 places give about 11 m, 5 places about 1.1 m, and 6 places about 11 cm. To show a building on a map, 5 places are enough. But many digits don't mean GPS measured to that precision.

How do I open a photo's latitude and longitude in Google Maps?

Convert DMS to decimal, and paste it into the Google Maps search box as latitude, longitude separated by a comma, like "35.681236, 139.767125." Put the photo into the Photo Exif & Location Checker and it does this conversion and gives map links automatically.