Convert Lat to Decimal: Degrees, Minutes, Seconds

This calculator converts latitude (or longitude) coordinates from degrees, minutes, and seconds (DMS) into decimal degrees (DD). You enter the degrees, minutes, and seconds, and it returns the decimal value, which is the format used by most mapping tools and GPS devices.

Formula

The conversion from DMS to decimal degrees is a simple division problem:

Decimal Degrees = Degrees + (Minutes / 60) + (Seconds / 3600)

• Degrees (°): the whole number part of the coordinate (e.g., 40 for 40°N).
• Minutes (‘): the fractional part expressed in minutes (1 degree = 60 minutes).
• Seconds (“): the finer fractional part (1 minute = 60 seconds, so 1 degree = 3600 seconds).

Because there are 60 minutes in a degree and 60 seconds in a minute, you divide minutes by 60 and seconds by 3600 to convert them into decimal parts of a degree. The result is a single number like 40.446111.

Worked Example

Using the default values from the calculator: 40 degrees, 26 minutes, 46 seconds.

1. Convert minutes to degrees: 26 / 60 = 0.433333…
2. Convert seconds to degrees: 46 / 3600 = 0.012777…
3. Add them all together: 40 + 0.433333 + 0.012777 = 40.446111

The calculator rounds to 6 decimal places, giving 40.446111°. That is the same result you get from the formula above.

When to Use Decimal Degrees vs. DMS

Latitude and longitude can be written in several formats, and knowing which one you have is essential before converting.

• Decimal Degrees (DD): e.g., 40.446111, -79.982222. Used by Google Maps, most GPS units, and nearly all programming libraries. Easy for calculations because it is a single number.
• Degrees, Minutes, Seconds (DMS): e.g., 40°26’46″N. The traditional format for nautical charts and many printed maps. It is human-readable but awkward for math.
• Degrees and Decimal Minutes (DMM): e.g., 40°26.767′. Used in some aviation and marine contexts. You get this by dividing the seconds by 60 and adding to the minutes.

Convert to decimal degrees when you need to plot a point on a digital map, calculate distances, or feed coordinates into software. Convert to DMS when you need to read a paper map or communicate a location in the traditional format.

How to Handle Negative Coordinates (South and West)

Latitude is positive north of the equator and negative south. Longitude is positive east of the Prime Meridian and negative west. When converting a coordinate that includes a hemisphere letter (N, S, E, W), you must apply the sign manually.

• N or E → positive decimal degrees
• S or W → negative decimal degrees

For example, 40°26’46″S is -40.446111, and 79°58’56″W is -79.982222. The calculator above assumes positive values; if your coordinate has a negative sign, just add the minus sign to the result.

Common Mistakes and How to Avoid Them

Several errors are common when converting coordinates manually or with a calculator.

• Forgetting the sign: Leaving out the negative sign for southern or western coordinates places your point on the opposite side of the world.
• Mixing up minutes and seconds: Minutes range from 0 to 59, seconds from 0 to 59. If you see a value like 40°60′, it is not valid; it should be 41°00′.
• Using the wrong divisor: Some people divide minutes by 100 instead of 60. That yields a wrong decimal.
• Rounding too early: Rounding minutes or seconds to fewer decimal places before converting can shift the point by several meters. Keep 4-6 decimal places for typical GPS accuracy.

As a rule, one degree of latitude is about 111 kilometers (69 miles). One minute is about 1.85 km (1.15 miles), and one second is about 30.9 meters (101 feet). For longitude, these distances shrink as you move away from the equator, so the same second of longitude is smaller at high latitudes.

Accuracy and Limits of the Conversion

Decimal degrees with 6 decimal places give precision to about 0.11 meters (4 inches) at the equator, which is more than enough for most mapping needs. With 5 decimal places, precision is about 1.1 meters. With 4 decimal places, about 11 meters. If you only need to locate a city, 2 or 3 decimal places is fine.

The conversion itself is exact—it is just a change of units. The only limits come from the source data. If your DMS values are rounded to the nearest second, the decimal result carries that same uncertainty. For example, a coordinate given to the nearest second has an inherent error of up to ±0.5 seconds, which is about ±15 meters (50 feet) in latitude. That is fine for most purposes but not for survey-grade work.

Frequently Asked Questions

What is the difference between lat and long in decimal degrees?

Latitude (lat) measures north-south position, from 0° at the equator to 90° at the poles. Longitude (long) measures east-west, from 0° at the Prime Meridian to 180° east or west. In decimal degrees, latitude is positive north of the equator, and longitude is positive east of Greenwich. Both use the same conversion formula.

How do I convert decimal degrees back to DMS?

Take the decimal part and multiply by 60 to get minutes. Then take the fractional part of those minutes and multiply by 60 to get seconds. For example, 40.446111: the whole number is 40°, the decimal .446111 × 60 = 26.76666, so 26′, then .76666 × 60 = 46.0, so 46″. The result is 40°26’46”.

Why do some coordinates have a negative sign?

Negative decimal degrees simply mean south of the equator (for latitude) or west of the Prime Meridian (for longitude). For example, -33.8688 is Sydney, Australia (south), and -70.6693 is Santiago, Chile (west). When converting from DMS, you add the negative sign if the coordinate has an S or W designation.

Which format should I use for Google Maps?

Google Maps accepts decimal degrees (e.g., 40.446111, -79.982222) directly in the search box. It also accepts DMS with symbols (e.g., 40°26’46″N 79°58’56″W). For most applications, decimal degrees are easier because they are a single number and require no parsing.

How many decimal places do I need for a GPS coordinate?

For general navigation, 5 decimal places (about 1.1 meters) is more than enough. For geocaching or surveying, 6 decimal places is common. More than 6 is rarely useful because consumer GPS accuracy is typically 3-5 meters. The calculator above gives 6 decimal places by default.

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in deg | Degrees | ° | 40 | 0
in min | Minutes | ' | 26 | 0
in sec | Seconds | " | 46 | 0
out dd | Decimal degrees | ° | deg + min/60 + sec/3600 | 6