Why 4 or 5 digits of GPS position is fine

Accuracy vs precision. They’re not the same thing. And six digits (or more) of GPS shows that you’re mixing them up and confusing yourself. And likely confusing your app’s users.

Precision is the level of detail in how you describe your measurements. How many decimal places do you have? If you use eight decimal places for GPS location that’s your precision.

Accuracy of a measurement is a way to determine how close to reality you are. If your GPS position is very accurate, then your true location is inside a small circle around your measured GPS location. If it’s not very accurate, you’re true position is somewhere in a larger circle around your GPS position.

(Actually, it’s not a circle, it’s an ellipse since 3D conic projection from the GPS satellite onto a flat surface creates an ellipse — but we can for small areas approximate the surface of the earth as flat. And fortunately for engineers, for small enough areas, there’s not going to be much difference between the area of that ellipse vs a circle.)

In displaying a location to the user of your app you will generally want your precision to be about the same as your accuracy. Otherwise you can be implying more accuracy than you actually have. If you have a ruler with only centimeter markings you don’t want to quote millimeter measurements.

The accuracy of commercial GPS measurements is 5–10 meters at best (might be worse). The Eiffel Tower in Paris is at 48.85838° N, 2.29457° E. Since the distance per degree is about 111.2km, we can see that four decimal places of precision implies 11.12 meters (36 feet) of accuracy and five places implies 1.11 meters (3.6 feet) accuracy. We need between 4 and 5 decimal places of precision to capture all the available GPS accuracy.

But if I showed that location as 48.858265° N, 2.294538° E (with six places) then I would be instead implying an accuracy of 11.12 cm (4.4 inches) or about 100 times smaller than a regular GPS can achieve. And those people that use eight digits are implying an accuracy of 0.11 cm (0.04 inches). This is clearly ridiculous.

Surveying GPS units that cost thousands of dollars can get 1–2 cm resolution by using some special techniques and hardware. But that’s not available to the typical GPS or to your cell phone GPS. And your GPS or cell phone could likely be less accurate due to satellite position, ionespheric conditions, nearby buildings and other potential interference. So unless you’re using a surveying GPS, use four digits. Five digits at the most and only if you don’t want to loose any accuracy. Usually four is fine.

Is 111.2km always the distance between degrees?

Well, no. That was a simplification I made above. That’s the difference between degrees of latitude (the horizontal ones) at the equator. But longitude lines converge at the poles, so the closer to the poles you are — the higher your latitude — the shorter the distance is between latitude degrees.

So the above calculation is a largest-case distance. It might be less. It will be less unless you’re located on the equator.

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