# Easy way to calculate distance between two GPS coordinates

I'm studying for my EASA PPL(A) exam, and for some questions for the Navigation exam, I'm requested to calculate the distance between two points, like so:

What is the distance from VOR Brünkendorf (BKD) (53°02?N, 011°33?E) to Pritzwalk (EDBU) (53°11'N, 12°11'E)?
A. 24 km
B. 42 NM
C. 24 NM <--- this is the correct answer
D. 42 km

I'm given also the following attached chart:

What's the best method to apply in order to calculate the distance? Should I apply a formula or "just" by looking at the chart?

One minute of latitude is equal to 1 nautical mile of distance, and one minute of longitude is equal to $$\cos({\rm latitude})$$ nautical miles. So the distance between two points can be computed to a good approximation as:

$$\sqrt{(\text{difference in latitude})^2+(\text{difference in longitude}\times \cos({\text{latitude}))^2}}$$

So, in this case:

$$\sqrt{9^2+(\cos(53^\circ)*38)^2}\approx 24.6~\rm nm$$

• Note that this approximation only works well for small distances (which is the case here). For points that are thousands of nautical miles apart, this won't work... Commented Feb 4, 2023 at 8:58
• @Bianfable Of course not. But the same thing is true of a chart: the projection used on a chart is pretty much the same approximation, so this method is valid basically any time you would be using a chart to measure distances. Commented Feb 4, 2023 at 9:26
• This seems like a lot more work. Commented Feb 4, 2023 at 16:14
• One minute of latitude is equal to one minute of latitude, and one nautical mile is equal to 1852 meters. "One minute of latitude" is not a constant measurement because the Earth is not a perfect sphere. Commented Feb 4, 2023 at 17:06
• @randomhead Technically true, but that's like saying "the length of one meter stick is the length of one meter stick, and one meter is equal to the distance light travels in a vacuum in 1/299792458 seconds. The length of a meter stick is not a constant measurement because meter sticks expand and contract when the temperature changes and not every meter stick is exactly the same length to begin with." No measuring tool is perfect, but "one minute of latitude equals 1 nautical mile" is plenty accurate for the precision demanded in aviation. Commented Feb 4, 2023 at 18:07

One word: Measure.

I'm not even sure how you would calculate such a thing, and you can't get the answer by "just" looking at it either.

Use a plotter, or put the straight edge of a piece of paper between the points, mark it with a pencil, and compare it to the scale of miles in the legend of the chart.

Alternately, compare distance to the tick marks on a line of longitudinal. Each minute of a degree is equal to a nautical mile. (see red lines in picture below for reference.)

On a multiple choice question like this you could probably put your fingers on the screen and estimate close enough to distinguish between 42 and 24 nm.

• Yes, I was having that as an option. But the issue is that the exam will be on computer, so the charts will be digitally available. Also, the chart doesn't have any scale on it. Can I assume that the scale of aeronautical charts is usually 1:500000 Commented Feb 4, 2023 at 6:21
• I added some detail to my answer. Commented Feb 4, 2023 at 6:40
• "On a multiple choice question like this you could probably put your fingers on the screen and estimate close enough to distinguish between 42 and 24 nm." Unfortunately, 42 kilometers is 23 nautical miles, which might be too close for finger estimating. Commented Feb 4, 2023 at 6:49
• Hi @Chris, I was doing exactly the same, and somehow I guessed it. But was also curious if there is a formula to calculate it. Using a plotter should be fairly simple. Thanks for the suggestion. Commented Feb 4, 2023 at 7:18
• @randomhead, technically that's true. In practice, the distinction is completely irrelevant. Commented Feb 4, 2023 at 22:42