Calculating distance from Lat/Long GPS Coordinates

I have a large dataset of 80,000 + rows with Lat / Long coordinates in Deg/Mins/Secs. It is simple to convert these to decimal degrees. Could anyone assist with the right formula to calculate distance from these coordinates and then to convert the distance into Speed?

For reference I am trying to calculate speed over ground (SOG) for a ship.

The data is per second. Is it necessary to calculate distance per second or would it be more accurate to convert the data per second into minutes and then calculate from there ?

Thanks

I don't know if the above solution works but I'll lay out the process alternatively.

For this you use the Haversine Formula which is well laid out in wikipedia. (I'd show the formulas but classically they are discussed with Greek letter variables so it's better for you to read it from there to learn it "properly".)

The only 2 things that you HAVE to get from the page, if you want to skip over the theory (trouble awaits you young Luke with that course, though), are the hav(theta) formula using Sine and Cosine (SIN, COS), and the formula for d(distance) slightly below that. Look for the word "explicitly" for the simplified formula version for d. Beside SIN and COS you'll need to use ASIN and SQRT.

Note that you will need to first convert degrees to radians (multiply each number of degrees by PI() / 180).

There is a complexity that some might be tempted to gloss over, which is the component "r" which is the radius of the earth. Unfortunately that varies from place to place on the planet. You'll have to decide how to address that. You can get a ballpark result by using the mean earth radius but then present your results with a margin of error disclosure.

The wiki article discusses that and other vital caveats. It's a good article to learn from. Otherwise I would suggest learning Haversine from another source, such as the footnote references in wikipedia.

I might caution you not to stumble over terminology as you appear to use the terms "minutes" and "seconds" both as a trigonometric measurement, and as a measure of time, which will be the next step after computing distance. (I'm just saying that I myself might stumble and make temporary missteps from that.)

As to expressing speed per minute or per second, wouldn't you want to use per hour? If your time measurements are in seconds, divide by 60 for number of minutes, then divided by 60 again for number of hours, and speed is distance divided by time. When you say "convert ... and then calculate from there" I don't follow what you would then calculate, other than the simple division of distance over time.

As far as which is more accurate, for speed per time second, minute, or hour, each should give equivalent precision to about 15 significant digits.