I honestly don't think your GPS is 100% accurate.
What is it? iPhone? Android? Garmin? Unless it's a precision instrument I wouldn't sware on it from the witness stand. The math is solid, period.
If your speedo is off, it's off no matter what tire is on it.
a 245/45 tire has a 110.25mm sidewall and a 245/50 has a 122.5mm sidewall *IF* your OEM tires are worn down by 5/16" it is 7.9mm shorter. So a *worn* OEM is ~20mm shorter than a 50, and around the circumference that makes a big deal.
Summing it up, it's impossible that there would be *no* difference in speedometer readings, and you would never *feel* that difference. The only way you'll know is to do the math, or ask a police officer to clock you.
(And even theirs are off and need calibrated regularly)
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