Gearing speed math help

I’ve been considering a chainring and cassette with more teeth and have been spinning around in the math in what this looks like from a top speed/velocity perspective when outside. I’ve found a few different calculators online but if I try to recreate the underlying math I can never get to the same speed in MPH.

Assuming I have the following equipment:
48T 1x chainring
10/33 SRAM cassette (10,11,12,13,14,15,17,19,21,24,28,33)
28mm tires

And assuming I’m looking at the top end speed only at a cadence of 100 and a gear ratio of 4.8 (48T and 10T)

Speed = Wheel circumference × Gear ratio × RPM

Wheel circumference is (622mm + 28 × 2) × pi = 2048.32 mm

Speed = 2048.32 mm × 4.8 × 100 = 983,192.84

Then according to this website to get to km/h you multiply by 60 and divide by 1,000,000, which gets you to 58.99 km/h

To get to mph multiply by 1.609344 and the answer is 36.66 mi/h at 48T/10 gear at 100 cadence

However when I look at difference bicycle speed gearing calculators I get different results. For example with the calculator linked below I get 38.12 mi/h. Where is my calculation off?

Depends on tire size.

Wheel circumference ≠ tire circumference

If you play with this gear calculator, you can see that speed increases with tire width, because increases in tire width imply increases in tire radius as well.

Generally speaking, 48:10 is plenty tall, it is equivalent to 53:11 ≈ 4.82.

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Wheel circumference (622mm + 28 × 2) × pi = 2130.00mm (not 2048.32).
Putting that into the rest of the calculation gives 38.12 mph.

Yes! Thank you! It turns out I had inadvertently put +2 instead of *2.

In this formula the 28 is the 28mm tire size. If you were running 32s the circumference would be slightly longer. The formula takes that into account if you change that number but it assumes a tubular shape, it does not take into account deformation from lower pressure.

I often spin out 48/10 so I’m looking to see how much larger of a chainring would be needed to go a little faster on the top end, without making hill climbing excessively difficult. Currently my easiest gear is 48/33 (1.45) and I don’t want to make it too much more difficult as I already need to do ~400-500w on steep hills just to make it up already.

If I go to a 52T front and 10/36 rear theoretically I’d have an easy gear that’s about the same and one extra high speed gear, with spacing not being too bad. Or I could go with a 44T max gravel cassette and bump the chainring up to a 54 or 56, but there are less options for that size that include a powermeter in the chainring (currently running the SRAM 1x aero chainring but the options there are only 48T, 50T, or 52T). Perhaps there’s a track/sprint chainring I’ll find that works well with a bolt in PM.

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What’s your cadence when spinning out a 48x10? 110 RPM will get you to 41.9 mph/67.5 kph.

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I’ll be totally spun out at around 130 rpm, which gets to about 50mph. This is down a hill. On flat ground I’ll sprint up to about 38-42mph or so before the cadence feels too high. I can sprint longer if I’m able to keep the cadence between 90-100 or so.

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This calculator only goes up to 120rpm and estimates 46mph at 120rpm in 48x10 gearing with 28-622 tire:

this link should be setup for you to play around with:

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