## Wheel diameter to speed/RPM chart

Discussions related to motors other than hub motors.
This includes R/C motors, botttom bracket, roller and geared drives.
spinningmagnets
100 GW
Posts: 10789
Joined: Dec 21, 2007 10:27 pm
Location: Ft Riley, NE Kansas

### Wheel diameter to speed/RPM chart

When contemplating a non-hub motor, the maximum motor RPM target and gearing equations can get complex. By selecting the lowest top speed that can satisfy your performance needs, torque will be maximized across the resulting rpm band.

From reading here, most builders have settled on wheel diameter and top speed desired when they begin pondering motor Kv selection, voltage to be used, and gear-down options. I have compiled this chart to make the process a little easier.

This link is a pedal cadence calculator (thanks, Drunkskunk), but if the sprocket and chainring tooth-count numbers entered are the same (1:1) then the pedal-cadence will be the same as the rear-wheel rpm.

http://www.machars.net/bikecalc.htm

If you want to use a tire with an odd outside diameter (such as a fat moped tire on a 20-inch bicycle wheel, which would typically be 22-inches), you go to the tire selection and click on “other", then enter a number of the tire outside diameter into the next square in inches (decimals allowed, 1/4-inch is 0.25).

For instance, if using a custom tire with an outside diameter of 60-centimeters, you would use an online conversion calculator, then enter the result of 23.62 (inches) into the cadence calculator Other---> wheel (using 1:1 gears) to find the top-speed/rpm result. Suggestions welcome...
________________________________________
Here's another method:

(10 mph x 5280 feet/mile) / 60 min per hr = 880 feet per min, so...10-MPH = 880 feet per minute

The diameter of the wheel is X inches. In one revolution, it travels a distance equal to the circumference of the wheel, which is Pi times the diameter:
(X inches x 3.14159) / 12 inches = Y feet (if X is 26-inches, Y = 6.81 feet)

Then we just calculate the number of revolutions needed to travel 880 feet:
(880 feet/min) / (Y feet/rev) = Z RPM (880 / 6.81 = 129.3 RPMs for 10-MPH)...which is equal to 12.9 for 1-MPH

XXXXXXXXXXXXXXXXXXXXXXXXXXXXX

http://www.onlineconversion.com/

1 mph = 1.609 kph
1 kph = 0.621 mph

XXXXXXXXXXXXXXXXXXXXXXXXXXXXX

29 inch tire

11.6 RPM per one-MPH

XXXXXXXXXXXXXXXXXXXXXXXXXXXXXX

27.5 inch tire

12.2 RPM per one-MPH

XXXXXXXXXXXXXXXXXXXXXXXXXXXXXX

26-inch tire
1 mph = 12.93 rpm
1 mph = 1.609 kph
1 kph = 8.10 rpm

MPH (km/h) = RPM
01__(1.61)___12.9
02__(3.22)___25.9
03__(4.83)___38.8
04__(6.44)___51.7
05__(8.05)___64.7
06__(9.65)___77.6
07__(11.26)__90.5
08__(12.87)__103.4
09__(14.48)__116.4
10__(16.09)__129.3
11___(18)___142
12___(19)___155
13___(21)___168
14___(23)___181
15___(24)___194
16___(26)___207
17___(27)___220
18___(29)___233
19___(31)___246
20___(32)___259
21___(34)___272
22___(35)___285
23___(37)___297
24___(39)___310
25___(40)___323
26___(42)___336
27___(43)___349
28___(45)___362
29___(47)___375
30___(48)___388
31___(50)___401
32___(51)___414
33___(53)___427
34___(55)___440
35___(56)___453
36___(58)___465
37___(60)___478
38___(61)___491
39___(63)___504
40___(64)___517
MPH (km/h) = RPM

XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX

24-inch tire
1 mph = 14.00 rpm
1 mph = 1.609 km/h
1 kph = 8.80 rpm

MPH___(km/h)___RPM
01__(1.61)___14
02__(3.22)___28
03__(4.83)___42
04__(6.44)___56
05__(8.05)___70
06__(9.65)___84
07__(11.26)__98
08__(12.87)__112
09__(14.48)__126
10__(16.09)__140
11___(18)___154
12___(19)___168
13___(21)___182
14___(23)___196
15___(24)___210
16___(26)___224
17___(27)___238
18___(29)___252
19___(31)___266
20___(32)___280
21___(34)___294
22___(35)___308
23___(37)___322
24___(39)___336
25___(40)___350
26___(42)___364
27___(43)___378
28___(45)___392
29___(47)___406
30___(48)___420
31___(50)___434
32___(51)___448
33___(53)___462
34___(55)___476
35___(56)___490
36___(58)___504
37___(60)___518
38___(61)___532
39___(63)___546
40___(64)___560
MPH (km/h) = RPM

XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX

22 inch diameter tire (Pirelli ML75 moped tire on a 20-inch rim)

15.3 RPM per one-MPH

XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX

20-inch tire
1 mph = 16.81 rpm
1 kph = 10.50 rpm

10 mph (16 kph) = 168 rpm
11 (18) = 185
12 (19) = 202
13 (21) = 219
14 (23) = 235
15 (24) = 252
16 (26) = 269
17 (27) = 286
18 (29) = 303
19 (31) = 319
20 (32) = 336
21 (34) = 353
22 (35) = 370
23 (37) = 387
24 (39) = 403
25 (40) = 420
26 (42) = 437
27 (43) = 454
28 (45) = 471
29 (47) = 488
30 (48) = 504

XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX

16 inch tire

21 RPM per one-MPH

XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
Last edited by spinningmagnets on Sep 23, 2013 5:28 pm, edited 11 times in total.

jdcburg
100 W
Posts: 175
Joined: Aug 03, 2009 1:50 pm
Location: massachusetts usa

### Re: Wheel diameter to speed/RPM chart

Spinning magnets - Nice work. I've attached a little Excel table that is less detailed but more compact. Also it includes 700c tires. Another tack would be to use http://www.arachnoid.com/bike/ to do some calculations for you. You can put your motor rpm in where it says pedal cadence, your motor sprocket where it says front sprocket teeth and up to 12 potential rear sprockets where it says rear sprocket teeth to see the effect of different sprockets. You can even put up to 4 motor sprocket sizes in - jd
Attachments
wheel rpms.JPG (61.19 KiB) Viewed 37317 times
In theory, there is no difference between theory and practice. But in practice, there is - Yogi Berra

spinningmagnets
100 GW
Posts: 10789
Joined: Dec 21, 2007 10:27 pm
Location: Ft Riley, NE Kansas

### Re: Wheel diameter to speed/RPM chart

Excellent chart sir! Very useful, thank you. I think the gear calculator link that you provided is a little easier to use for the most frequent gearing questions compared to the well-known Sheldon Browns Bicycle Gear Calculator, but just for laughs, here it is also:

http://sheldonbrown.com/gears/index.html

Russell
10 MW
Posts: 2164
Joined: Nov 22, 2008 3:08 pm
Location: State of Wisconsin, USA

### Re: Wheel diameter to speed/RPM chart

While the chart is good for getting in the ballpark in practice the overall diameter of a 700C tire for example varies greatly depending on the size. Therefore I simply use a little math to calculate speed at various RPM's, or vice-versa.

Example: 700C x 50mm

Diameter = 622mm + (2 x 50mm) = 722mm
Circumference = 722mm x 3.1416 = 2268mm
Divide circumference by 25.4 to get inches then that number by 12 to get feet or 7.44 ft

With that you can calculate the speed for any RPM

For 250 RPM;

7.44 ft/rev x 250 rev/min x 60 min/hr x 1 mi/5280 ft = 21.1 MPH

or if say you know the speed is 20 MPH then solve for RPM;

20 mi/hr x 5280 ft/mi x 1 hr/60 min x 1 rev/7.44 ft = 237 RPM

You can also easily calculate bike speed at various pedaling cadences

For example say I pedal at 90 rev/min with a 42 front chainring and 13 tooth rear cog using that same 700C x 50mm tire;

42/13 = 3.23

3.23 x 90 rev/min x 7.44 ft/rev x 1 mi/5280 ft x 60 min/hr = 24.6 MPH

-R
Jeep Comanche Trekking Bike w/YOUE geared motor, 42 lbs + 15 lb rear trunk bag w/12S 16Ah LiPo battery, tools, etc., 21A controller, 700 x 40C tires. 27 MPH.

My other E-Bikes: Nashbar Steel Flatbar

DasDouble
100 kW
Posts: 1025
Joined: Jul 12, 2015 1:35 pm
Location: GERMANIA :D

### Re: Wheel diameter to speed/RPM chart

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deronmoped
10 kW
Posts: 804
Joined: Oct 06, 2008 11:55 am

### Re: Wheel diameter to speed/RPM chart

Here is a great calculator from "Electric Scooter Parts", there are actually two of them, a Top Speed and Gear Ratio Calculator for a non jack shaft type and a Jack shaft type. Just input the motor speed, gears and tire diameter, it gives you the gear ratio and speed. http://www.electricscooterparts.com/mot ... ratio.html

ColdRider
10 mW
Posts: 20
Joined: Mar 30, 2016 9:10 pm

### Re: Wheel diameter to speed/RPM chart

That's great tool and works well too Thanks Spinningmagnet ,Here is a tool I did use many times it may lack extreme precision but has served me well over time ,I find it long to fill in but that is what a Hobbyist/Enthousiast DIY E-Biker want at least thats what I got ->Fun

-> http://cyclurba.fr/braquet.php

Enjoy
I am working on it !
Safety Lighting System Planned

Will post them soon

spinningmagnets
100 GW
Posts: 10789
Joined: Dec 21, 2007 10:27 pm
Location: Ft Riley, NE Kansas

### Re: Wheel diameter to speed/RPM chart

Merci beaucoup, mon ami.

[Thank you, my friend.]

atarijedi
100 W
Posts: 178
Joined: Jul 18, 2016 7:16 am

### Re: Wheel diameter to speed/RPM chart

Here is a tool I use to calculate speed, RPM, etc...

For hub motors, you put the differential at 1, for non-hub motors, you need to put the total ratio from motor to rear wheel.

JackElliott
1 mW
Posts: 14
Joined: Jun 13, 2016 9:42 am

### Re: Wheel diameter to speed/RPM chart

Good stuff. Anyone make a similar but for IGHs?
Jack Elliott
Bend, Oregon, USA

Chalo
100 GW
Posts: 6439
Joined: Apr 29, 2009 11:29 pm
Location: Austin, Texas

### Re: Wheel diameter to speed/RPM chart

Sheldon Brown's internal gear calculator will give output as pedal RPM per speed and speed per pedal RPM, as well as other formats.