# Speed calculation with Diameter and RPM

Hi I am working on a robotics project and I need help with Distance calculation. The diameter of the wheels are $7$ cm or $75$ mm , and the speed on the wheels are constant at all the time whenever its given the command to rotate, The wheels rotates at the rate of 200 Revolutions per Minute. (on a flat surface without any obstacle)

I need to calculate the Distance(meters) it would travel if i make the wheels to rotate for 4 seconds, I can do that by Speed = Distance/time formula, but for that I would require the Speed of the wheels. I do not know the formula for Speed | velocity calc with RPM and Diameter of the wheels.

I found this tool for the conversion http://www.neugartusa.com/ptformula/speed_rpm.htm for my job , where from the top i selected [Speed at diameter d and rpm n ], But i dont know if i am on the right path.. I need to know if i am using the right tool for my calculation and also the formula that it uses.

You can get the speed of the (middle point) of the wheel if you multiply the nr. of rev. with the distance from the ground (where the wheels roll on) to the center of the wheels.

$v = r\omega$

Where omega is the angular velocity, r the distance from the center of wheel to the plane it rolls on, v the velocity. Vc is what you want (see image).

You have 200 rpm, from which you need to find $\omega$. The formula to convert rpm to $\omega$ is: $\omega = rpm \cdot \frac{\pi }{{30}}$, in your case that's $\omega = 200 \cdot \frac{\pi }{{30}} = 20.943$. Your diameter is 75 (mm) which is 0.075 (m) now you need to multiply anglular velocity ($\omega$ ) with the radius (see image where says "your distance") to get the velocity of the center of the wheel Vc.

${v_c} = \omega \cdot r = \omega \cdot \frac{d}{2} = 20.433 \cdot \frac{{0.075}}{2} = 0.785\,\,\,\,\,\frac{m}{s}\$

• So if the RPM is 150 (w) and the radius (r) is 35mm then my Vc is 150x35 = 5250 mm/s or 5.2 m/s ... is it ? :/ – Sanju Mar 16 '14 at 16:46
• Well you got the formula right but the unit conversion is not. If you wanna get the speed in m/s you should convert the RPM to RPS (rev. per second), the millimeters to meters and then multiply. $\frac{{150(RPM)}}{{60}} = \frac{{15}}{6} = 2.5\,\,\,(\frac{1}{s})$ – hackYou Mar 16 '14 at 16:55
• 35 (mm) are 0.035 (m) multiplied by 2.5 (rev.per second) gives us 0.0875, so the result should be 0.0875 (m/1) not 5.2 (m/s) – hackYou Mar 16 '14 at 17:03
• it means the tool over there is not giving me the accurate value. Could u please check that online tool ? neugartusa.com/ptformula/speed_rpm.htm when I enter the diameter 75 mm and RPM 150 it gives me 0.589 m/s ,, I am not saying its correct , because everything on internet cannot be precise... Please just have a look so that I can tell me teacher of its inaccuracy. Its something very important for me. thanks – Sanju Mar 16 '14 at 18:40
• First I wanted to give you some hints so you could do it byyourself but there you have it now. And btw that websites calculations are accurate! – hackYou Mar 16 '14 at 20:00