How can I calculate the speed?

Answer

I assume each tooth generates a pulse through the magnetic sensor.

If so, then only the number of teeth is important to determine the frequency. Let’s call this number of teeth ‘N’. The diameter of the gear and the thickness of the teeth are not important here.

The speed is usually expressed in the number of revolutions per minute. Let’s call this ‘T’. The frequency is usually expressed in pulses per second or ‘hertz’. Let’s call this F. So we will continue to calculate with these units.

When the shaft rotates 1 revolution, N pulses are generated at the sensor. If the shaft rotates 1 revolution per minute, N pulses per minute or N/60 per second or N/60 hertz are generated. If the shaft rotates at 60 rpm, then N*60 pulses per minute are generated or N*60/60 = N hertz. So the formula for the frequency is F = N*T/60.

If the shaft rotates at 4000 rpm and if there are eg 30 teeth on the gear, then the frequency of the pulses is equal to 30*4000/60 = 2000 hertz or 2 Khz.

When converting the frequency to a voltage signal (let’s call this V) you will again have to take into account one factor, namely the ratio between hertz and volts. Suppose you get 1 volt at 1000 hertz. Then the voltage is equal to V = F/1000 or V = (N*T)/(60*1000). So in our example this becomes: 30*4000/60*1000 = 2 volts. At 1000 revolutions per minute you will get 0.5 volts.

Good luck with your circuit and be careful with rotating parts: safety is important here!