If the pitch is d metres, and the angular velocity is w radians/s, then the linear velocity is (w * d)/(2 pi)

The you can use the power equations to deduce torque

power = v * F = w * T

where v and F are linear velocity and force, w and T are angular velocity and torque, all in SI units (very

important)

So given if you want 0.3m/s at 100N, that's 30 watts, and with a leadscrew of 10mm pitch

w = 2 pi * v / 0.01 = 188 rad/s = 1800 rpm.

You can also calculate rpm directly from linear velocity and pitch: rpm = 60 * v / d