# How to calculate torque of a 4-pole BDC hobby motor

I have a hobby motor that claims to be a 2200KV motor. This particular one is a 4-pole motor.

Using a drill, I spun the motor at 1312 RPM. On an oscilloscope I see 1.3V peak-to-peak waveform between two of the phases (a pretty distorted sine-ish wave) having a frequency of 43.73 Hz.

Converting this frequency into radians per second, I get 274.649 radians per second. Calculating KT from this I get 0.65 volts peak / 274.649 rads/sec = 0.002367 N*M/Amp, which just seems really low.

Since the motor is a 4-pole motor, whose electrical frequency is twice the mechanical frequency, should I have used half the frequency seen on the oscilloscope? That would make the calculation 0.65 volts peak / 137.325 rads/sec = 0.0047333 NM*Amp, which might seem more reasonable.

I guess the main question is -- when calculating torque constant by dividing the back-EMF voltage by radians per second, is it the radians per second of the shaft speed itself, or radians per second of the back-EMF frequency (which increases for each pole-pair)?