BLDC Motor - supply current vs line to line current
Expanding on Charles Cowie's answer,

The relationship between power input from the supply and power absorbed by the motor is obvious, but deriving an exact relationship between supply current and phase current is not. 

If you are considering a 3 phase BLDC motor with 6 step commutation (not sine wave drive) some assumptions can be made:-


Phase-to-phase voltage is an AC trapezoid wave, with peak voltage equaling the supply voltage.   
Motor current in each phase line approximates a bipolar 'square' wave with a duty cycle of 2/3, 1/3 flowing at full supply voltage and the other 1/3 while voltage is ramping down to zero.  


From this information it should be possible to calculate the rms current. However in practice the current waveform may vary dramatically depending on motor inductance, back-emf, mechanical load and PWM ratio, making calculations much more complex because motor and controller characteristics must be included. Accurately measuring rms phase current can also be challenging. 

Here are some scope traces of a motor I tested. In the first image the motor is running free. Phase-to-phase voltage is a well defined trapezoid, but current has a large ripple component and high crest factor (2.4A peak vs 1.3A DC supply current). 



The second trace shows current in a heavily loaded motor. Here we see the current waveform has become more 'square' but has a slope due to winding inductance. Peak phase current is now only slightly higher than DC supply current:-

  

The third trace was taken at a higher supply voltage, but with PWM lowered to 60% to get the same motor output power. The waveform has become triangular, with current recirculating through the controller during the 40% PWM 'off' time (downward slope of the triangle wave). During this time no current is drawn from the power supply, so average motor current is 100/60 = 1.67 times higher than the power supply current. Peak phase current is even higher, in this case ~3.3 times higher.