Force is also measured in Newtons and if you applied a force of one Newton on an object in the direction of motion to move it in a straight line for one meter, then you will have done work on the object equal to one Newton-Meter or one Joule. (The work done on an object to move it in a straight line when the force is applied in the direction of motion is W = F*d.) If this work was done over a period of one second, then the power required to do it was one Joule per second which is equal to one Watt.
If you apply a force of F lbs perpendicular to a lever arm of length d ft., then you are applying a torque equal to F*d to the arm. The circumference of a circle with radius d ft. is 2*pi*d so if the force F causes the arm to rotate one revolution, then you have done work equal to F* (2*pi*d) which after some rearranging is F*d*2*pi or Torque times 2pi. So the work done per revolution is Torque times 2 pi.
Work = (Torque*2pi) / revolution. If we have r revolutions, then the total work done is
[(Torque*2pi) / revolution] * [ r revolutions] = Torque*2pi*r. Now if these r revolutions occurred in one minute, then the Power required to perform this work was Torque*2pi*r divided by 60 seconds
= (Torque*2pi*r) / 60 s = Torque*2pi* (r / 60s) or Torque*2pi*rpm and which has units of ft*lbs /s.
And since there is one hp per 550 ft*lbs / s we have
Horsepower = [(Torque*2pi) *(rpm)] / [ (550 ft*lbs / s)] where rpm = revs/60s
Therefore Hp = Torque*rpm / 5252