What is the relationship between torque and horsepower?

Answer

You can’t just convert torque into power and vice versa.
Although there is a connection, you still need a third physical quantity : the speed of revolution.

If you consider keeping the revolution speed constant, then torque and power are proportional.
That means that if your torque increases 2 times, the power also increases 2 times, and vice versa.

The relationship between torque and power is expressed by the following formula:
P = T x omega
Here P is the power in Watts [W]T the torque in Newton meters [Nm] and omega is the angular velocity in radians per second [rad/s].
This formula essentially states that, work = force x displacement in the direction of the force, for a circular motion.

You can also use the formula in a more practical form:
P[kW] = Txn / 9549
Here P is the power in kilowatts [kW]T the torque in Newton meters [Nm] and n is the speed of revolution in revolutions per minute. 9549 is a dimensionless factor.