Is a motor HP torque directly proportional to the increasing HP among identical motors? Say you have three motors:


*

*Motor 1 = .10 HP with x torque, performing task A

*Motor 2 = 1 HP with y torque, performing task A

*Motor 3 = 10 HP with z torque, performing task A
If the motors are the exact same model and type of motor, just a larger HP, then would the torque be directly proportional to the increase in HP for the same or proportional task?
For example, if the above statement is true, then torque could be calculated as follows:


*

*x = (the constant)

*y = 10x

*z = 100x
Basically I want to know if I can use the above method I came up with in order to easily determine which motor to use for a project if my work load is higher (or lower) than I originally expected when I determine that I need a particular motor for the task.
 A: If motor A does the same job as motor B, but with a 10x greater load, and the mechanical advantage (gearing etc) is the same, then I would expect that the torque that A supplies is ten times greater as well.
But that is not quite how you phrased the question. It necessarily follows that a higher HP motor can supply greater torque - at least, with the right gearing it should be able to.  Put differently - if I need to lift 900 kg at a speed of 1 m/s, I need to expend approximately 10 HP of power. With the right gear box, the 10 HP motor will be able to do that. The 1 HP motor will not. It might be able to lift the weight, but not at that speed.
There is no obvious relationship I can think of that fixes the relationship between these quantities, and "different versions of the same model" of a motor (with such different ratings) doesn't make me feel comfortable to say "yes you can do that".
I don't know there is a shortcut to doing the experiment, or reading the data sheet of the motor more carefully. But maybe someone reading my ramblings will be compelled to write a better answer...
A: There is a missing variable to calculate torque of those motors which is rotational speed or RPM.
If all 3 motors deliver those powers at the same rpm then yes, torque is proportional to HP:
M    POWER   TORQUE     ROT.SPEED.
M1       1        1              1
M2      10       10              1
M3     100      100              1

But they could also provide the same torque at different rpm:
M    POWER   TORQUE     ROT.SPEED.
M1       1        1              1
M2      10        1             10
M3     100        1            100

Or any combination in-between.
Power, torque and rpm are linked by the equation:
$$\text{power} = \text{torque}\times\text{rpm}$$
