Short answer
Torque answers how much turning action is applied; horsepower expresses how quickly work is done. Rotational speed connects them: power equals torque times angular velocity, so torque alone does not establish horsepower. 1
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| Question or attribute | Torque | Horsepower |
|---|---|---|
| What is it? | A rotational quantity | A unit of power |
| What does it describe? | Turning action about an axis | Rate of doing work |
| What completes the connection? | Angular velocity | Torque and angular velocity |
| Source example | Shaft torque in newton-meters | Rated shaft output in hp |
These are different descriptions of the same rotational operation, not competing units for one quantity. 1 2
What each thing is
Torque enters the calculation of rotational work through the angle turned. For constant torque, work equals torque times angular displacement. Power adds the time dimension: it measures the rate at which that work occurs. Horsepower expresses that rate; the DOE guide uses 0.7457 kilowatts per horsepower. 1 2
Key differences
The central equation is P = τω: power equals torque multiplied by angular velocity. At the same torque, higher rotational speed means greater power. At the same power, higher speed means less torque. Those comparisons require corresponding operating conditions; a torque number and a horsepower number without speed do not reveal the full relationship. 1
How to tell them apart
Read the quantity and its operating context. A value in hp reports power; a shaft value in newton-meters reports torque. To connect them, identify the rotational speed and use compatible units. The limit: units alone do not establish whether a power figure is rated output, actual output, or electrical input. 1 2
Where they overlap
Torque and horsepower can describe the same shaft at the same moment. They are not independent once speed is known: any two of torque, angular velocity, and power determine the third. This is why knowing speed makes a power specification more informative about turning action. 1
Edge cases
A stationary shaft can have applied torque but zero rotational mechanical power: when angular velocity is zero, the torque–speed product is zero. That does not establish zero electrical consumption. The DOE guide distinguishes a motor’s electrical input from its mechanical output and identifies their difference as losses. 1 2
Why the distinction exists
The distinction separates turning action from the rate of energy transfer. Torque acting through an angle determines rotational work; dividing work by elapsed time gives power. Keeping these quantities separate lets the same equations describe slow rotation with substantial torque and faster rotation with less torque at equal power. 1
Common misconceptions
A horsepower rating is not necessarily the power being delivered now. The DOE example estimates 15 hp of actual output from a 25-hp motor at 60% load. Likewise, higher torque does not automatically mean higher horsepower: rotational speed remains part of the calculation. 2 1
Examples
Two cases illustrate the boundary. OpenStax’s propeller example combines 90,000 watts with 300 rpm to obtain about 2,865 newton-meters: power and speed together establish torque. Hypothetically, two shafts delivering equal torque at different speeds would deliver different power; doubling speed while holding torque constant doubles power. 1