Depends. Here's what the beanie-heads at NASA say:
A perfectly efficient 2 horsepower engine would deliver enough power to generate 100 pounds of thrust at a velocity of 11 feet/sec. Suppose we increase the speed to 22 feet/sec. We would now cover the 110 feet distance in 5 seconds. The work would still be 11,000 foot-pounds (100 pounds of thrust for 110 feet). But the power required is now 2200 foot-pounds per second, or 4 horsepower. Increased horsepower lets you fly faster with the same amount of thrust, or it lets you generate more thrust at the same velocity.
Got that one on a 135 oral once. At sea level, it's basically a one to one ratio. As you ascend you have to account for all the changing variables, but that is your basic answer.
They are totally different measures of two totally different things. Thrust is a force. No velocity is required or implied by thrust. Horsepower is a measure of the rate at which work is done. In other words, Power is a force applied over a given distance in a given period of time.
To convert from thrust to Horsepower the equation:
HP = [Thrust (pounds) X Velocity (knots)]/ 325 (375 if you use MPH instead of knots)
Works pretty well.
For a simple rule of thumb:
At 325 knots, (or 375 MPH) 1 lb of thrust is roughly equal to 1 horsepower.
Altitude has nothing to do with it, with the exception that depending on engine type, thrust will generally vary with altitude.
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