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How many horsepower does the Falcon 9 have?
Short answer
Rockets aren't measured in horsepower, but in thrust: the Falcon 9's first stage's nine Merlin engines deliver 7,686 kN (1,710,000 lbf) combined at sea level, and the second stage 981 kN (220,500 lbf). A horsepower figure would be misleading, because a rocket's power increases with flight speed.

Why horsepower isn't used for rockets
Horsepower is a unit of power, that is, of work per unit of time. A rocket engine, on the other hand, is described by thrust, because its power depends on how fast the vehicle is flying at any given moment: the same engine "produces" almost nothing on the launch pad and many times more just before shutdown, even though the thrust stays nearly constant. A single horsepower figure for a rocket would always force the question of at what point in the flight it was measured. That's why manufacturers and agencies give the figure in kilonewtons or pounds of force.
The Falcon 9's figures
The first stage runs on nine Merlin engines and reaches, at sea level, 7,686 kN (1,710,000 lbf) combined; each one separately delivers up to 845 kN (190,000 lbf) at that altitude. The second stage carries a single Merlin optimized for vacuum, with 981 kN (220,500 lbf), which only fires after separation, already at high altitude. For comparison: the Saturn V's first stage's five engines generated 7.5 million pounds of thrust, several times the Falcon 9's figure. The difference is explained by the mission: a lunar flight requires a very different liftoff mass than putting a satellite into orbit.
What thrust means in practice
Payload is derived from thrust and the amount of fuel available, and that's the most relevant figure for rockets: it indicates what the rocket actually carries, not how much noise it makes doing it. Added to that is reusability: the first stage is designed to survive re-entry and be recovered.
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