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Central air vs ceiling fan — with a catch

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Here's a question for you amateur (and professional?) HVAC engineers out there:

In my personal situation, which uses less electricity: Running the central air conditioning, or using a ceiling fan?

No matter how humid it gets, I don't like turning the thermostat below 75°.  So if it feels a bit warm, I turn on a ceiling fan i what ever room I'm in to make up the difference.  But recently I've started wonder if that's the most economical solution.

The conventional wisdom my whole life has been that ceiling fans are cheaper than central air conditioning.  But there's a complication: I'm on Houston's downtown central chilling system.

I pay a flat fee for access to the chilling system, so my variable expense is to the electric company based on how much the central air fan runs to spread the system's cold air around my home.

When it gets hot, the central air fan will run for a few minutes until it brings the temperature back into range, and then turn off.  Whereas, if I run the ceiling fan, it's on and using electricity the whole time I'm in the room.

Is a central air fan more efficient than a ceiling fan?  Especially if I only use the ceiling fan in the room I'm inhabiting at the time, while running the chiller fan lowers the temperature across the entire 1,100-square-foot apartment?

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