Experts at the University of Central Florida studied four different models of fan at various speeds for a year to determine how much energy they used under different circumstances. They found that fans set on medium speed, moving an average of 2.5 times as fast as they do at low speed, used an average of 3.1 times as much energy. Fans set on high speed, moving an average of 3.6 times faster than low speed, used an average of 7.6 times as much energy.
Not only do ceiling fans use more energy when they move faster, they use their energy much less efficiently. In other words, the faster the fan turns, the more energy it wastes without making anything cooler. The Louisiana study shows that using two fans set on low speed will produce about as much cooling as one set on medium but will use much less energy. Four fans on low speed will produce more cooling than one set on high and still use a lot less energy.
A large part of the reason for this is because of the relationship between speed and energy. The kinetic energy, or "energy of movement," of any moving object is proportional to its speed squared. In other words, doubling something's speed takes four times as much energy.
Ceiling fans us the least amount of energy when they are turned off, of course. If you want to save on your cooling bills by using fans, then you have to be aware of how you are using them. Turn them off when nobody is in the room. If you are using your ceiling fan in conjunction with an air conditioning system, then you must remember to set the air conditioner thermostat a couple of degrees higher than you usually do. If you forget to do this, it will keep turning on just as often as it did without the fan, and your costs will actually increase.