Equations For Shooting A Basketball

There is a science to everything. A mathematical equation can explain virtually anything you may want an answer for. In basketball, understanding the physics of the game can help you become a better shooter and player. Learn about angle and force, and practice these principles, to improve your game.

Shot Angle

The diameter of a basketball hoop is 18 inches, and the diameter of the basketball is only 9. To look at those numbers makes shooting a basketball seem easy. But John Fontanella, Ph.D., author of "The Physics of Basketball," explains that the angle at which the average person shoots a basketball actually makes the target of the hoop smaller.

To gain a perspective of what the degrees may look like, a 90-degree angle would be throwing the ball directly up toward the ceiling. A 0-degree angle would be throwing the ball directly in front of you toward the wall. In between that, is the 45-degree angle.

Fontanella explains that the closer you get to the 90-degree angle, the more of the 18-inch diameter you are utilizing, therefore making the hoop, which is your target, bigger.

Anyone who knows enough about basketball, however, knows that the key to shooting a basketball isn't an exaggerated arched shot. That wouldn't allow you to have as much control as possible. So what's the most efficient angle for shooting a basketball?

Dr. Fontanella suggests that it depends on your height. The listing that he gives on this subject starts from a 5-foot-4 player shooting from a 52 degree angle, to a 7-foot player shooting at a 49-degree angle.

He also explains that the distance between you and the basket would make a difference as to what your shooting angle will be. The closer you are to the basket, the higher your toss should be.

Shot Force

You'll have to be able to judge how much velocity, or force, to put on the ball at the various places on the basketball court if you want to develop that shooter's touch.

Because the force depends on how far you are from the basket, you will need to know the distance, or range.

A three-point shot is about 25 feet from the basket; a foul shot is 15. University of Georgia professor Jim Wilson solves the force question by using the equation, Range = ((v^2) sin(2a))/32. He does this using a 45-degree angle. He takes the range, 25 feet, and multiplies it by 32 to come up with 800. Then he square roots that, coming to the conclusion of 28 feet per second, which translates to 19 miles per hour.

So to shoot a three-pointer, at a 45-degree angle, you'd have to throw the ball about 19 mph. Using that same formula, to shoot a free throw, it comes out to be 15 mph. To shoot a two-foot shot, 5 mph.

The Variable: Practice

When you practice your shot, you're practicing the above equations. However, the Worsley School suggests that the above science isn't enough to make you a good shooter. Ray Allen, one of the best shooters in the NBA, emphasizes practice. He says that whatever it is you do to make baskets, "do the same exact thing every time you shoot ... find a rhythm. You should get 'lift' on your jump shot every single time." Meaning, you should jump the same way every time you shoot the ball.

So, in essence, the overall equation would be, consistency equals your shot times practice squared.

If you find your particular jump shot equation, and practice, you will be surprised at how much your jump shot percentage increases.