The Continental grip is a good choice when you serve.
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As a beginning tennis player you probably gripped the racket in a way that seemed most comfortable, then played all your shots with the same grip. As you become more advanced, however, you'll learn the advantages of changing your grip when you hit forehands, backhands, serves and volleys. The Continental and Eastern grips are two basic styles that work best in different situations on the court.
Eastern and Continental Form
The Continental grip may be the style you used as a beginner, if you were told to "shake hands with the racket." Hold the racket in front of you with the racket face perpendicular to the court, then simply grip the handle. The "V" shape formed by your thumb and index finger should lie on top of the grip and slightly to the left, if you're right-handed. This is also known as the 11 o'clock position, using the butt end of the grip as an imaginary clock face. For lefties, the V shape rests on the 1 o'clock spot. Eastern grips vary, depending on your shot. For the forehand, rotate your hand clockwise so the V shape is at about 2 o'clock. Move in the opposite direction for the Eastern backhand, placing the V shape at about 10 o'clock. Reverse the directions if you're left-handed.
Continental Grip Advantages
The Continental is a fairly neutral grip you can use for either forehands or backhands. That makes it the best choice for hitting volleys. When you're at the net you typically don't have time to change your grip after your opponent hits the ball, so you need a grip from which you can hit a forehand or backhand. The Continental grip is good for overhands and most serves because it allows you to snap your wrist easily on contact to gain extra power. It's harder to hit topspin groundstrokes using the continental style, but the grip is a solid choice for hitting sliced backhands or for playing high balls that bounce to about shoulder height.
Eastern Grip Advantages
The Eastern grip is best for hitting most groundstrokes, particularly topspin shots. The Eastern forehand and backhand grips let you square the racket head to the ball naturally. Swing horizontally with an Eastern grip to drive flat groundstrokes, or swing in a low-to-high arc and brush the back of the ball to hit topspin shots. The Eastern forehand and backhand grips aren't far apart, relative to the more extreme Western grips, so it's easier to change grips between shots. The Eastern backhand grip also lets you put some extra spin on kick serves.
You can grip the racket in different ways to hit two-handed backhands, but using the Continental grip for your bottom hand carries some advantages. It's close to the Eastern forehand grip -- even more so than the standard Eastern backhand grip -- which makes it easy to switch grips when necessary. And, because the top hand controls the two-handed shot, you can easily replicate an Eastern or Western backhand grip with the top hand.