The Ultimate Weapon
In professional tennis, the serve is the only shot in the game over which a player has absolute, 100% control. It is a violent, kinetic chain that transfers energy from the ground, through the legs and torso, and ultimately into the racket head. A world-class serve can easily exceed 130 mph, giving the returner less than 400 milliseconds to react.
Calculating the Velocity
While professional tournaments use Doppler radar guns (like the 'Hawk-Eye' system) to measure the exact speed of the ball immediately after it leaves the racket, you can calculate the average speed of a serve mathematically if you know the flight time and the distance traveled.
The Formula
Speed is a simple calculation of distance divided by time. Because the tennis court is 78 feet long, a serve that lands exactly on the service line has traveled roughly 60 feet diagonally from the server's racket.
Speed (fps) = Distance / Time
Average Speed vs. Peak Speed
It is critical to understand that this formula calculates the Average Speed over the entire flight of the ball. Because a tennis ball is incredibly light and fuzzy, it experiences massive aerodynamic drag. A serve that is clocked by a radar gun at 130 mph right off the racket will bleed off nearly 50% of its velocity due to air resistance and the friction of bouncing off the court, crossing the baseline at roughly 65 mph.