How this calculator works
The calculator treats the jump as a vertical launch under standard gravity. The leap is the rise of the centre of mass; the time to rise and fall back to takeoff height is twice the takeoff speed divided by gravity. The rim height reached is standing reach plus leap, minus a clearance allowance. A player who can palm the ball needs only their hand at rim level, while a player who cradles the ball must lift the ball itself above the rim, so the full 23.87 cm diameter of a size 7 ball is added. Standing reach is measured with shoes on, one arm up and fingers extended. The model ignores horizontal travel, arm extension during the jump and the fact that most dunkers reach higher than their standing reach because they extend at the peak.
Formula
Horizontal rim: leap = rim height + clearance - standing reach. Rim reached: rim height = standing reach + leap - clearance, where clearance is 0 for a palmed ball or 0.2387 m for a cradled size 7 ball. Hang time = 2 x sqrt(2 x g x leap) / g. Takeoff speed = sqrt(2 x g x leap). Jump energy = mass x g x leap, with g = 9.80665 m/s2.
Worked example
A player with a 2.30 m standing reach wants a 3.048 m rim and can palm the ball. The leap needed is 3.048 - 2.30 = 0.748 m. Takeoff speed is sqrt(2 x 9.80665 x 0.748) = 3.83 m/s and hang time is 0.781 s. An 80 kg player produces 80 x 9.80665 x 0.748 = 587 J. A 2.20 m reach with a 0.90 m leap and a cradled ball reaches 2.20 + 0.90 - 0.239 = 2.86 m.
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Frequently asked questions
Which rim heights does this use?
Eight feet for ages 7 and 8, nine feet for ages 9 to 11, and ten feet (3.05 m) for age 12 and up and all official FIBA and NBA play. Local leagues may use other heights.
Why does palming the ball change the answer?
A palmed ball sits alongside the hand, so a hand at rim height is enough. A cradled ball has to rise above the rim, which adds about one ball diameter to the leap required.
Is standing reach the same as height?
No. Standing reach is usually 15 to 25 cm more than height because the arm is raised. Measure it against a wall with shoes on and fingers extended.