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Basketball Leap Geometry and Ballistic Energy

Calculate clearance height, ideal launch speed, airborne time and gravitational energy from reach and hoop dimensions.

  • Formula & worked example
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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

Private by default

Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

A 3.048 m hoop, 2.5 m reach and 0.15 m clearance require 0.698 m rise; 70 kg at standard gravity 9.80665 m/s² needs ideal gravitational energy 479.15291900 J.

Rise = hoop height − reach + palm clearance; launch speed = √(2gh); same-height flight time = √(8h/g); energy = mgh.

Worked example

Enter these known values and leave the other values blank.

Hoop type
7th grade or above (standard hoop)
Standing reach
2.5 m
Palm size
15 cm
Body mass
70 kg
Gravitational acceleration
1 g
Hoop height
3.048 m
Minimum vertical leap
69.8 cm
Hang time
0.7546 sec
Jumping energy
479.2 J
Initial jumping speed
3.7 m/s

Assumptions and limitations

  • Use measured reach and clearance. Assume point-mass vertical ballistic motion, constant gravity, no air resistance and landing at launch height. Jumping energy is gravitational work, not a force or predicted metabolic calorie cost. Hoop presets are nominal imperial heights; their captured school-grade descriptions are not universal youth-sport requirements.
  • Clear an unknown before solving an available inverse branch, and lock independent known values when comparing measurements. Use compatible units; a one-way score or lookup does not supply an inverse.

Common questions

What does this result represent?

Use measured reach and clearance. Assume point-mass vertical ballistic motion, constant gravity, no air resistance and landing at launch height. Jumping energy is gravitational work, not a force or predicted metabolic calorie cost. Hoop presets are nominal imperial heights; their captured school-grade descriptions are not universal youth-sport requirements.

Can I work backward from an answer?

Where the captured equation supplies an inverse, clear the unknown and enter independent known values. Rounded scores, one-way outputs and fixed lookup choices do not uniquely recover inputs.

References

Use exactly nine international feet for the nine-foot hoop preset. Zero additional hand clearance is valid; negative clearance is invalid. Feet per second squared use exactly 0.3048 meters per second squared, replacing a rounded reciprocal factor.

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