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Projectile Kinetic Energy and Exact Customary Units

Relate positive projectile mass, nonnegative speed and kinetic energy, with exact customary conversions and the positive speed inverse.

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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.

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Formula and method

A 1 kg mass moving at 10 m/s has kinetic energy 50 J, or about 36.8781 ft·lbf in the initial energy control. Select joules to display 50 J.

E = ½mv²; E_ft·lbf = m_gr v_ft/s² / (171616375/381)

Worked example

Enter these known values and leave the other values blank.

Projectile mass
1 kg
Projectile speed magnitude
10 m/s
Translational kinetic energy
36.88 ft-lb

Assumptions and limitations

  • Mass is positive; speed and kinetic energy are nonnegative. These are speed magnitudes and translational kinetic energy, not momentum or an energy-transfer prediction. Mass uses mass units, not gravitational force weight. This is a classical nonrelativistic estimate: speeds must be below 299,792,458 m/s and should be much smaller for physical accuracy.
  • For grains and feet/second, the exact international-unit denominator is 171616375/381. One grain is 1/7000 international avoirdupois pound, one foot is 0.3048 m and pound-force uses standard gravity 9.80665 m/s². The captured rounded 450240 denominator is corrected in all inverses.
  • Two independent measures determine the third except zero speed plus zero energy, which cannot identify a unique positive mass. A supplied positive mass and zero energy give zero speed; positive mass and zero speed give zero energy. The inverse chooses the nonnegative square root.
  • Select compatible units and clear an unknown before solving. The formula does not account for rotational energy, deformation, drag or how energy transfers to another object.

Common questions

Why does this use a different denominator from 450240?

The usual rounded denominator changes the energy slightly. This workflow derives the conversion from the international grain and foot plus standard gravity, using 171616375/381 throughout.

Can I find mass from zero speed and zero energy?

No. Every positive mass at rest has zero translational kinetic energy, so those two zeros do not determine one mass.

Does the inverse give a signed velocity?

No. It returns a nonnegative speed magnitude √(2E/m). Direction is not contained in kinetic energy.

References

A finite projectile has positive mass. Speed and kinetic energy can be zero; zero speed plus zero energy does not uniquely determine mass. The classical model excludes speeds at or above light speed; physical accuracy requires speeds much smaller than light speed. Positive energy requires positive speed. Derive kinetic energy from exact international grain, foot, pound-force and standard gravity: for grains and feet/second, E in foot-pounds-force uses denominator 171616375/381, replacing the captured rounded 450240 in every inverse.

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