What are the equations for the strong and weak force, like how for the Electrostatics the equation is $F_c= k*Q*q/(r*r)$. I understand to an extend what the strong and weak forces are. However, I would like to know what the equations for calculating the forces. Also can you explain how the equations works and define the variables.

I understand that they may not be as simple and as pretty and the electrostatic one.

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    $\begingroup$ Half of this question duplicates physics.stackexchange.com/q/8452 $\endgroup$ Mar 8, 2015 at 22:41
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    $\begingroup$ Also relevant: xkcd.com/1489 $\endgroup$ Mar 8, 2015 at 22:41
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    $\begingroup$ The weak interaction acts over such short distances and so, well, weakly compared to the strong and electromagnetic interactions that there is nothing to be gained by expressing it in a "as a function of distance" form. The only way anyone bother to write it down in as a Lagrangian or Hamiltonian contribution. I generally campaign for speaking of "four fundamental interactions" rather than "four fundamental forces". $\endgroup$ Mar 8, 2015 at 23:31
  • $\begingroup$ Hmmm ... FrankH takes a crack at it in this answer to another related question. Don't know if that is really correct or not. $\endgroup$ Mar 8, 2015 at 23:34
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    $\begingroup$ The question is essentially a duplicate of physics.stackexchange.com/q/39229/2451 $\endgroup$
    – Qmechanic
    Mar 8, 2015 at 23:47

1 Answer 1


There is and there isn't an equation. What I mean is that there is no universal equation for all cases. For example, the equation for strong force $V(r) = - \frac{4}{3} \frac{\alpha_s(r) \hbar c}{r} + kr$ only applies to quarkonium. This is different for the gravity equation which applies in all cases.

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    $\begingroup$ Can you explain what these variables mean please? $\endgroup$
    – ThisIsMe
    Mar 8, 2015 at 23:09
  • $\begingroup$ If that is the equation for the strong force for quarkonium, is there one for the weak force as well? $\endgroup$
    – ThisIsMe
    Mar 8, 2015 at 23:13
  • $\begingroup$ V(r) is the potential of the strong force, k is field energy per unit length, c is the speed of light, and h-bar is Planck's constant over 2pi $\endgroup$
    – Jimmy360
    Mar 8, 2015 at 23:14
  • $\begingroup$ I dont know of an equation for weak force in quarkonium $\endgroup$
    – Jimmy360
    Mar 8, 2015 at 23:21
  • $\begingroup$ The weak force is called weak because its strength is very much smaller than the electromagnetic. In addition the 1/r potential appears in electromagnetism and gravity because the exchanged boson is massless ( photon, graviton) . The weak interaction is mediated with the W and Z which lead to immediate decays for unstable particles and no long range effects as with electromagnetism and gravity. Only at unification energies and higher one could talk of a single form for the unified electroweak force. ( I assume 1/r potential but may be wrong) $\endgroup$
    – anna v
    Jun 18, 2015 at 3:08

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