Equation for what? Length at resonance? Feed point impedance? Other interesting parameters?
Antennas are one of those things where it takes a long time to develop intuition, and there are no simple formulas for anything, just useful models that get you close, and simulation programs that work well enough to give an answer within your manufacturing tolerances. (All models are wrong, some are useful.)
So start with a couple of fundamental ideas: 1) Accelerate an electron, get a photon. 2) An antenna is a transformer that couples the end of your feed line to free space.
The reason the general family of dipole antennas is efficient is that the Ohmic resistance is usually around an Ohm or less, and the "radiation resistance" can be raised to around 70 to 80 Ohms. So 80/(80+1) is the ratio of energy coupled to space versus total energy input. Pretty good efficiency.
In a center fed dipole, the driving voltage creates an electrostatic force that attempts to slosh electrons in the conductor one way or the other. At resonance, a small amount of energy input creates lots of sloshing, because the driving voltage just needs to give a boost to the resonant sloshing. Off resonance, effectiveness is much lower. Actual length at resonance depends on the length:diameter ratio of the conductor, the dielectric constant of the surrounding medium, the height above ground, and the dielectric constant and conductivity of the ground. If you know all of those, the dipole can be modeled as a just barely tractable boundary value problem.
The empirical formulas that you see usually assume a practical conductor diameter and practical height. You might enjoy playing with one of the NEC2-based antenna modeling programs out there. NEC2-family solvers do "method of moments", where each wire is chopped up into segments, and then for an N-segment model, an NxN matrix of mutual inductances models the coupling among wire segments.
The ARRL Antenna Book takes more time to explain fundamentals than the Handbook. The ARRL also publishes an antenna physics book that I haven't read. I notice that PhD committee chair for the author of the Antenna Theory web site we are yakking about was Balanis, who wrote a pretty good book called "Antenna Theory" -- but the book assumes you are an EE graduate student with at least a semester of multi-dimmensional DiffEQ beyond the elementary DiffEQ course.