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The integrated electron number density along the line of sight, conventionally quoted in $\mathrm{pc}\mathrm{c}{\mathrm{m}}^{-3}$. A dispersion measure is a column, not a unique distance: converting it into distance requires a model of the interstellar medium. A clumpy nearby column and a longer dilute column can give the same pulsar dispersion delay.

Assume a cold, unmagnetized, weakly collisional plasma, a small fractional bandwidth and $\omega \gg {\omega }_p$. The dispersion relation is ${\omega }^2=c^2{k}^2+{\omega }_p^2$, with ${\omega }_p^2=n_e{e}^2/({ϵ}_0{m}_e)$. The group velocity and propagation time areThe lower frequencies arrive later. Taking the magnitude of the frequency derivative over $\Delta \omega$ givesFor a nonuniform line of sight, replace $n_{e}L$ by the dispersion measure $\int n_{e}dl$. The light travels at the group velocity, not at the phase velocity.

Use the preceding electron density as the line-of-sight mean, $L/c=2000\mathrm{yr}$, $\omega =2\pi (1.4\times 10^9){\mathrm{s}}^{-1}$ and $\Delta \omega =2\pi (4.0\times 10^7){\mathrm{s}}^{-1}$. ThenThis estimate corresponds to dispersion measure about $69.5\mathrm{pc}\mathrm{c}{\mathrm{m}}^{-3}$. A cloud density inferred from absorption need not equal the actual path average, so a real pulsar may differ even at the same distance.