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The exact range is a separation beyond which the semivariogram reaches its sill. A Gaussian semivariogram with nonzero structured variance approaches its sill asymptotically and therefore has infinite exact range. Software range parameters may instead specify a scale.

For an intrinsically stationary random field, the semivariogram is $\gamma (h)=\frac{1}{2}\mathrm{Var}[Z(s+h)-Z(s)]$. It is even and vanishes at zero. With constant mean, a second-order stationary field has $\gamma (h)=C(0)-C(h)$. An isotropic model writes it as a function of nonnegative distance.

The sill is the large-distance level of a semivariogram when that limit exists. For covariance tending to zero, the sill is the total marginal variance; a nugget plus a structured component has total sill ${\tau }^2+{\sigma }^2$. A nonzero constant covariance component is invisible to the semivariogram.