Cross-quarter days are those midway between the equinoxes and solstices. In Celtic tradition they are named Imbolc, Beltane, Lughnassad and Samhain. For example, Imbolc (in the northern hemisphere) is midway between the northern winter solstice and the northern spring equinox, and Beltane is midway between the northern spring equinox and the northern summer solstice.

When we attempt to define the cross-quarter days more exactly we find that there are two interpretations, and thus two methods of calculation, which give slightly different results. These two methods are called the 'mean sun' method and the 'true sun' method. The mean sun method assumes that the Earth moves at a constant speed in a circular orbit around the Sun. The true sun method calculates a cross-quarter day based on the time at which the Earth reaches that point in its orbit which is spatially (geometrically) exactly halfway between its positions at the solstice (or equinox) and the subsequent equinox (or solstice).

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