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In this article we obtain the Horn-Li-Merino formula for computing the gap as well as the spherical gap between two densely defined unbounded closed operators. As a consequence we prove that the gap and the spherical gap of an unbounded closed operator are 1 and √2 respectively. With the help of these formulae we establish a relation between the spherical gap and the gap of unbounded closed operators. We discuss some properties of the spherical gap similar to those of the gap metric.

The Horn-Li-Merino formula for the gap and the spherical gap of unbounded operators