We present a time-efficient lower bound κ on the number of gates in Toffoli-based reversible circuits that represent a given reversible logic function. For the characteristic vector s of a reversible logic function, κ(s) closely approximates σ-lb(s), which is known as a relatively efficient lower bound in respect of evaluation time and tightness. The primary contribution of this paper is that κ enables fast computation while maintaining a tightness of the lower bound, approximately equal to σ-lb. We prove that the discrepancy between κ(s) and σ-lb(s) is at most one only, by providing upper and lower bounds on σ-lb in terms of κ. Subsequently, we show that κ can be calculated more efficiently than σ-lb. An algorithm for κ(s) with a complexity of 𝓞(n) is presented, where n is the dimension of s. Experimental results comparing κ and σ-lb are also given. The results demonstrate that the two lower bounds are equal for most reversible functions, and that the calculation of κ is significantly faster than σ-lb by several orders of magnitude.