The original formula proposed to estimate variable-volume single-pool (VVSP) Kt/V was Kt/V = -In(R - 0.008 * t - f * UF/W), where in the Kt/V range of 0.7 to 1.3, f = 1.0 (* denotes multiplication). This formula tends to overestimate Kt/V as the Kt/V increases above 1.3. Because higher Kt/V values are now commonly delivered, the validity of both the urea generation term (0.008 * f) and correction for UF/W were explored by solving VVSP equations for simulated hemodialysis situations, with Kt/V ranging from 0.6 to 2.6. The analysis led to the development of a second-generation formula, namely: Kt/V = -In(R - 0.008 * t) + (4-3.5 * R) * UF/W. The first and second generation formulas were then used to estimate the modeled VVSP Kt/V in 500 modeling sessions in which the Kt/V ranged widely from 0.7 to 2.1. An analysis of error showed that this second-generation formula eliminated the overestimation of Kt/V in the high ranges found with the first-generation formula. Also, total error (absolute value percent error + 2 SD) was reduced with the second-generation formula. These results led to the proposal of a new formula that can be used for a very wide range of delivered Kt/V.