Two linear approximations of variable-volume, single-pool Kt/V were compared. Each is based on the corrected postserum/preserum urea nitrogen ratio (R), called R', where R' = R - 0.03 - UF/W (UF/W being the ratio of the ultrafiltrate volume removed to the postdialysis weight). The two formulas were derived by construction of tangents to the exponential curve y = -In(R') at approximately 1.0 and 1.3, namely, y = 2 - 2.7(R') and y = 2.2 - 3.3(R'), respectively. The linear formulas were compared with each other and to our previous logarithmic formula -In(R - 0.008*t - UF/W). All were compared with the modeled Kt/V using a variable-volume, single-pool kinetic model in 500 dialysis sessions, with Kt/V ranging from 0.7 to 2.1. Analysis of error uncovered systematic errors in all the formulas. However, each of the new linear formulas had very little systematic error in the Kt/V range it was designed for, over a span of 0.6 - 0.7 Kt/V units. Outside this range the linear formulas underestimate the variable-volume, single-pool modeled Kt/V, but, barring two-pool or other technical errors, they do not markedly overestimate Kt/V in any Kt/V range. The total error with the new linear formulas was an acceptable 5%, in the range they were designed for. The results suggest that precise estimates of Kt/V can be derived using linear formulas as long as a given Kt/V range is targeted.