Using SCUKM, we constructed recurrence formulae expressing weekly pre- and post-dialysis urea levels. Then we mathematically derived simple methods to estimate Kt/V0 and the urea generation rate (G) per unit urea distribution space post-dialysis (V0), which only required the measurement of pre- (C) and post-dialytic blood urea concentrations (C0) of a single hemodialytic session (two-point method). Underlying fundamental assumptions were: (i) patients receive weekly scheduled hemodialysis; (ii) the ultrafiltration rate, intradialytic urea generation, interdialytic water increase rate, and residual renal function are small enough to be retained only as the leading term in the formulae. In the derivation, we proved relations: C = f(Kt/V0)G/V0, and C0 = g(Kt/V0)G/V0, which state that both C and C0 are directly proportional to G/V0, and that the proportional constants are functions of Kt/V0. Errors of the formulae were also checked to make the limitation of the approximations clear. The present formulae exactly reproduced Kt/V0 and G/V0 of virtual patients strictly obeying the SCUKM in a computer simulated model. Using the blood urea nitrogen concentration data of 20 actual patients, we compared our method with the usual three-point method and obtained substantial correlations between them (r = 1.00 for Kt/V0, r = 0.98 for G/V0). Finally, we proposed convenient and easily calculable new formulae, which give sufficiently accurate Kt/V0 and G/V0.