Experimental methods and mathematical relationships were devised based on quantitative estimation of number of in vivo osteosarcoma cells and alkaline phosphatase levels from individual animals during the natural course of growth of the tumor implant. A least square regression plot of the experimental values gave the equation C = α + γ In A where α = intercept, σ = slope, A = total alkaline phosphatase/mouse, and C = the number of tumor cells/mouse. The average tumor cell number and the increase in alkaline phosphatase are time-related events and were expressed by two equations which then permitted estimation of the growth of the murine osteosarcoma before the event had taken place. © 1980, SAGE Publications. All rights reserved.