Bacteria Growth Calculator

N = N0 x 2^(t/g), where N0 is the starting cell count, t is the elapsed time, and g is the doubling (generation) time in the same time unit. Example: start with 100 E. coli cells doubling every 20 minutes; after 7 hours (21 doublings) N = 100 × 2²¹ = 209,715,200 cells.

The time one doubling takes. E. coli in rich medium at 37 C doubles about every 20 minutes; many species take hours. This calculator accepts any doubling time you enter.

g = t / log2(N1/N0). Example: 1,000 cells grow to 1,000,000 in 4 hours: that is 9.966 doublings, so g = 240 / 9.966 = 24.08 minutes per doubling.

mu = ln(2) / g, the continuous growth-rate constant. For a 20-minute doubling time, mu = 2.079 per hour, meaning the culture multiplies about 8-fold every hour while in log phase.

t = g x log2(target/N0). Example: growing from 100 cells to 1,000,000,000 cells with 20-minute doublings takes 23.25 generations = 7 hr 45.07 min.

Optical density at 600 nm: how cloudy the culture looks, proportional to cell density in the linear range. Rule of thumb for E. coli: OD600 1.0 is about 800,000,000 cells/mL, so OD600 0.5 is about 400,000,000 cells/mL. It is strain, medium, and instrument dependent, so calibrate with plate counts for exact work.

Lag (cells adapt, no division), log or exponential (doubling at a constant rate - the only phase this model describes), stationary (nutrients exhausted, net growth zero), and death or decline (cells die faster than they divide).

Nutrients run out and waste products accumulate, so the culture hits its carrying capacity (stationary phase) and eventually declines. The exponential formula is only valid during log phase.

No. This tool assumes binary fission with a constant doubling time. Yeast budding is roughly exponential in log phase, but viruses and mammalian cells follow different kinetics.

Any - minutes, hours, or days - as long as the doubling time and the elapsed time use the same unit. The calculator converts between units for you.

The math is exact but biology caps it: no flask sustains 2^100 cells. Outputs far beyond about 10^9 to 10^12 cells/mL exceed physical carrying capacity, so treat huge results as what unchecked exponential growth would give, not as a prediction.

Those are different jobs. Use our exponential-logarithmic-equations-calculator to solve exponential equations step by step, or our log-2 calculator to evaluate log base 2 of a number directly.