Free Growth Rate Constant Calculator
Calculate the specific growth rate constant and predict population size at a future time point.
Specific Growth Rate (k)
0.0866 1/h
Specific Growth Rate (k) vs Doubling Time (td)
Exponential Growth Prediction
With a known growth rate, you can predict future population sizes during exponential growth.
Formulas
k = ln(2) / td (growth rate from doubling time)
N(t) = N0 × e^(kt) (population at time t)
These predictions are valid only during log-phase growth. In reality, nutrients become limiting and growth slows as the population approaches carrying capacity.
Example Calculation
Starting with 1000 cells, doubling time 8 hours, predict at 48 hours.
- 01k = ln(2) / 8 = 0.0866 h⁻¹
- 02Generations = 48 / 8 = 6.0
- 03N(48) = 1000 × e^(0.0866 × 48) = 1000 × e^4.159 = 1000 × 64 = 64,000 cells
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