Growth Rate Constant Calculator Formula
Understand the math behind the growth rate constant calculator. Each variable explained with a worked example.
Formulas Used
Specific Growth Rate (k)
growth_rate = kPredicted Population at t
predicted_pop = n0 * exp(k * predict_time)Generations in Time t
generations = predict_time / doubling_timeVariables
| Variable | Description | Default |
|---|---|---|
n0 | Initial Population (N0) | 1000 |
doubling_time | Doubling Time (td)(hours) | 8 |
predict_time | Prediction Time (t)(hours) | 48 |
k | Derived value= log(2) / doubling_time | calculated |
How It Works
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.
Worked Example
Starting with 1000 cells, doubling time 8 hours, predict at 48 hours.
n0 = 1000doubling_time = 8predict_time = 48
- 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
Ready to run the numbers?
Open Growth Rate Constant Calculator