How to Calculate Specific Growth Rate of Bacteria

Specific Growth Rate of Bacteria Calculator

The starting quantity (CFU/mL or Optical Density).

The quantity after the growth period.

The duration of the growth period (usually in hours).

Calculation Results:

Specific Growth Rate (μ): h⁻¹

Doubling Time (g): hours

Number of Generations (n):

function calculateBacterialGrowth() { var n0 = parseFloat(document.getElementById('initialPopulation').value); var nt = parseFloat(document.getElementById('finalPopulation').value); var t = parseFloat(document.getElementById('timeInterval').value); var resultContainer = document.getElementById('growthResultContainer'); if (isNaN(n0) || isNaN(nt) || isNaN(t) || n0 <= 0 || nt <= 0 || t <= 0) { alert("Please enter valid positive numbers for all fields. Initial and Final values must be greater than zero."); return; } if (nt <= n0) { alert("Final population must be greater than the initial population for growth rate calculation."); return; } // Calculation of Specific Growth Rate (mu) // mu = (ln(Nt) – ln(N0)) / t var mu = (Math.log(nt) – Math.log(n0)) / t; // Calculation of Doubling Time (g) // g = ln(2) / mu var g = Math.log(2) / mu; // Calculation of Generations (n) // n = (log10(Nt) – log10(N0)) / log10(2) var n = (Math.log10(nt) – Math.log10(n0)) / Math.log10(2); document.getElementById('muValue').innerText = mu.toFixed(4); document.getElementById('doublingTimeValue').innerText = g.toFixed(2); document.getElementById('generationsValue').innerText = n.toFixed(2); resultContainer.style.display = 'block'; }

Understanding the Specific Growth Rate of Bacteria

In microbiology, the specific growth rate (μ) is a critical parameter that describes how quickly a microbial population increases in size during the exponential (log) phase. It represents the increase in biomass or cell number per unit of time per unit of biomass/cells.

The Mathematical Formula

The specific growth rate is derived from the first-order kinetic equation for microbial growth:

μ = (ln(N_t) – ln(N₀)) / t

• N₀: Initial cell concentration or Optical Density (OD).
• N_t: Final cell concentration or Optical Density at time t.
• t: The time interval during which exponential growth occurred.
• ln: Natural logarithm.

What is Doubling Time (g)?

Doubling time, also known as generation time, is the time required for a population of bacteria to double in size. It is inversely proportional to the specific growth rate. The formula is:

g = ln(2) / μ ≈ 0.693 / μ

Example Calculation

Imagine you are culturing E. coli. You measure the Optical Density (OD₆₀₀) at the start of the log phase and again 3 hours later:

• Initial OD (N₀): 0.10
• Final OD (N_t): 0.80
• Time (t): 3 hours

First, calculate μ:

μ = (ln(0.80) – ln(0.10)) / 3 = ((-0.223) – (-2.302)) / 3 = 2.079 / 3 = 0.693 h⁻¹

Next, calculate doubling time (g):

g = 0.693 / 0.693 = 1.0 hour

Phases of Bacterial Growth

1. Lag Phase: Bacteria adapt to new environment; no immediate increase in cell number.
2. Log (Exponential) Phase: Constant growth rate; cells divide at their maximum rate. (This calculator is intended for this phase).
3. Stationary Phase: Growth rate equals death rate due to nutrient depletion or waste accumulation.
4. Death Phase: Living cells decline as conditions become toxic.

Note: When using Optical Density (OD) as a proxy for population, ensure you are within the linear range of your spectrophotometer (typically OD 0.1 to 0.8) for accurate results.