function calculateGrowthRate() {
// Clear previous errors
var errorDiv = document.getElementById('errorDisplay');
var resultsDiv = document.getElementById('results');
errorDiv.style.display = 'none';
resultsDiv.style.display = 'none';
// Get Input Values
var odStart = parseFloat(document.getElementById('odStart').value);
var timeStart = parseFloat(document.getElementById('timeStart').value);
var odEnd = parseFloat(document.getElementById('odEnd').value);
var timeEnd = parseFloat(document.getElementById('timeEnd').value);
var unit = document.getElementById('timeUnit').value;
// Validation
if (isNaN(odStart) || isNaN(timeStart) || isNaN(odEnd) || isNaN(timeEnd)) {
errorDiv.innerHTML = "Please enter valid numeric values for all fields.";
errorDiv.style.display = 'block';
return;
}
if (odStart <= 0 || odEnd <= 0) {
errorDiv.innerHTML = "Optical Density (OD) must be greater than 0.";
errorDiv.style.display = 'block';
return;
}
if (timeEnd 0) {
doublingTime = Math.log(2) / mu;
} else if (mu === 0) {
doublingTime = 0; // No growth
} else {
// Negative growth (death phase), doubling time is not applicable in the standard sense
doublingTime = Infinity;
}
// Number of generations: n = (log10(OD2) – log10(OD1)) / log10(2)
// Or simply: n = (t2 – t1) / doublingTime
var generations = 0;
if (doublingTime > 0 && doublingTime !== Infinity) {
generations = deltaT / doublingTime;
}
// Update UI
var unitSuffix = (unit === "hours") ? "h⁻¹" : "min⁻¹";
var timeSuffix = (unit === "hours") ? "hours" : "minutes";
document.getElementById('resMu').innerHTML = mu.toFixed(4);
document.getElementById('unitMu').innerHTML = unitSuffix;
if (mu > 0) {
document.getElementById('resGenTime').innerHTML = doublingTime.toFixed(2);
} else {
document.getElementById('resGenTime').innerHTML = "N/A (No Growth)";
}
document.getElementById('unitGenTime').innerHTML = timeSuffix;
document.getElementById('resGenerations').innerHTML = generations.toFixed(2);
resultsDiv.style.display = 'block';
}
How to Calculate Bacterial Growth Rate from OD
Understanding bacterial kinetics is fundamental to microbiology, biotechnology, and fermentation processes. The most common method to track this growth is by measuring Optical Density (OD), typically at a wavelength of 600nm (OD600), using a spectrophotometer. This calculator helps researchers and students instantly determine the specific growth rate (μ) and doubling time based on OD readings taken during the exponential (log) phase.
What is Specific Growth Rate (μ)?
The specific growth rate, denoted as μ (mu), represents the rate at which the bacterial population increases per unit of time. It depends on the microbial strain, the composition of the medium, temperature, and other environmental conditions. It is calculated during the exponential phase where cells are dividing at a constant rate.
In the exponential phase, the rate of increase in biomass is proportional to the initial biomass:
ln(OD₂) – ln(OD₁) = μ (t₂ – t₁)
The Formulae Used
To calculate the specific growth rate manually, you can use the following rearranged formula:
μ = (ln(OD₂) – ln(OD₁)) / (t₂ – t₁)
Where:
ln is the natural logarithm.
OD₁ is the optical density at the start time (t₁).
OD₂ is the optical density at the end time (t₂).
Calculating Doubling Time (Generation Time)
Once you have the specific growth rate, calculating the doubling time (often denoted as g or td) is straightforward. This is the time it takes for the bacterial population to replicate exactly once.
Doubling Time = ln(2) / μ ≈ 0.693 / μ
How to Perform the Experiment
Inoculate: Start your bacterial culture in the desired medium.
Sample: Take OD600 readings at regular intervals (e.g., every 30 minutes).
Plot: Create a semi-log plot (Time on X-axis, Log(OD) on Y-axis).
Identify Log Phase: Look for the linear portion of the graph. This is the exponential phase.
Calculate: Select two points (t₁, OD₁) and (t₂, OD₂) from this linear section and enter them into the calculator above.
Why Use Optical Density (OD)?
While OD does not measure viable cell count directly (it measures light scattering caused by cells), it is a rapid, non-destructive method that correlates linearly with cell concentration within a specific range (usually OD 0.1 to 1.0). If your samples exceed OD 1.0, it is recommended to dilute them before measuring to maintain accuracy according to Beer-Lambert law principles.