Relative Growth Rate Calculator

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Relative Growth Rate Calculator

Calculate the exponential growth rate of a population, organism, or investment over time.

Starting size, mass, or quantity.
Ending size, mass, or quantity.
The duration of growth (days, hours, years, etc.)

Results:

Relative Growth Rate: 0 per unit of time

Percentage Growth: 0%

What is Relative Growth Rate (RGR)?

The Relative Growth Rate (RGR) is a measure used to quantify the speed of growth relative to the size of the individual or population. Unlike absolute growth rate, which measures how much something grows in total, RGR accounts for the initial size, making it a "rate per unit of existing material." It is a fundamental metric in plant physiology, ecology, and microbiology.

The RGR Formula

To calculate the mean relative growth rate over a specific time interval, the following logarithmic formula is commonly used:

RGR = (ln(W2) - ln(W1)) / (t2 - t1)
  • W1: Initial value (weight, height, or population size)
  • W2: Final value after the time period
  • t2 – t1: The total time elapsed between measurements
  • ln: The natural logarithm

Practical Example

Suppose you are tracking the biomass of a seedling. On Day 1, its weight is 2.0 grams. On Day 10, its weight has increased to 5.5 grams.

Step Calculation
1. Log of Final (ln 5.5) ~1.7047
2. Log of Initial (ln 2.0) ~0.6931
3. Difference 1.0116
4. Divide by Time (9 days) 0.1124 g/g/day

Why RGR Matters

In biology, RGR helps researchers compare plants of different sizes. A smaller plant may have a lower absolute growth rate than a large tree, but its relative growth rate might be much higher because it is investing more energy into new tissue formation. In finance, this logic is similar to looking at the "compound growth rate" of an asset.

Common Use Cases

  1. Agriculture: Evaluating the efficiency of different fertilizers on crop growth.
  2. Bacteriology: Determining the generation time of a bacterial colony.
  3. Economics: Analyzing the growth of startups compared to established corporations.
  4. Environmental Science: Measuring the recovery rate of a forest after a wildfire.
function calculateRGR() { var w1 = parseFloat(document.getElementById("initialValue").value); var w2 = parseFloat(document.getElementById("finalValue").value); var time = parseFloat(document.getElementById("timePeriod").value); var resultBox = document.getElementById("rgrResultBox"); var rgrValDisplay = document.getElementById("rgrValue"); var rgrPercDisplay = document.getElementById("rgrPercentage"); var rgrExpl = document.getElementById("rgrExplanation"); // Validation if (isNaN(w1) || isNaN(w2) || isNaN(time) || w1 <= 0 || w2 <= 0 || time <= 0) { alert("Please enter positive values for all fields. Initial and Final values must be greater than zero."); resultBox.style.display = "none"; return; } if (w2 < w1) { rgrExpl.innerText = "Note: The final value is smaller than the initial value, indicating a negative growth rate (decline)."; } else { rgrExpl.innerText = "This indicates the rate of increase per unit of time based on an exponential growth model."; } // Formula: RGR = (ln(W2) – ln(W1)) / t var rgr = (Math.log(w2) – Math.log(w1)) / time; var rgrPercentage = rgr * 100; // Output rgrValDisplay.innerText = rgr.toFixed(5); rgrPercDisplay.innerText = rgrPercentage.toFixed(2); resultBox.style.display = "block"; }

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