How to Calculate Relative Growth Rate

Relative Growth Rate Calculator

Relative Growth Rate (RGR) is a fundamental metric used in biology, ecology, and economics to measure the speed at which a quantity increases relative to its size. Unlike absolute growth rate, which simply tells you the total amount gained, RGR provides a standardized rate that allows you to compare the growth efficiency of different systems regardless of their initial scale.

This calculator is specifically designed to compute the exponential relative growth rate, which is the standard method for analyzing biological growth (such as plant biomass) or continuous population expansion.

The Relative Growth Rate Formula

The most accurate way to calculate RGR, assuming exponential growth over a specific time interval, is using the natural logarithms of the sizes. This accounts for the compounding nature of growth.

RGR = (ln(W₂) – ln(W₁)) / (t₂ – t₁)

Where:

• ln = The natural logarithm
• W₁ = The initial size (weight, height, or number)
• W₂ = The final size
• t₂ – t₁ = The time interval duration

Step-by-Step Calculation Example

Let's look at a practical example from plant biology. Suppose you are measuring the growth of a seedling.

• Initial Weight (W₁): 5 grams
• Final Weight (W₂): 15 grams
• Time Period (t): 10 days

Step 1: Find the Natural Logs
Calculate the natural logarithm (ln) of both weights:
ln(15) ≈ 2.708
ln(5) ≈ 1.609

Step 2: Find the Difference
Subtract the initial log from the final log:
2.708 – 1.609 = 1.099

Step 3: Divide by Time
Divide the result by the time interval (10 days):
1.099 / 10 = 0.1099 g·g^-1·day^-1

This result implies that for every gram of plant tissue, the plant produces roughly 0.11 grams of new tissue per day.

Why Use Relative vs. Absolute Growth?

Absolute Growth Rate (AGR) measures the simple change: (Final – Initial) / Time. In the example above, the plant gained 1 gram per day. However, a 5g plant gaining 1g/day is growing much "faster" physiologically than a 100g plant gaining 1g/day.

Relative Growth Rate (RGR) normalizes this. It reveals the efficiency of the growth. It is essentially the "interest rate" of the biological system. A high RGR indicates a highly efficient multiplier effect.

Doubling Time

Once you know the RGR, you can calculate how long it takes for the value to double in size using the "Rule of 70" (or more accurately, ln(2)):

Doubling Time = ln(2) / RGR ≈ 0.693 / RGR

Using the example above: 0.693 / 0.1099 ≈ 6.3 days to double in weight.