Relative growth rate (RGR) measures how fast something grows relative to its current size. The standard formula is RGR = (ln W2 − ln W1) / (t2 − t1), where W1 and W2 are the sizes at two time points, ln is the natural logarithm, and t1 and t2 are the corresponding times. This gives you a growth rate per unit of existing size per unit of time, making it possible to compare growth across organisms or populations of very different sizes.
What the Formula Means
The formula works by comparing the natural logarithm of two size measurements taken at different times. “Size” is usually dry weight in biology, but it can be any measurable quantity: biomass, population count, revenue, cell number. The natural log transformation is what makes the rate “relative.” Instead of telling you how many grams were added (that would be absolute growth rate), it tells you the proportional increase, adjusted for how big the organism already was.
Think of it like compound interest. A savings account earning 5% annually grows at the same relative rate whether it holds $100 or $10,000, even though the dollar amounts added each year are very different. RGR captures that percentage-style rate of increase.
The units reflect this proportional nature. In plant biology, RGR is typically expressed as g g⁻¹ day⁻¹ or g g⁻¹ week⁻¹. Because the grams cancel out, you can also think of the units as simply “per day” or “per week,” representing the fractional increase in size over that time period.
Step-by-Step Calculation
Here’s how to work through it with real numbers. Say you measured a plant’s dry weight at 2.0 g on day 0 and 5.5 g on day 14.
- Step 1: Take the natural log of each weight. ln(2.0) = 0.693. ln(5.5) = 1.705.
- Step 2: Subtract the first from the second. 1.705 − 0.693 = 1.012.
- Step 3: Divide by the time interval. 1.012 / 14 = 0.072.
The RGR is 0.072 g g⁻¹ day⁻¹, meaning the plant increased by about 7.2% of its current mass each day over that two-week window.
A Common Calculation Mistake to Avoid
If you’re calculating RGR from a group of plants (or any replicated samples), the order of operations matters. A natural instinct is to average the raw weights first, then take the natural log of those averages. This introduces a statistical bias that gets worse as variability among individuals increases, as the time interval grows longer, or as sample size increases.
The correct approach: log-transform each individual weight first, then average the logged values. In formula terms, use the mean of ln(W) rather than ln(mean of W). The difference can be small in tightly controlled experiments, but in field studies with high variability it can meaningfully skew your results.
How RGR Differs From Absolute Growth Rate
Absolute growth rate is simply the change in size divided by time: (W2 − W1) / (t2 − t1). It tells you the raw amount gained per day or per week. A tree adding 50 g of biomass per week has a higher absolute growth rate than a seedling adding 2 g per week, but the seedling may have a much higher relative growth rate because it’s doubling its mass rapidly while the tree is barely changing proportionally.
This distinction matters whenever you’re comparing organisms of different sizes. A 1 g seedling that reaches 3 g in a week has an absolute growth rate of about 0.29 g/day but an RGR of 0.157 g g⁻¹ day⁻¹. A 500 g shrub that reaches 510 g in the same week has a higher absolute rate (1.43 g/day) but a far lower RGR (0.003 g g⁻¹ day⁻¹). RGR reveals that the seedling is growing much more efficiently relative to its own body size.
What Drives RGR in Plants
In plant biology, RGR breaks down into two measurable components: leaf area ratio (LAR) and net assimilation rate (NAR). LAR is how much leaf surface area a plant deploys per unit of its total biomass. NAR is how much new dry matter the plant produces per unit of leaf area per unit of time. RGR equals the product of these two: RGR = LAR × NAR.
For most herbs and grasses, differences in LAR explain most of the variation in RGR between species. Plants that allocate more biomass to thin, expansive leaves tend to grow faster in relative terms. The underlying driver is usually specific leaf area, which is how much surface a leaf provides per gram of leaf tissue. Thin leaves with high surface area capture more light per unit of investment.
Temperature shifts the balance. Research on subantarctic and alpine grasses found that at low growth temperatures, NAR (the photosynthetic efficiency side) accounted for most of the differences in RGR between species. At higher temperatures, LAR became equally or more important. So which component matters most depends on the environmental context you’re studying.
Calculating RGR in a Spreadsheet
In Excel or Google Sheets, the formula translates directly. If your initial weight is in cell B2, your final weight is in B3, your start time is in C2, and your end time is in C3, the formula is:
=(LN(B3)-LN(B2))/(C3-C2)
For a batch of replicates, remember the bias issue. Log each individual weight in a helper column using =LN(B2), then use =AVERAGE() on those logged values for each time point. Subtract the average of logged initial weights from the average of logged final weights, then divide by the time interval.
If your data includes more than two harvests and you want to track how RGR changes over time, you can calculate it for each consecutive pair of time points. This gives you a curve showing whether relative growth is accelerating, steady, or declining, which is typical as plants get larger and RGR naturally slows.
Why RGR Tends to Decline Over Time
One important feature of RGR: it almost always decreases as organisms get bigger. Larger plants allocate more biomass to structural support (stems, roots) and proportionally less to photosynthetic tissue. This means LAR drops, pulling RGR down with it. The same pattern holds in populations, economies, and other growth contexts. Early-stage growth looks explosive in relative terms, and then naturally plateaus.
This means comparisons between species or treatments are only valid when the organisms are measured at similar sizes or developmental stages. Comparing the RGR of a fast-growing species measured as a small seedling against a slow-growing species measured as a larger juvenile will exaggerate the difference. Matching initial size as closely as possible gives you the cleanest comparison.