Understand the relationship
The reasoning behind the result
Relative growth rate uses logarithmic dry-mass change
RGR = [ln(W2) − ln(W1)]/Δt
For positive dry masses, the log difference expresses proportional change and is independent of the mass unit when the same unit is used at both times. Dividing by elapsed time gives the mean relative growth rate for that interval.
A positive value supports a conditional doubling time ln(2)/RGR; a negative value supports a descriptive halving time ln(2)/|RGR|. Neither is a forecast.
Destructive harvests require a declared comparison statistic
Plant dry mass is often measured destructively, so time points can describe different sampled plants. Classical group mean RGR uses the difference between mean ln(individual dry mass) at the harvests. Entering each group's geometric mean preserves that mean-log quantity because ln(geometric mean) equals mean ln(mass).
Taking ln of an arithmetic group mean is generally different because logarithms do not commute with averaging. The calculator can still describe the change of entered arithmetic means, but that result must be labelled as log change of those aggregate estimates rather than replicate-aware classical mean RGR.
A selected series is an equal-weight log-linear description
ln(Wi) = a + r(ti − tearliest) + εi
The series mode sorts harvests by time and fits ordinary unweighted least squares after centering coordinates for numerical stability. Every record and residual stays visible.
R² and RMS log residual summarize the selected estimates under this line. They are not confidence intervals, biological replication or proof of constant exponential growth.
Zero and decline remain valid records
An exactly unchanged or numerically unresolved interval is reported with zero RGR. A resolved decrease retains a negative RGR rather than being rejected for lacking growth.
Zero or negative mass cannot enter a logarithm and therefore requires a different measurement or censoring model outside this calculator.
Follow the numbers
Two-harvest mean relative growth rate
- Use W1 = 2 g at day 0 and W2 = 8 g at day 14.
- The dry-mass ratio is 8/2 = 4.
- The natural-log change is ln(4) = 1.38629436.
- Mean RGR is 1.38629436/14 = 0.0990210258 d⁻¹.
- The conditional doubling time is ln(2)/0.0990210258 = 7 d.
The result is the mean logarithmic rate across the declared harvest interval; it does not show the path between harvests or predict later mass.
Quick guide
How to use this calculator
- Use the same positive dry-mass definition, tissue inclusion and biological population at every entered time.
- Choose two harvests for an interval mean or enter only a deliberately selected set of comparable harvest estimates for a descriptive log-linear fit.
- Inspect the chronological dry-mass and residual ledger before using the fitted rate.
- Report the time interval, mass basis and sampling design with the rate; do not treat the fitted relationship as a future-growth law.
Calculation method
Calculation and interpretation
Summarize relative change in a consistently defined positive plant dry-mass quantity without selecting a growth phase, extrapolating future mass or grading plant performance.
Mean RGR = [ln(W2) − ln(W1)]/(t2 − t1); selected-series RGR = unweighted OLS slope of ln(W) against time
Worked example
Two-harvest mean relative growth rate
The result is the mean logarithmic rate across the declared harvest interval; it does not show the path between harvests or predict later mass.
Mean RGR = [ln(W2) − ln(W1)]/(t2 − t1); selected-series RGR = unweighted OLS slope of ln(W) against time
Supported inputs
Precision and limits
Positive comparable dry mass only
Every dry-mass estimate must be positive and use the same tissue and drying basis. Zero, censored and composition-changing records need another model.
No automatic phase or outlier selection
The fit uses every entered row with equal weight and does not select a linear phase, remove points or search for a maximum rate.
No extrapolation
Doubling or halving time restates the fitted or interval rate. It is not a forecast, treatment recommendation or proof that the rate remains constant.
No inferential or replicate model
For group harvests, classical mean-log analysis requires individual log masses or entered geometric means. Logging an arithmetic mean is a different descriptive statistic. Individual plants and technical replicates also require an appropriate sampling and error model; R² and RMS residual do not supply it.
Numerical support
Positive dry-mass estimates support 10⁻¹² through 10¹² in the selected mass unit. Time coordinates support magnitudes through 10¹² and must resolve as distinct; a fit retains 3–30 harvest estimates. The 32-machine-epsilon response rule is a computation boundary, not a biological zero.
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