Relative Growth Rate Calculator
Enter the initial and final dry weights and the time interval to compute relative growth rate RGR = (ln W₂ − ln W₁) / (t₂ − t₁), evaluating the daily dry-matter gain per unit existing dry weight.
Input Data
Results
At a glance:Relative growth rate (RGR) is a core metric of plant growth analysis, defined as the increase in dry weight per unit existing dry weight per unit time: RGR = (ln W₂ − ln W₁) / t, where W is dry weight and t the time interval (days), unit g·g⁻¹·day⁻¹. It answers: how fast does the plant grow relative to its current size — the 'relative' part normalizes by existing mass, like GDP growth vs total GDP. In growth analysis RGR connects to two more basic quantities via RGR = NAR × LAR: NAR (net assimilation rate, dry-matter gain per unit leaf area per unit time) and LAR (leaf area ratio, leaf area per unit total dry weight). So RGR is jointly decided by 'leaf photosynthetic efficiency (NAR)' and 'biomass allocation to leaves (LAR)'. Seedlings usually have high RGR (plenty of light, small size, high relative growth), then RGR gradually declines as plants mature and allocate more to stems/roots/structural tissue — one reason rapid early growth matters in crops.
Formula
Relative growth rate: RGR = (ln W₂ − ln W₁) / t.
Equivalent: RGR = (ln(W₂/W₁)) / t.
Growth relation: RGR = NAR × LAR.
$$RGR = \frac{\ln W_2 - \ln W_1}{t} = \frac{\ln(W_2 / W_1)}{t}$$$$RGR = NAR \times LAR$$How to Use
- Enter the initial dry weight W₁ and final dry weight W₂ (g).
- Enter the time interval t (days) between samplings.
- The right panel shows RGR (g·g⁻¹·day⁻¹); larger means faster relative growth.
RGR across growth stages (illustrative)
| Stage | Typical RGR (g·g⁻¹·day⁻¹) | Note |
|---|---|---|
| Seedling (rapid growth) | 0.15 – 0.30 | High light use efficiency and small size |
| Vegetative growth | 0.10 – 0.20 | Growth slowly declining |
| Maturity | < 0.05 | Most dry matter goes to storage/reproduction |
| Stress / poor conditions | near 0 or negative | Growth stalls or shrinks |
Ranges are general references; actual RGR varies with species, light, nutrients, and temperature. Compare at the same stage and conditions.
Case Studies
RGR over a growth period
A plant: initial W₁ = 2 g, after 10 days W₂ = 10 g.
RGR = (ln 10 − ln 2) / 10 = (2.3026 − 0.6931) / 10 = 0.16095 day⁻¹.
Means each gram of dry weight gains about 0.161 g per day — a typical seedling-phase value.
Comparing two crops' growth speed
Crop A: W 1→8 g in 10 days; crop B: W 1→4 g in 10 days (same start).
A: RGR = ln8/10 ≈ 0.2079 day⁻¹; B: RGR = ln4/10 ≈ 0.1386 day⁻¹.
Same starting mass, A's relative growth is faster; comparing RGR reveals growth-speed differences for varietal selection.
FAQ
Why use a natural logarithm (ln) for RGR?
Because plant dry weight grows approximately exponentially over short periods, the increase is proportional to current mass. Modeling W = W₀·e^(RGR·t) and inverting gives RGR = (ln W₂ − ln W₁)/t, the daily growth rate relative to existing mass — like compound-interest rate. Using ln naturally captures this 'proportional-to-current-size' growth.
How does RGR differ from absolute growth rate?
Absolute growth rate is total dry-weight gain per unit time (g/day), telling you how much biomass is added; RGR is that gain relative to existing dry weight (g·g⁻¹·day⁻¹), telling you growth speed relative to plant size. A large plant may have big absolute gain but low RGR; a seedling the opposite. RGR better compares growth vigor across different sizes.
What does RGR = NAR × LAR mean?
Growth analysis has a core identity: RGR = NAR × LAR. NAR is dry-matter gain per unit leaf area per unit time (leaf efficiency), LAR is leaf area per unit total dry weight (leaf allocation share). Their product returns RGR, showing growth speed is jointly set by 'leaf productivity' and 'leaf share' — a key framework for analyzing growth.
Why does RGR decline with growth stage?
Seedlings are small with unshaded leaves that use light efficiently, so RGR is high; as plants enlarge, stems/thickened support and roots/storage tissue accumulate, leaf-area share (LAR) drops and lower leaves are shaded (NAR falls), so RGR declines. That is why rapid early growth matters in crops — capture the high-RGR window.
How to measure dry weight and interval accurately?
Harvest and dry representative plants to constant weight (about 65–70°C), measure at two time points, and use the elapsed days as t. Sampling must be at the same growth stage and environment, with enough replicates to reduce error. RGR is a differential over the interval, so both dry-weight points and the time must be accurate.
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References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.