Relative Growth Rate Calculators

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Relative growth rate (RGR) is the rate of increase in plant biomass per unit of existing biomass per unit time, expressed as g/g/day or mg/g/day. It integrates the efficiency with which a plant acquires resources and converts them to new biomass. RGR is a central metric in plant ecology, crop science, and comparative plant physiology. It can be decomposed into net assimilation rate (NAR) — photosynthetic efficiency — and leaf area ratio (LAR) — the amount of leaf area deployed per unit plant biomass, providing mechanistic insight into growth differences among species or treatments.

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RGR Formula

RGR = (ln W₂ − ln W₁) / (t₂ − t₁)

W₁ and W₂ = dry biomass at times t₁ and t₂. Units: g g⁻¹ day⁻¹ or mg g⁻¹ day⁻¹. Example: plant grows from 2.0 g to 3.2 g in 10 days: RGR = (ln 3.2 − ln 2.0) / 10 = (1.163 − 0.693) / 10 = 0.047 g/g/day = 47 mg/g/day.

Decomposing RGR

RGR = NAR × LAR

  • NAR (Net Assimilation Rate): Net dry matter increase per unit leaf area per time (g/m²/day) — reflects photosynthetic efficiency
  • LAR (Leaf Area Ratio): Total leaf area per unit plant biomass (m²/g) — reflects how much leaf is deployed per unit investment

LAR can be further decomposed: LAR = SLA × LMF, where SLA = specific leaf area and LMF = leaf mass fraction.

RGR Values in Plants

Fast-growing crop plants and weeds (e.g., sunflower, lambsquarters): RGR 150–350 mg/g/day. Slow-growing woodland herbs and stress-adapted perennials: 50–100 mg/g/day. Slow-growing stress-tolerant shrubs (heathers, Mediterranean plants): 10–50 mg/g/day. High RGR correlates with high SLA, high leaf N, and rapid tissue turnover — the 'fast' end of the leaf economics spectrum.

RGR in Crop Science

Crop growth rate (CGR) = RGR × plant biomass density (g/m²/day at the field scale). Harvest index (HI) = grain/total dry matter — the fraction of total biomass in the harvested organ. Maximizing HI through breeding (as in Green Revolution semi-dwarf wheat and rice) has been as important as raising RGR for improving yields.

Glossary

Relative Growth Rate (RGR)
The rate of dry biomass increase per unit biomass per day: RGR = (ln W₂ − ln W₁)/(t₂ − t₁); units g/g/day or mg/g/day; central metric in plant growth analysis.
Net Assimilation Rate (NAR)
Dry matter production per unit leaf area per day (g/m²/day); reflects photosynthetic efficiency; one of two components of RGR = NAR × LAR.
Leaf Area Ratio (LAR)
Total leaf area per unit total plant dry mass (m²/g); reflects the amount of photosynthetic surface deployed per unit biomass investment; LAR = SLA × leaf mass fraction.

Frequently Asked Questions

RGR = (ln W₂ − ln W₁) / (t₂ − t₁), where W₁ and W₂ are plant dry biomass at the start and end of the measurement period, and t is time in days. Always use dry mass (oven-dried at 70°C to constant weight), not fresh mass, as water content varies. Example: 0.5 g to 1.0 g in 14 days: RGR = (ln1.0 − ln0.5)/14 = 0.693/14 = 0.0495 g/g/day = 49.5 mg/g/day.

RGR (relative growth rate) is the overall growth efficiency. It decomposes as RGR = NAR × LAR. NAR (net assimilation rate) measures how much dry matter is produced per unit leaf area per day — it reflects photosynthetic efficiency minus respiratory losses. LAR (leaf area ratio) is total leaf area divided by total plant mass — it reflects how much leaf area the plant deploys per gram of investment. A plant can have high RGR by having high NAR, high LAR, or both.

High specific leaf area (SLA = leaf area / leaf mass) means thin, light-capturing leaves that maximize LAR per unit leaf investment. High LAR gives high RGR (since RGR = NAR × LAR) without requiring especially high photosynthetic rate per unit area. Fast-growing plants (weeds, crop plants, early successional species) invest in quantity of leaf area rather than thick, durable leaves. This is the core fast–slow trade-off in the leaf economics spectrum: fast growers sacrifice leaf longevity and defense for rapid area deployment.

RGR decreases with: nutrient limitation (especially N and P reduce leaf N and photosynthetic capacity, lowering NAR); shade (reduces light-use efficiency and NAR); drought (stomatal closure reduces CO₂ uptake); cold temperatures (reduce enzyme activity and nutrient uptake); and genetic strategy (stress-tolerant species inherently have lower maximum RGR). Plants can compensate for low NAR through higher LAR, but there are biophysical limits to how thin and fragile leaves can be in stressful environments.