NAR (Net Assimilation Rate) Calculators

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Net assimilation rate (NAR) is a classical plant growth analysis parameter measuring the rate of dry mass increase per unit leaf area per unit time. It represents the net photosynthetic efficiency of a plant — the balance between carbon gained through photosynthesis and carbon lost through respiration, integrated at the whole-plant level. NAR is expressed in g/m²/day or mg/cm²/day. Together with leaf area ratio (LAR), it determines relative growth rate: RGR = NAR × LAR. High NAR indicates efficient carbon gain per unit leaf investment, influenced by light, nitrogen, temperature, and CO₂.

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NAR Formula

NAR = (W₂ − W₁) × [ln(LA₂) − ln(LA₁)] / [(LA₂ − LA₁) × (t₂ − t₁)]

W = dry mass; LA = leaf area; t = time. This formula assumes continuous proportional growth and gives units of g/m²/day.

Simplified (short intervals): NAR ≈ ΔW / (LA_mean × Δt), where LA_mean = (LA₁ + LA₂)/2.

RGR = NAR × LAR

Relative growth rate (RGR, g/g/day) = NAR × LAR. NAR measures efficiency per unit leaf area. LAR (leaf area ratio, m²/g) measures the quantity of leaf area per unit plant mass. A plant can achieve high RGR through high NAR (efficient photosynthesis), high LAR (lots of leaf area per gram), or both. Research shows that most interspecific variation in RGR is explained by LAR rather than NAR.

Factors Influencing NAR

  • Light: Higher irradiance increases NAR up to light saturation point
  • Leaf N concentration: Higher N → more Rubisco → higher photosynthetic capacity → higher NAR
  • Temperature: Optimal: 20–30°C for most temperate crops; declines below 10°C and above 35°C
  • CO₂: Elevated CO₂ increases NAR in C3 plants by reducing photorespiration

NAR Values

Fast-growing crops (sunflower, maize): NAR 10–20 g/m²/day. Moderate (wheat, soybean): 5–15 g/m²/day. Slow-growing woodland herbs: 1–5 g/m²/day. Stressed or shade-grown plants: < 1 g/m²/day.

Glossary

Net Assimilation Rate (NAR)
Whole-plant dry mass increase per unit leaf area per day (g/m²/day); reflects net photosynthetic efficiency; one of two components of RGR = NAR × LAR.
Leaf Area Ratio (LAR)
Total leaf area per unit plant dry mass (m²/g); reflects how much photosynthetic surface is deployed per unit biomass; LAR = SLA × leaf mass fraction; major driver of RGR variation.
Relative Growth Rate (RGR)
Fractional biomass increase per unit biomass per day: (ln W₂ − ln W₁)/(t₂ − t₁); decomposes as RGR = NAR × LAR; the primary whole-plant growth performance metric.

Frequently Asked Questions

NAR measures whole-plant photosynthetic efficiency — the increase in dry mass per unit leaf area per day. Full formula: NAR = (W₂−W₁) × [ln(LA₂)−ln(LA₁)] / [(LA₂−LA₁) × (t₂−t₁)]. For short intervals: NAR ≈ ΔW / (mean leaf area × Δt). Units: g/m²/day. Example: plant grows from 2 g to 3 g in 14 days with mean leaf area 50 cm² (0.005 m²): NAR ≈ 1 / (0.005 × 14) = 14.3 g/m²/day.

Gas exchange net photosynthesis (A, μmol CO₂/m²/s) measures instantaneous carbon exchange of individual leaves under controlled conditions. NAR is a whole-plant, time-integrated measure using dry mass change — it captures net carbon balance across the entire plant including all respiring tissues (roots, stems, old leaves) over days. NAR is therefore always lower than leaf-level A. While A gives mechanistic insight into leaf-level processes, NAR integrates allocation, respiration costs, and temporal variation into a single growth efficiency value.

Studies across plant species consistently find that most of the variation in RGR (= NAR × LAR) is explained by LAR rather than NAR. This is because: (1) plants can rapidly adjust leaf area ratio by producing thin, high-SLA leaves without needing to evolve fundamentally better photosynthetic biochemistry; (2) NAR is constrained within a narrower range by the biochemical limits of Rubisco and electron transport chains; (3) investing in many thin leaves (high LAR) scales more predictably with growth than small improvements in leaf-level efficiency. Differences in SLA are the primary driver of LAR differences.

NAR (net assimilation rate) and ULR (unit leaf rate) are often used synonymously in classic plant growth analysis literature — both describe dry mass increase per unit leaf area per time. Some authors use ULR specifically for the simplified approximation (ΔW / mean LA × Δt) and NAR for the formula using logarithmic leaf area terms. In modern usage, both terms appear in the literature for the same concept. The key formula — whatever the name — quantifies whole-plant photosynthetic efficiency per unit leaf area and remains an important parameter in comparative plant physiology.