NAR Calculator
Enter the plant dry weights, leaf areas at two sampling times, and the interval in days to compute the net assimilation rate (NAR), the dry-matter gain per unit leaf area per unit time — a core growth-analysis metric.
Input Data
Results
At a glance:Net assimilation rate (NAR), also called unit leaf rate (ULR), is a core metric of plant growth analysis: the dry matter accumulated per unit leaf area per unit time, representing the average net photosynthetic productivity of the whole leaf canopy (after subtracting respiration). When leaf area changes during the observation, NAR uses the integral-mean formula: NAR = (W₂ − W₁)/(t₂ − t₁) × (ln A₂ − ln A₁)/(A₂ − A₁), where W is plant dry weight, A leaf area, t time; this formula assumes dry weight and leaf area are approximately linearly related over the period. NAR connects to two other growth-analysis quantities: relative growth rate RGR = NAR × leaf area ratio LAR — 'how fast it grows' is jointly decided by 'leaf production efficiency' and 'leaf share of the whole plant'. Early in growth NAR is usually higher, then declines as the canopy closes and lower leaves are shaded.
Formula
Net assimilation rate: NAR = (W₂ − W₁)/(t₂ − t₁) × (ln A₂ − ln A₁)/(A₂ − A₁).
When A₁ = A₂ it reduces to: NAR = (W₂ − W₁)/(t₂ − t₁) ÷ A.
Growth relation: RGR = NAR × LAR (leaf area ratio).
$$NAR = \dfrac{W_2 - W_1}{t_2 - t_1} \times \dfrac{\ln A_2 - \ln A_1}{A_2 - A_1}$$$$RGR = NAR \times LAR$$How to Use
- Enter the start plant dry weight W₁ and leaf area A₁.
- Enter the end dry weight W₂, leaf area A₂, and the interval in days.
- The tool instantly shows NAR (g·cm⁻²·day⁻¹); larger means higher average leaf productivity.
Growth-analysis quantities related to NAR
| Metric | Definition | Meaning |
|---|---|---|
| NAR (unit leaf rate) | Dry-matter net gain per unit leaf area per unit time | Average productivity of leaves |
| RGR (relative growth rate) | Dry-weight gain per unit existing dry weight per unit time | Whole-plant relative growth speed |
| LAR (leaf area ratio) | Leaf area ÷ total dry weight | Share invested in light-catching area |
| Relation | RGR = NAR × LAR | Growth = efficiency × leaf share |
NAR reflects the 'quality' efficiency of leaves, LAR the 'quantity' share of leaves; their product gives RGR.
Case Studies
NAR during a growth period
A plant: start W₁ = 5 g, A₁ = 200 cm²; after 10 days W₂ = 15 g, A₂ = 600 cm².
Dry-weight gain = (15 − 5) ÷ 10 = 1 g/day; log term = (ln600 − ln200) ÷ (600 − 200) ≈ 0.002747 cm⁻².
NAR = 1 × 0.002747 ≈ 0.002747 g·cm⁻²·day⁻¹, i.e. about 0.00275 g dry matter added per cm² leaf per day.
Simplified case with unchanged leaf area
If both samplings give the same leaf area A₁ = A₂ = 400 cm², and dry weight rose 10 g in 10 days.
The log term reduces to 1/A = 1/400, NAR = (10 ÷ 10) × (1/400) = 0.0025 g·cm⁻²·day⁻¹.
The formula simplifies to dry-weight gain divided directly by leaf area, handy for quick estimates.
FAQ
Why is there a natural logarithm (ln) in the formula?
Because leaf area usually changes continuously during observation, using only the start or end area biases the result. Growth analysis assumes dry weight varies approximately linearly with leaf area; integrating over time to get the time-average yields the log term (ln A₂ − ln A₁)/(A₂ − A₁), the reciprocal of the log-mean leaf area over the period — closer to continuous growth than a simple average.
What are the units of NAR?
This calculator shows g·cm⁻²·day⁻¹ — grams of dry matter per cm² leaf area per day. Literature also uses g·m⁻²·day⁻¹ (multiply cm² by 10000 when converting) or weeks as the time unit. Always unify dry-weight, leaf-area, and time units and state them clearly in reports.
Is NAR the same as photosynthetic rate?
Not exactly. Instantaneous photosynthetic rate is gas exchange of a specific leaf at a given moment and light; NAR is the 'net' dry-matter accumulation of the whole canopy over a period, after subtracting whole-plant (including non-photosynthetic organs) respiration, averaging leaves of different ages and light conditions. So NAR is an integrative productivity index, usually lower than the theoretical maximum instantaneous photosynthesis.
Why does NAR decline with growth stage?
Early plants are small with few, unshaded leaves that receive ample light, so NAR is high; as plants grow and the canopy closes, lower and inner leaves are shaded, their photosynthetic efficiency drops, even becoming net respiration, pulling down the whole-plant average — so NAR declines with stage. That is also why RGR is typically highest in the seedling phase.
How does NAR connect to relative growth rate RGR?
Growth analysis has a core identity: RGR = NAR × LAR. RGR is the daily dry-weight gain per unit existing dry weight; LAR is leaf area ÷ total dry weight. Multiplying them returns RGR. This shows growth speed is jointly set by 'leaf production efficiency (NAR)' and 'share invested in leaves (LAR)' — a powerful framework for analyzing plant growth.
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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.