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Plant Biology & Photosynthesis

Net Assimilation Rate Two-Harvest Workbench

Calculate classical interval net assimilation rate from two comparable dry-mass and leaf-area harvests using a stable logarithmic mean area.

Biology · experimental measurements

Relate total dry-mass change to the logarithmic mean projected leaf area across one declared harvest interval without equating the result with instantaneous photosynthesis.

Private calculations in your browser · explicit inputs and model boundaries
Example preview · Mass and leaf area increaseDry mass and projected leaf area relative to the first harvest
101.251.751.53.51.755.2527Total dry-mass ratioProjected leaf-area ratioTime since first harvest (d)Ratio to first-harvest value
Total dry-mass ratioProjected leaf-area ratio

Both series are normalized to 1 at actual time 0 d, so unlike units remain separate while their interval changes can be compared. NAR uses the signed dry-mass change and 0.0577078016 m² logarithmic mean leaf area; the lines do not reconstruct unmeasured trajectories.

  1. 1EnterProvide the known values
  2. 2CalculateResults update automatically
  3. 3VerifyReview the details and units
Try an example

Describe the biological unit, tissue included in total dry mass, leaf-area convention and comparability of both harvests.

Enter values in selected time unit.

Enter values in selected mass unit.

Enter values in selected area unit.

Enter values in selected time unit.

Enter values in selected mass unit.

Enter values in selected area unit.

Calculation result

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Understand the relationship

The reasoning behind the result

Classical NAR normalizes dry-mass gain by interval leaf area

NAR = (ΔW/Δt)/Alog

The numerator is change in consistently defined total plant dry mass per time. The denominator Alog is the logarithmic mean of the two positive total projected leaf areas.

This gives dry mass per projected leaf area per time under the entered harvest conventions.

The logarithmic mean preserves the classical two-harvest equation

Alog = (A2 − A1)/[ln(A2) − ln(A1)]

When leaf area changes, the logarithmic mean is the area that makes the compact gain/(time × area) form equal to the classical expression. It lies between the two positive endpoint areas.

When A2 equals A1, the continuous limit is Alog = A1. The calculator evaluates that limit directly instead of producing an indeterminate 0/0.

NAR and RGR remain distinct

RGR = [ln(W2) − ln(W1)]/Δt

RGR expresses proportional total dry-mass change per time. NAR expresses absolute dry-mass change per logarithmic mean leaf area and time. Both are reported because one cannot be substituted for the other.

Specific leaf area and leaf mass fraction are further allocation traits; they are not inferred from two total leaf-area values.

Net assimilation rate is not instantaneous photosynthesis

Classical NAR, also called unit leaf rate in some literature, integrates whole-plant dry-mass change across the harvest interval. Respiration, allocation, tissue turnover, changing area and sampling all contribute to the observed balance.

The result does not estimate instantaneous carbon assimilation, gas exchange, carbon-use efficiency or a causal treatment effect.

Follow the numbers

Two harvests with increasing mass and area

  1. Use W1 = 2 g, W2 = 4 g, A1 = 400 cm² = 0.04 m², A2 = 800 cm² = 0.08 m² and Δt = 7 d.
  2. The logarithmic area change is ln(0.08/0.04) = ln(2).
  3. The logarithmic mean area is (0.08 − 0.04)/ln(2) = 0.0577078 m².
  4. Dry-mass gain rate is (4 − 2)/7 = 0.285714 g/d.
  5. NAR is 0.285714/0.0577078 = 4.951051 g m⁻² d⁻¹.

The value is a two-harvest whole-plant dry-mass balance per logarithmic mean projected leaf area, not a direct photosynthesis measurement.

Quick guide

How to use this calculator

  1. Use comparable total dry-mass and projected leaf-area definitions at two ordered harvest times.
  2. Enter each harvest in one consistent unit pair; conversion to g, m² and the selected time unit is explicit in the results.
  3. Inspect the logarithmic mean leaf area and signed dry-mass gain that form the denominator and numerator.
  4. Describe the result as an interval whole-plant growth-analysis quantity, not an instantaneous leaf gas-exchange measurement.

Calculation method

Calculation and interpretation

Relate total dry-mass change to the logarithmic mean projected leaf area across one declared harvest interval without equating the result with instantaneous photosynthesis.

NAR = [(W2 − W1)/(t2 − t1)] × [ln(A2) − ln(A1)]/(A2 − A1) = dry-mass gain / (time × logarithmic mean leaf area)

Worked example

Two harvests with increasing mass and area

The value is a two-harvest whole-plant dry-mass balance per logarithmic mean projected leaf area, not a direct photosynthesis measurement.

NAR = [(W2 − W1)/(t2 − t1)] × [ln(A2) − ln(A1)]/(A2 − A1) = dry-mass gain / (time × logarithmic mean leaf area)

Supported inputs

Precision and limits

Two comparable harvests

The equation requires positive leaf areas, positive total dry-mass estimates, an ordered time interval and matching tissue/area definitions across harvests.

Classical interval approximation

Two endpoints do not show within-interval trajectories. Strongly nonlinear or irregular growth and leaf-area paths may require a richer functional growth analysis.

No gas-exchange inference

NAR does not produce instantaneous photosynthesis, respiration, carbon concentration, stomatal behavior or carbon-use efficiency.

No inferential uncertainty

Group means, destructive samples and nested leaves need an appropriate statistical design. The calculator does not derive confidence intervals or treatment significance.

Numerical support

Positive total dry-mass estimates support 10⁻¹² through 10¹² and positive projected leaf areas support 10⁻¹² through 10¹⁵ in their selected input units. Time coordinates support magnitudes through 10¹² and must resolve as ordered. The 32-machine-epsilon mass-response rule is a computation boundary, not a biological zero.

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