Leaf Area Index Calculator
Leaf area index from leaf area and ground area — or from plant density and leaves per plant — with the fraction of sunlight the canopy intercepts by Beer's law.
Leaf area index is the one-sided leaf area per unit of ground: a LAI of 3 means three square metres of leaf over every square metre of soil.
How the leaf area index calculator works
Leaf area index is the one-sided leaf area per unit of ground: a LAI of 3 means three square metres of leaf over every square metre of soil. Crops peak around 3 to 6; a rainforest reaches 8 or more.
Light interception follows Beer's law with an extinction coefficient near 0.5: a LAI of 3 intercepts 78% of the light, and going to 6 only adds 17 more points. That saturation is why yield stops rising with more leaf.
Formula: LAI = leaf area / ground area; intercepted = 1 − e^(−k × LAI)
Worked examples
| Inputs | Leaf area index | Note |
|---|---|---|
| A crop at 8 plants per m² | 3.6 | LAI 3.6, 83% intercepted |
| Early season | 0.96 | a sparse canopy |
| A dense planting | 9 | saturated |
FAQFrequently asked questions
What is leaf area index?
Total one-sided leaf area divided by the ground area beneath it. It is dimensionless: a LAI of 4 means four layers of leaf, on average, over every point.
What LAI does a crop need?
Around 3 to 4 to intercept most of the light. Beyond 5 or 6 the extra leaves shade each other and cost more to grow than they return.
What is Beer's law here?
Light falls off exponentially through the canopy, with an extinction coefficient that depends on leaf angle — about 0.5 for most crops, lower for upright leaves.
How is LAI measured?
Destructively, by harvesting and scanning leaves; or optically, from the light transmitted through the canopy — which is this equation run backwards.
Why does interception saturate?
Because each layer intercepts a share of what reaches it. Once 90% is caught, the next layer can only work on the remaining 10%.
Where these figures come from
- NCBI Bookshelf — Molecular Biology of the Cell — growth kinetics and molecular conventions
- Wellcome Sanger Institute — a leading UK genomics institute
Last checked: September 2026. Formulas are the standard textbook forms; assumptions are stated on each page because they are where these models break.