Leaf Area Index (LAI) Calculator: Light Transmission, Harvest or Per-Plant
Calculate leaf area index from canopy light transmission (Beer–Lambert, with a fixed extinction coefficient or one from the sun angle and leaf angle distribution, plus a clumping correction), from harvested leaf area or leaf dry mass × specific leaf area over ground area, or from leaf area per plant × plant density. Shows light interception, the LAI for 95% interception, an interception curve and typical LAI values for crops and forests.
How it works
direct: LAI = leaf area ÷ ground area · from dry mass: leaf area = dry mass × SLA · per plant: LAI = leaf area per plant × plants per m² · light: LAI = −ln(I ÷ I₀) ÷ k (÷ Ω for clumping) · k from sun angle (ellipsoidal leaves): k = √(x² + tan²θ) ÷ (x + 1.774 (x + 1.182)^−0.733), which is 0.5 ÷ cos θ for random leaves · interception = 1 − e^(−k × LAI) · LAI for 95% interception = 3.0 ÷ k
Leaf area index is the area of leaf (one side) stacked over each square metre of ground. It governs how much sunlight a canopy can catch: each layer of leaves removes a share of the light passing through it, so the light reaching the ground falls exponentially with LAI. This is the Beer–Lambert law, with the extinction coefficient k describing how much shadow each unit of leaf casts; flat leaves and a low sun give a larger k, upright leaves a smaller one. The same law gives a quick field measurement: read photosynthetically active radiation (PAR) above and below the canopy and invert the exponential. You can enter k directly or let the calculator work it out from the solar zenith angle and the leaf angle distribution (Campbell’s ellipsoidal model, the one used by line ceptometers), and you can correct for clumped foliage with a clumping index. Commercial ceptometers also correct for leaf absorptivity and the diffuse share of light, so their readings can differ a little from this simple form. Direct methods divide harvested leaf area by the ground area it came from, or estimate leaf area from leaf dry mass and specific leaf area; the per-plant method multiplies leaf area per plant by plant density. Crops reach near-complete interception at around three to four layers, forests hold five or more, and beyond the critical LAI (95% interception) extra leaves sit in deep shade and cost more in respiration than they earn. That is why breeders favoured upright cereal leaves, which let light deeper into the canopy. The results show the interception, the LAI needed for 95% interception, a table and curve of interception against LAI, and typical values for crops and forests.
Worked example
With 1,800 µmol/m²/s above a wheat canopy and 250 µmol/m²/s at the soil, transmission is 250 ÷ 1,800 = 0.1389. With k = 0.5 the LAI is −ln(0.1389) ÷ 0.5 = 1.974 ÷ 0.5 ≈ 3.95, a closed crop canopy that intercepts 1 − e^(−0.5 × 3.95) = 86.1% of the light. Reaching 95% interception would need LAI ≈ 3.0 ÷ 0.5 = 6.0, about 2 more units of leaf. Harvesting 2.4 m² of leaf from a 0.5 m² quadrat would give LAI 4.8 directly, and 60 g of dry leaf at an SLA of 200 cm²/g from the same quadrat gives 1.2 m² of leaf, LAI 2.4.
Sources: Wikipedia: Leaf area index (definition, direct and indirect methods, SLA, ceptometers)
Frequently asked questions
What extinction coefficient should I use?
Around 0.3–0.5 for grasses and cereals with upright leaves, 0.5 for randomly angled leaves and 0.7–0.9 for flat broad leaves such as clover, beans or many tree canopies. k also rises as the sun gets lower (0.5 ÷ cos of the zenith angle for random leaves), so use the sun-angle option for direct-sun readings, or calibrate k against a harvested plot.
What is a good LAI for a crop?
Most field crops need an LAI of about 3–4 by flowering to intercept around 90–95% of the light. Peak values of 4–7 are common in wheat, maize and soybean; above the critical LAI extra leaf adds little yield.
Why does my ceptometer give a lower LAI than harvesting?
Light methods see the canopy silhouette, so clumped foliage (needles bunched on shoots, gaps between crowns or rows) looks like less leaf. Use diffuse light, many readings and a clumping index: true LAI = effective LAI ÷ Ω.
How do I measure LAI without a leaf-area meter?
Harvest the leaves from a known ground area, measure the area of a sub-sample (scan or photograph it on a grid), dry and weigh both, and scale up with the specific leaf area: total leaf area = total dry mass × sub-sample area ÷ sub-sample mass.
Is LAI one-sided or total leaf area?
For flat leaves LAI uses one side of the leaf. For conifer needles the recommended definition is half the total surface area per unit ground area, which keeps values comparable between leaf shapes.
Related calculators
Textbook ecology, forestry and quantitative-genetics formulas with simplifying assumptions. Field constants (z, k, h², efficiencies) vary by system — use locally calibrated values for management or research decisions.