Photosynthesis Rate and Light Response Calculator

The light response curve

The rate of photosynthesis depends on light intensity, but not linearly. Two distinct regions:

• At low light: each photon adds proportionally to photosynthesis (quantum-yield-limited)
• At high light: the enzymes (especially Rubisco) become rate-limited, no matter how much extra light

The rectangular hyperbola captures this:

A_net = (Amax × I) ÷ (I + Ik) − Rd

Where:

• A_net: net CO₂ assimilation (µmol CO₂/m²/s)
• Amax: maximum gross photosynthetic rate at light saturation
• I: incident light intensity (µmol photons/m²/s PAR)
• Ik: light intensity at which photosynthesis is half-maximum
• Rd: dark respiration rate (CO₂ released even in darkness)

The “net” part is important. Plants respire 24/7 — they consume CO₂ via photosynthesis and produce CO₂ via mitochondrial respiration. The net A is the balance.

The two critical light thresholds

Light Compensation Point (LCP): the light intensity at which net A = 0. Photosynthesis exactly balances respiration. Below LCP, the plant is losing carbon. For most plants, LCP is 10-50 µmol/m²/s — about the equivalent of a brightly-lit office.

Light Saturation Point: the light intensity above which further increases give no additional photosynthesis. Typically when A_net reaches 90% of Amax. Plant strategies diverge sharply here:

PAR — the units that matter for plants

Plants use Photosynthetically Active Radiation (400-700 nm) — the visible spectrum, excluding UV and IR. PAR is measured in µmol photons/m²/s — number of photons hitting a square meter per second.

Reference PAR values:

• Full sunlight at noon (clear day): 1,800-2,200 µmol/m²/s
• Sunset / heavy overcast: 50-400 µmol/m²/s
• Bright office lighting: 5-15 µmol/m²/s (no plant grows in this)
• Indoor grow lights (LED, mid-tier): 200-800 µmol/m²/s
• Greenhouse on cloudy day: 300-600 µmol/m²/s
• Direct sun under shade cloth (50% shade): 900-1,100 µmol/m²/s

A common confusion: lux (commonly cited in indoor light meters) and PAR are not interchangeable. Lux is weighted to human eye sensitivity (peaks at green, where plants don’t care). For converting:

• Sunlight: 1 PAR µmol/m²/s ≈ 54 lux
• Cool white LED: 1 PAR ≈ 70 lux
• Warm LED: 1 PAR ≈ 55 lux

So 10,000 lux of sunlight ≈ 185 PAR; 10,000 lux of cool LED ≈ 143 PAR.

C₃ vs C₄ photosynthesis

The most important distinction in plant biochemistry:

C₄ plants concentrate CO₂ near Rubisco using PEP carboxylase, reducing photorespiration losses. This is why corn (C₄) thrives at high light and temperature while wheat (C₃) actually does better in cooler conditions. The agricultural implication: C₄ crops dominate the tropics.

Quantum yield — the molecular efficiency

At low light, each photon absorbed converts to chemistry with some quantum yield φ. Theoretical maximum is 1 photon → 1 CO₂ fixed, but actual values are roughly:

• C₃ plants: 0.045-0.060 mol CO₂/mol photons
• C₄ plants: 0.055-0.075

So at low light, a C₄ plant is about 25% more efficient per photon. This is invisible at high light where Rubisco saturates, but matters in shaded or seasonal conditions.

Photoinhibition — when too much light damages plants

Above 1,500-2,000 µmol/m²/s, especially with concurrent stress (heat, drought), plants can experience photoinhibition — light damages the Photosystem II complex faster than it can be repaired. The plant shows wilting, leaf burn, or chlorosis. This is why:

• Greenhouse growers use shade cloth even on sunny days
• Indoor growers don’t crank LED to maximum
• Forest plants underneath gaps experience leaf burn when overstory is removed

The repair of damaged D1 protein in PSII is the rate-limiting step in recovery from photoinhibition — taking hours to days.

Practical greenhouse and indoor growing application

For commercial indoor crops (lettuce, herbs, cannabis):

• Lettuce: DLI (Daily Light Integral) target is 12-17 mol/m²/day. At 200 PAR for 18 hours = 13 mol/day ✓
• Tomato: DLI target 20-30 mol/m²/day. Requires 400-500 PAR for 14-16 hours
• Cannabis flowering: 35-45 PAR DLI, requires 800-1,200 PAR for 12 hours
• Microgreens: 6-10 PAR DLI, sufficient at 100-150 PAR

Above DLI saturation, you get diminishing returns and risk photoinhibition. Below DLI threshold, plants stretch, thin out, and yield collapses.

Environmental modifiers

The simple light response curve ignores temperature, CO₂, water, and nutrients. In reality:

• CO₂ enrichment (1,000-1,400 ppm in greenhouses) raises Amax by 20-40% in C₃ plants
• Temperature affects Amax (Q10 ≈ 2 around the optimum)
• Water stress closes stomata, reducing CO₂ uptake — limits Amax
• Nitrogen deficiency reduces Rubisco, lowering Amax
• Diurnal patterns: Amax is often higher midday than morning/afternoon at the same PAR

A full plant model uses the Farquhar-von Caemmerer-Berry biochemical model, which incorporates all these. The simple hyperbola here is a useful first approximation.

Bottom line

For sun-grown crops, you’re optimizing for high Amax and operating near light saturation (1,000-1,500 PAR for C₃, 2,000+ for C₄). For indoor crops, target the species-specific DLI (Daily Light Integral) rather than instantaneous PAR. The light compensation point matters most when calculating whether a low-light location can support growth at all — below LCP, the plant is just respiring and starving.