Leaf Transpiration Rate Calculator
Calculate leaf transpiration rate from stomatal conductance, leaf temperature, and relative humidity.
Returns results in mol/sq m/s and mm per day.
Why plants transpire
A plant uses about 100-1000 water molecules for every 1 CO₂ molecule it fixes through photosynthesis. The water loss happens through the same stomata that let CO₂ in — there’s no way to keep one open while closing the other. For most plants, 95-98% of water uptake from soil ends up evaporating through leaves, never appearing in any biomass.
Transpiration isn’t waste, though — it serves three real functions:
- Cools the leaf (each gram of water evaporated removes 2,260 J of heat)
- Drives nutrient uptake by creating water mass flow from roots upward
- Maintains turgor through the steady water column
The trade-off between CO₂ gain and water loss is fundamental to plant ecology and is what the Water Use Efficiency (WUE) metric quantifies.
The Fick’s Law transpiration equation
Transpiration follows Fick’s law for diffusion:
E = gs × VPD ÷ P
Where:
- E: transpiration rate (mol H₂O/m²/s)
- gs: stomatal conductance (mol H₂O/m²/s)
- VPD: vapor pressure deficit between leaf and air (kPa)
- P: atmospheric pressure (kPa, typically 101.3 at sea level)
The math says: transpiration = (how open stomata are) × (how much drier air is than leaf interior) ÷ (atmospheric pressure).
Vapor Pressure Deficit (VPD) — the driving force
The leaf interior is essentially 100% relative humidity (saturated at leaf temperature). The air outside is typically drier. The vapor pressure deficit is the difference:
VPD = es(T_leaf) − ea VPD = es(T_leaf) × (1 − RH ÷ 100) [if leaf and air same temperature]
Where es is the saturation vapor pressure at temperature T:
es = 0.6108 × exp(17.27 × T ÷ (T + 237.3)) kPa [Tetens equation]
VPD is the single biggest driver of transpiration. Doubling VPD roughly doubles water loss.
| Temperature (°C) | es (kPa) | VPD at 50% RH (kPa) |
|---|---|---|
| 10 | 1.23 | 0.61 |
| 15 | 1.71 | 0.85 |
| 20 | 2.34 | 1.17 |
| 25 | 3.17 | 1.59 |
| 30 | 4.24 | 2.12 |
| 35 | 5.62 | 2.81 |
| 40 | 7.38 | 3.69 |
Notice how VPD climbs exponentially with temperature, even at the same RH. A 10°C rise at 50% RH triples the VPD from 0.61 to ~2 kPa. This is why plants struggle in hot, dry weather: not just heat itself, but the dramatically higher water demand.
Optimal VPD for plant growth
| Plant stage | Target VPD (kPa) | Notes |
|---|---|---|
| Seedlings, cuttings | 0.4-0.8 | Low VPD prevents drying |
| Vegetative growth | 0.8-1.2 | Optimum for most species |
| Flowering | 1.0-1.5 | Slightly higher |
| Mature production | 1.0-1.6 | Balance between transpiration and stress |
| Stress threshold | > 2.0 | Stomata close, growth stops |
| Severe stress | > 3.0 | Possible wilting, photoinhibition |
Commercial greenhouse VPD control is now standard — temperature alone doesn’t tell you whether plants are stressed; VPD does.
Stomatal conductance (gs) — what the plant controls
While VPD is set by environment, gs is set by the plant. Plants can close stomata in minutes via guard cell osmoregulation. Typical values:
| State | gs (mol H₂O/m²/s) |
|---|---|
| Fully closed (drought, dark) | 0.001 - 0.01 |
| Partially closed (mild stress, dim light) | 0.05 - 0.10 |
| Open (normal day, well-watered) | 0.15 - 0.30 |
| Wide open (humid day, abundant water) | 0.30 - 0.50 |
| Theoretical max | ~0.6 |
Plant species also differ in their default open state:
- C₃ crops (wheat, rice): max gs ≈ 0.3
- Tomato: 0.4-0.5
- Sunflower: up to 0.6
- Trees: 0.15-0.25 (typically lower)
- Cacti and CAM plants: stomata open only at night (when VPD is low)
Converting to mm/day
For agriculture and irrigation, transpiration is typically expressed as mm of water per day:
E_mm/day = E (mol/m²/s) × 18 (g/mol) × 86,400 (s/day) ÷ 1000 (g/L) ÷ 1 (density) ≈ E × 1.555
Typical transpiration rates:
- Well-watered tomato crop: 4-6 mm/day
- Well-watered corn: 5-8 mm/day
- Mature forest: 2-4 mm/day
- Desert shrub: 0.2-1 mm/day
- Drought-stressed crop: 0.5-2 mm/day
- Hot dry day at high VPD: up to 10-15 mm/day
For perspective: a 1 mm/day transpiration rate is 1 liter of water per square meter per day — that’s substantial agricultural water demand.
Water Use Efficiency (WUE) — the agricultural goal
WUE is the ratio of carbon fixed to water lost:
WUE = A ÷ E
Higher WUE = more carbon per unit water. This is what drought-tolerant crops are bred for. C₄ plants (corn, sorghum, sugarcane) have inherently higher WUE than C₃ plants (wheat, rice, soybean) — typically 2x.
CAM plants (cacti, succulents, pineapple) have the highest WUE — they open stomata only at night, store CO₂ as malate, and “release” it during the day for photosynthesis. WUE can be 5-10x higher than C₃ plants.
Stomatal closure feedback
Plants don’t just respond to environment — they respond to their own water status. When leaf water potential drops, the hormone ABA (abscisic acid) signals stomata to close. The cascade:
- Soil dries
- Root sensors detect dryness
- ABA produced in roots
- ABA transported to leaves
- Guard cells lose turgor
- Stomata close
- Transpiration drops; CO₂ uptake also drops
This is why drought-stressed plants stop growing even before they wilt — they’ve shut down stomata to conserve water, but this also stops photosynthesis.
The leaf-air temperature gap
The Fick’s law formula assumes T_leaf = T_air. In reality, transpiring leaves are 2-5°C cooler than surrounding air (evaporative cooling). On a hot day with closed stomata (drought stress), leaves can be 5-10°C warmer than ambient — because the cooling has stopped.
Thermal imaging of crops can detect water stress before visible wilting: stressed leaves show up hotter on IR cameras. Agricultural drones routinely use this for precision irrigation.
Worked example
A well-watered tomato leaf at 25°C in 60% RH air, gs = 0.2 mol/m²/s:
- es(25°C) = 0.6108 × exp(17.27 × 25 ÷ 262.3) = 0.6108 × 5.20 = 3.17 kPa
- VPD = 3.17 × (1 − 0.6) = 1.27 kPa
- E = 0.2 × 1.27 ÷ 101.3 = 2.51 × 10⁻³ mol/m²/s
- E_mm/day = 2.51 × 10⁻³ × 1.555 × 86,400 / 1000 ≈ 3.9 mm/day
That’s a typical, healthy transpiration rate.
Bottom line
Transpiration is the cost of doing photosynthesis. VPD is the dominant environmental driver; gs is what the plant controls. For commercial growers, maintaining VPD in the 0.8-1.4 kPa range optimizes photosynthesis while minimizing stress. For drought-resistance breeding, the goal is higher WUE — more carbon per liter of water lost.