Penman-Monteith Calculator
Compute FAO-56 reference evapotranspiration ET₀ (mm/day) from mean temperature, wind speed, relative humidity, net radiation and soil heat flux. The internationally recognized most accurate crop-water-demand baseline.
Input Data
Results
At a glance:The FAO-56 Penman-Monteith method is the reference evapotranspiration (ET₀) standard defined by the UN Food and Agriculture Organization (FAO) in Irrigation and Drainage Paper No. 56. It is internationally recognized as the most accurate, region-comparable ET₀ algorithm, merging two mechanisms in one equation: energy balance (available radiation drives evaporation) and aerodynamics (wind and air dryness remove vapour): ET₀ = [0.408 Δ(Rn − G) + γ·900/(T+273)·u₂·(es − ea)] ÷ [Δ + γ(1 + 0.34 u₂)]. Here Δ is the slope of the saturation vapour-pressure curve, γ the psychrometric constant, Rn net radiation, G soil heat flux, u₂ wind speed at 2 m, and (es − ea) the vapour-pressure deficit (air dryness). es is computed from temperature and ea = es × RH ÷ 100. ET₀ represents the evapotranspiration rate of a standard reference grass under ample water; actual crop demand ETc = Kc × ET₀.
Formula
Saturation vapour pressure: es = 0.6108 × exp(17.27 T ÷ (T + 237.3)).
Curve slope: Δ = 4098 × es ÷ (T + 237.3)²; actual vapour pressure ea = es × RH ÷ 100.
Penman-Monteith: ET₀ = [0.408 Δ(Rn − G) + γ·(900/(T+273))·u₂·(es − ea)] ÷ [Δ + γ(1 + 0.34 u₂)].
$$e_s = 0.6108\,\exp\!\left(\frac{17.27\,T}{T + 237.3}\right)$$$$\Delta = \frac{4098\,e_s}{(T + 237.3)^2}, \quad e_a = e_s \times \frac{RH}{100}$$$$ET_0 = \frac{0.408\,\Delta\,(R_n - G) + \gamma\,\frac{900}{T + 273}\,u_2\,(e_s - e_a)}{\Delta + \gamma\,(1 + 0.34\,u_2)}$$How to Use
- Enter mean daily temperature T, 2 m wind speed u₂ and relative humidity RH.
- Enter net radiation Rn (MJ·m⁻²·day⁻¹) and soil heat flux G (usually 0 on a daily scale).
- The tool returns ET₀ (mm/day) plus es, ea and Δ; multiply by the crop coefficient Kc to get crop water demand ETc.
How each weather factor affects Penman-Monteith ET₀
| Weather factor | ET₀ when rising | Mechanism |
|---|---|---|
| Net radiation Rn ↑ | increases | Supplies more energy for evaporation (energy term) |
| Temperature T ↑ | increases | Raises saturation vapour pressure and slope Δ |
| Wind speed u₂ ↑ | increases | Faster removal of near-surface vapour (aerodynamic term) |
| Relative humidity RH ↑ | decreases | Shrinks vapour-pressure deficit (es − ea), lowering drive |
ET₀ is set by both energy supply and air dryness/turbulence; largest on sunny, dry, windy, hot days; smallest when overcast, humid and calm.
Case Studies
Typical summer day in Hong Kong
Midsummer day: T = 28°C, u₂ = 2 m/s, RH = 70%, Rn = 12 MJ·m⁻²·day⁻¹, G = 0.
es ≈ 3.78 kPa, Δ ≈ 0.22 kPa/°C, ea = 3.78 × 0.70 ≈ 2.65 kPa.
Penman-Monteith gives ET₀ ≈ 4.60 mm/day; with crop Kc = 1.1, ETc ≈ 5.06 mm/day.
Cool, humid day has lower ET₀
Cool day: T = 20°C, u₂ = 1 m/s, RH = 60%, Rn = 8 MJ·m⁻²·day⁻¹, G = 0.
Lower temperature reduces es and Δ; weaker wind weakens the aerodynamic term.
ET₀ ≈ 2.83 mm/day, clearly below midsummer; irrigation can be reduced accordingly.
FAQ
How to choose between Penman-Monteith and Hargreaves?
Penman-Monteith is the FAO standard with the highest accuracy but needs full data: temperature, humidity, wind and net radiation. Hargreaves needs only Tmax, Tmin and tabulated extraterrestrial radiation, with low data demand, suited to stations with missing records. Use Penman-Monteith when full weather data are available; otherwise use Hargreaves as an approximation (this site also has an ET₀ Hargreaves calculator).
Where do I get net radiation Rn?
Rn is the net radiation absorbed at the surface, equal to net shortwave minus net longwave. It can be computed from a station's sunshine hours and solar radiation observations together with albedo and surface temperature following FAO-56 steps, or taken directly from a net radiometer. With only sunshine or cloud data, use the FAO empirical formula to estimate solar radiation first, then Rn.
Must I enter soil heat flux G?
On a daily time scale, heat flowing into the soil by day and out at night roughly cancels, so G is usually small; FAO-56 recommends simply using 0, which is this calculator's default. Only for hourly scales or special surfaces should G be estimated separately (e.g. as a fraction of net radiation). Keep 0 for daily use.
Why does higher humidity lower ET₀?
The aerodynamic drive for evapotranspiration comes from the vapour-pressure deficit (es − ea), i.e. how much more water vapour the air can hold. Higher relative humidity brings actual vapour pressure ea closer to saturation es, shrinking the deficit and the air's ability to carry away vapour, so ET₀ falls. This is why Hong Kong's humid weather has weaker evapotranspiration than drier areas at the same temperature.
Is the computed ET₀ the amount I should water?
Not exactly. ET₀ is the reference-grass evapotranspiration; actual crop demand ETc = Kc × ET₀ requires the crop coefficient Kc (varies by crop and stage). In practice irrigation also subtracts effective rainfall and considers soil water holding and irrigation efficiency. So ET₀ is the baseline; final irrigation volume is adjusted with crop, soil and rainfall conditions.
Related Tools
References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.