Penman–Monteith reference evapotranspiration
Turn daily weather observations into reference evapotranspiration, ET₀. The reference is a hypothetical grass 0.12 m tall, with a surface resistance of 70 s/m and an albedo of 0.23.
Calculate net radiation from sunshine hours or measured solar radiation, or enter measured net radiation directly. For crop water use, supply a crop coefficient: ETc = Kc × ET₀.
Inside the calculation
Daily step · angles in radiansValues appear when all selected inputs are valid.
| Quantity | Value | Formula used |
|---|---|---|
| Day of year, J | — | Days before selected month + day; includes leap day. |
| Mean temperature, T | — | (Tmax + Tmin) / 2 |
| Atmospheric pressure, P | — | 101.3 × [(293 − 0.0065z) / 293]5.26 |
| Psychrometric constant, γ | — | 0.000665P |
| Slope of vapour pressure curve, Δ | — | 4098e°(T) / (T + 237.3)² |
| Saturation vapour pressure, es | — | [e°(Tmax) + e°(Tmin)] / 2 |
| Actual vapour pressure, ea | — | [e°(Tmin) × RHmax/100 + e°(Tmax) × RHmin/100] / 2 |
| Vapour pressure deficit | — | es − ea |
| Wind at 2 m, u₂ | — | u when zw = 2 m; otherwise u × 4.87 / ln(67.8zw − 5.42) |
| Extraterrestrial radiation, Ra | — | (24 × 60 / π) × 0.0820dr × [ωs sin(φ) sin(δ) + cos(φ) cos(δ) sin(ωs)] |
| Daylight duration, N | — | 24ωs / π |
| Solar radiation, Rs | — | (0.25 + 0.50n/N) × Ra |
| Clear-sky radiation, Rso | — | (0.75 + 2 × 10⁻⁵z) × Ra |
| Net shortwave radiation, Rns | — | 0.77Rs |
| Net longwave radiation, Rnl | — | 4.903 × 10⁻⁹ × [(Tmax + 273.16)⁴ + (Tmin + 273.16)⁴] / 2 × (0.34 − 0.14√ea) × [1.35 × min(Rs/Rso, 1) − 0.35] |
| Net radiation, Rn | — | Rns − Rnl |
| Soil heat flux, G | — | Entered daily value |
| Radiation contribution | — | 0.408Δ(Rn − G) / D |
| Aerodynamic contribution | — | [γ × 900/(T + 273) × u₂ × (es − ea)] / D |
| Reference ET₀ | — | Radiation contribution + aerodynamic contribution |
| Crop ETc | — | Kc × ET₀, when Kc is supplied |
ET₀ = [0.408Δ(Rn − G) + γ × 900/(T + 273) × u₂(es − ea)] / [Δ + γ(1 + 0.34u₂)]
D = Δ + γ(1 + 0.34u₂) · e°(t) = 0.6108 × exp[17.27t / (t + 237.3)]
φ = latitude × π/180 · dr = 1 + 0.033cos(2πJ/365) · δ = 0.409sin(2πJ/365 − 1.39)
ωs = acos[clamp(−tan(φ)tan(δ), −1, 1)]
δ is solar declination; Δ is the vapour pressure curve slope. Sunset-angle clamping accommodates polar day or night. If clear-sky radiation is zero, the Rs/Rso calculation is undefined; use measured net radiation instead.
ET₀ in in/day = ET₀ in mm/day / 25.4 · ETc in in/day = ETc in mm/day / 25.4
How to use the calculator
- Select a radiation source. Enter sunshine hours, measured Rs, or measured Rn. For sunshine hours or Rs, provide the date and latitude. Enter elevation for atmospheric pressure.
- Enter daily temperature and humidity. Supply Tmax and Tmin, then select RHmax/RHmin, dew point, or mean RH.
- Enter wind and its measurement height. The calculator converts wind to 2 m. Set daily soil heat flux G, or leave it at 0.
- Read ET₀ and review the working. Results update automatically. Add Kc if you also need ETc. “Load FAO example” fills the example inputs, including wind measured at 10 m and Kc of 1.15.
Understanding the result
What does reference ET₀ represent?
ET₀ is the evapotranspiration of a hypothetical reference grass 0.12 m tall, with a surface resistance of 70 s/m and an albedo of 0.23.
Which radiation inputs can I use?
Use sunshine hours, measured solar radiation Rs, or measured net radiation Rn. Sunshine hours and measured Rs require date and latitude to calculate net radiation. Measured Rn needs no date or latitude.
How is crop evapotranspiration calculated?
Crop evapotranspiration is ETc = Kc × ET₀. Enter an optional crop coefficient Kc to calculate ETc. This calculator does not provide Kc values.
Which humidity measurements are supported?
Use maximum and minimum relative humidity, dew point temperature, or mean relative humidity. The selected method determines the actual vapour pressure ea used in the calculation.