Potential Evapotranspiration (Penman) Calculator

Input options

Choose how to supply humidity information

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Humidity input pathway

Select direct vapor pressures, or compute them from temperatures and humidity.

Mean air temperature (°C)

Used for Δ and general conditions.

Net radiation (Rn)

Daily net radiation at the surface.

Soil heat flux (G)

For daily steps, you may use 0.

Wind speed at 2 m (u₂)

Aerodynamic effect grows with wind.

Altitude

Used to estimate air pressure and γ.

Latent heat of vaporization (λ)

MJ/kg

Default works for typical daily conditions.

Formula used

This calculator uses a Penman combination form: ET₀ = [Δ/(Δ+γ)]·(Rn−G)/λ + [γ/(Δ+γ)]·f(u₂)·(eₛ−eₐ)

Δ is the slope of saturation vapor pressure curve (kPa/°C).
γ is the psychrometric constant (kPa/°C), from altitude pressure.
Rn net radiation and G soil heat flux (MJ/m²/day).
λ latent heat (MJ/kg), converting energy to equivalent water depth.
f(u₂)=6.43·(1+0.536·u₂) with u₂ in m/s, and (eₛ−eₐ) in kPa.

How to use this calculator

Enter mean temperature, net radiation, wind speed, and altitude.
Choose a humidity pathway: direct vapor pressures or computed weather.
Provide the remaining fields shown for your chosen pathway.
Press Calculate to show ET₀ above the form instantly.
Use CSV or PDF buttons to export your computed summary.

Example data table

Scenario	Tmean (°C)	Rn (MJ/m²/day)	u₂ (m/s)	Altitude (m)	es (kPa)	ea (kPa)	ET₀ (mm/day)
Dry, sunny day	26	14	2.5	200	3.36	1.80	~6.1
Humid, calm day	24	10	1.0	50	2.98	2.60	~3.2
Windy, mild day	18	8	4.0	500	2.06	1.35	~4.0

Values are illustrative and may vary with local conditions.

Potential Evapotranspiration and the Penman Approach

1) Why potential evapotranspiration matters

Potential evapotranspiration (PET) is the atmospheric demand for water vapor from a well-watered reference surface. It supports irrigation scheduling, reservoir operations, and drought assessment. Many climates see typical daily PET near 2–7 mm/day, changing with season, cloud cover, and wind. In semi-arid summers, clear breezy days may exceed 6 mm/day.

2) What Penman combines

The Penman method blends energy availability with aerodynamic transport. The energy part uses net radiation minus soil heat flux (Rn − G). The transport part grows with wind speed and vapor pressure deficit (e_s − e_a). That is why hot, dry, windy afternoons often push PET higher.

3) Radiation term and units

Radiation data may be reported as MJ/m²/day, W/m², or kWh/m²/day. Converting to MJ/m²/day keeps the physics consistent because the energy term is divided by latent heat λ (about 2.45 MJ/kg), yielding a water-depth equivalent in mm/day. For daily periods, G is frequently set close to zero.

4) Aerodynamic term and wind normalization

The aerodynamic component uses wind speed at 2 m height. Convert km/h, mph, or knots to m/s to avoid scaling errors. As a quick benchmark, 1 m/s is gentle flow, while 4–6 m/s can substantially raise PET even when radiation stays similar.

5) Vapor pressures and humidity pathways

Saturation vapor pressure e_s depends on temperature and rises nonlinearly. Actual vapor pressure e_a reflects atmospheric moisture. You can enter e_s and e_a directly, or estimate them from Tmax, Tmin, and humidity values when vapor pressures are not available.

6) Altitude, pressure, and psychrometrics

Altitude affects air pressure, which changes the psychrometric constant γ and the balance between the two terms. Higher elevations generally have lower pressure, slightly shifting the weighting. This matters when comparing sites, such as coastal stations versus upland basins.

7) Interpreting the components

Separating radiation and aerodynamic contributions helps explain day-to-day variability. If the radiation term dominates, focus on solar input, albedo, and cloudiness. If the aerodynamic term dominates, dry air and wind are driving losses, and PET may remain high during windy conditions.

8) Practical use and quality checks

PET is a reference demand; crop water use is often PET multiplied by a crop coefficient. Check that e_a does not exceed e_s, and verify Rn magnitudes for your season. Exporting CSV or PDF supports auditing, reporting, and time-series tracking.

FAQs

1) What does PET represent in this tool?

PET is the estimated daily evaporative demand from a well-watered reference surface. It is not soil moisture; it is a weather-driven atmospheric demand estimate.

2) Why does wind speed increase PET?

Wind replaces humid surface air with drier air and strengthens turbulent transport. This increases the aerodynamic part of the Penman estimate and can keep PET elevated.

3) Can I set soil heat flux G to zero?

For daily calculations, G is often small compared with net radiation. Many practical daily PET workflows assume G = 0, especially for reference surfaces.

4) Should e_a ever be higher than e_s?

No. If e_a exceeds e_s, the implied humidity is inconsistent with temperature. Recheck units, inputs, and sensor quality.

5) Which humidity option should I choose?

Use the direct pathway if you already have vapor pressures. Use the compute pathway if you have Tmax, Tmin, and relative humidity from a station.

6) How accurate is the Penman estimate?

Accuracy depends on input quality and representativeness. With good radiation, wind, temperature, and humidity data, Penman-based PET is widely used in water planning.

7) How can I convert PET to water volume?

Divide mm/day by 1000 to get m/day, then multiply by area in m². Example: 5 mm/day over 1,000 m² equals 0.005 × 1,000 = 5 m³/day.