Reference Evapotranspiration Calculator

Stephanie Ben-Joseph headshotEdited by: Stephanie Ben-Joseph

This reference evapotranspiration calculator estimates daily ET0 for a standardized, fully watered short grass surface using the FAO Penman-Monteith method. It is meant for people who have one day of weather observations, a station export, or a gridded climate summary and want a physically based baseline before turning that weather signal into irrigation depth or crop water use.

The output is expressed in millimeters per day and reflects the balance between energy at the surface, the drying power of the air, wind speed, and the effect of elevation on atmospheric pressure. Enter measurements from the same day and the same site whenever possible; the calculator converts elevation into pressure and the psychrometric constant so the result stays aligned with the daily FAO-56 form rather than a simplified rule-of-thumb estimate.

Formula: FAO Penman-Monteith equation for daily ET0

For a daily reference evapotranspiration estimate, the FAO-56 equation is usually written as:

This calculator uses the daily form, so the values you enter should describe one full day at one location rather than an hourly snapshot or a monthly average.

ET0 =0.408·Δ(Rn−G)+γ900·u_2·T(es−ea)T+273Δ+γ(1+0.34·u_2)

where ET0 is in mm/day when:

  • Rn is net radiation at the reference crop surface (MJ/m2/day)
  • G is soil heat flux density (MJ/m2/day)
  • T is mean daily air temperature at 2 m height (°C)
  • u2 is wind speed at 2 m height (m/s)
  • es is saturation vapor pressure (kPa)
  • ea is actual vapor pressure (kPa)
  • Δ is the slope of the saturation vapor pressure curve at temperature T (kPa/°C)
  • γ is the psychrometric constant (kPa/°C)

The calculator derives Δ from the temperature you enter and computes γ from elevation-adjusted atmospheric pressure, which keeps the aerodynamic weighting consistent with the FAO-56 reference form. Make sure the weather inputs all come from the same day, station, and unit system so the energy term and vapor-pressure term are describing the same atmospheric conditions.

Introduction: ET0 inputs for a reference grass day

Each field in this reference evapotranspiration calculator represents one weather variable required by the FAO Penman-Monteith equation for a single day at a single site.

  • Net Radiation Rn (MJ/m2/day): This is the surface energy that remains after incoming and outgoing shortwave and longwave radiation are balanced. Clear skies, longer sunshine duration, and intense solar input usually push this number higher, which in turn raises ET0.
  • Soil Heat Flux G (MJ/m2/day): This represents heat stored in or released from the soil during the day. For a daily reference grass estimate the value is often close to zero, so many users leave it at 0 unless a measured site-specific flux is available.
  • Mean Air Temperature T (°C): This is the daily average air temperature at the standard 2 m height. If your source reports minimum and maximum temperature separately, a midpoint is often used as a practical daily approximation when a more detailed energy balance is not available.
  • Elevation z (m): This is the height of the station or site above sea level. Higher elevation lowers the estimated air pressure, which slightly changes the psychrometric constant and therefore the ET0 result.
  • Wind Speed u2 (m/s at 2 m): This is the mean daily wind speed at the standard 2 m measurement height. If your weather source reports wind at a different height, it should be adjusted before use so the aerodynamic term stays comparable to the FAO reference form.
  • Saturation Vapor Pressure es (kPa): This is the vapor pressure of air at saturation for the temperature of the day. It is tied to how much moisture the air could hold if it were fully saturated.
  • Actual Vapor Pressure ea (kPa): This is the moisture already present in the air. It is usually estimated from relative humidity, dew point, or wet-bulb data, and it should describe the same day and site as es.

When data come from different services, double-check that radiation, humidity, wind, and temperature all describe the same 24-hour period. A mismatch of even one day can move ET0 enough to distort irrigation planning, especially when the weather changes quickly from cloudy and humid to hot and windy.

Interpreting the ET0 result for irrigation planning

The result from this reference evapotranspiration calculator is the daily ET0 depth, usually shown in mm/day. One millimeter of ET0 over 1 hectare corresponds to a depth of 1 mm of water, or approximately 10 m3 of water per hectare.

  • 0–2 mm/day: Very low atmospheric demand, often on cool, cloudy, or humid days.
  • 3–5 mm/day: Moderate demand, common in many temperate growing conditions.
  • 6–10+ mm/day: High demand, typical of hot, dry, and windy weather.

To estimate crop evapotranspiration (ETc) for a particular crop and growth stage, multiply ET0 by a crop coefficient Kc:

Formula: ET_c = K_c × ET_0

ETc=Kc×ET0

Crop coefficients change with canopy cover, rooting depth, and management, so the ET0 number is only the starting point. FAO-56 guides and local extension tables are the best place to choose Kc values that match your crop, its growth stage, and the way your field is actually managed.

Worked example: reference evapotranspiration on a warm midsummer day

Suppose the calculator receives a clear midsummer weather set for a reference grass surface:

  • Net radiation Rn = 15 MJ/m2/day
  • Soil heat flux G = 0 MJ/m2/day (daily time scale)
  • Mean air temperature T = 25 °C
  • Elevation z = 0 m (sea-level reference)
  • Wind speed u2 = 2 m/s
  • Saturation vapor pressure es = 3.17 kPa
  • Actual vapor pressure ea = 2.10 kPa

With those inputs, the calculator returns ET0 of about 5.27 mm/day, with Δ ≈ 0.189 kPa/°C and γ ≈ 0.067 kPa/°C. In plain language, the reference grass would lose a little over 5 mm of water during the day, which is a moderate-to-high atmospheric demand for a single day.

If you are growing a crop with a mid-season crop coefficient Kc of 1.15, then the crop evapotranspiration is approximately:

ETc = Kc × ET0

Using the rounded planning value of ET0 ≈ 5.5 mm/day, this gives ETc ≈ 6.3 mm/day. You would need to supply about this depth of water, adjusted for any effective rainfall and irrigation efficiency, to avoid water stress for that crop on that day.

Penman-Monteith vs. other reference ET methods for ET0

The FAO Penman-Monteith method is the reference choice when you have radiation, humidity, temperature, and wind data for ET0. Simpler equations can still be useful when records are sparse, but they usually trade physical detail for convenience and can drift farther from local conditions, especially when humidity and wind are the two variables that matter most.

MethodData requirementsTypical use caseComments
FAO Penman-MonteithRadiation (or sunshine), temperature, humidity, windReference standard for ET0 where full weather data existPhysically based and usually the most dependable daily ET0 estimate across climates
Hargreaves-SamaniTemperature, extraterrestrial radiationRegions with only temperature data availableHandy when data are limited, but more empirical and less stable across very different climates
Blaney-CriddleTemperature, daylight hoursLegacy irrigation planning, some arid and semi-arid regionsBest treated as a fallback method unless it has been tuned with local calibration

When your weather file includes the full ET0 set, Penman-Monteith is usually the better choice because each input maps directly to a physical driver of evaporative demand. If you are missing humidity or wind, a simpler method can still provide a starting point, but the result should be checked against local experience before it is used for scheduling.

Assumptions and limitations for reference ET0 estimates

  • Reference surface: ET0 assumes a hypothetical, well-watered, actively growing grass crop with a fixed height of about 0.12 m, surface resistance of 70 s/m, and albedo of 0.23. It is not a direct estimate of a specific crop until crop coefficients are applied.
  • Uniform conditions: The method assumes the weather and surface properties are fairly uniform over the area represented by the station or grid cell.
  • Daily time scale: Inputs and outputs are for a daily period. Short spikes in radiation or wind are blended into the day instead of being resolved hour by hour, which is appropriate for this calculator but not for sub-daily scheduling.
  • Measurement height and exposure: Wind speed and air temperature are assumed at 2 m height over short grass. Sheltered sites, rooftops, or unusual terrain can bias ET0 estimates, so exposed stations generally make better comparisons.
  • Climatic extremes: In very dry, advective, or strongly heterogeneous conditions, the reference equation may be less representative, and local calibration or lysimeter data may be needed.
  • Not a design recommendation by itself: ET0 is only one part of irrigation design. Soil water holding, rainfall timing, system efficiency, and crop rooting depth still matter when deciding how much water to apply.

Use ET0 from this calculator as a weather-based estimate, then combine it with field observations and local guidance before deciding when and how much to irrigate. The calculator is most useful when its output is treated as a daily benchmark rather than a final irrigation prescription.

How to use this reference evapotranspiration calculator step by step

  1. Enter Net Radiation R n (MJ/m²/day) using the unit and daily period shown by your weather source, not a weekly or monthly average.
  2. Enter Soil Heat Flux G (MJ/m²/day); for many daily ET0 checks this is 0, unless you have a better site-specific value for the date you are analyzing.
  3. Enter Mean Air Temperature T (°C) for the same day, then fill in the remaining weather fields so the whole set stays consistent and comparable.
  4. Run the calculation once, then try a second weather scenario such as a hotter, windier, or drier day to see how ET0 changes before you use it for irrigation planning or crop-water comparisons.

Arcade Mini-Game: Reference Evapotranspiration Calculator Weather Check

Use this quick arcade run to practice spotting the weather inputs that matter for ET0 and rejecting unit mix-ups, stale station data, or missing measurements before you trust the calculator output.

Score: 0Timer: 30sBest: 0

Start the game, then use your pointer or arrow keys to catch useful ET0 inputs and avoid bad assumptions about the weather record.

Enter weather data to estimate daily reference evapotranspiration.

Understanding reference evapotranspiration in this calculator's output

Reference evapotranspiration is the weather-driven water loss from a standard, well-watered grass surface. It is not a crop measurement on its own; instead, it is the baseline that irrigation scheduling starts from before crop coefficients translate the number into a particular field condition.

The FAO Penman-Monteith equation is used here because it matches the exact weather variables this calculator asks for. Net radiation and soil heat flux describe the energy side of the balance, temperature shapes the saturation vapor pressure curve, and wind plus vapor pressure deficit describe how quickly the air can carry moisture away. A daily form for the reference surface reads as follows:

0.408Δ(Rn−G)+γ900(T+273)u2(es−ea)Δ+γ(1+0.34u2) In this equation, Δ is the slope of the saturation vapor pressure curve at temperature T in kPa per degree Celsius, and γ is the psychrometric constant, about 0.067 kPa/°C near sea level and slightly smaller at higher elevations. The net radiation Rn represents the balance of incoming and outgoing shortwave and longwave energy, while G captures ground heat flux, often negligible over daily periods. The aerodynamic term uses the wind speed u2 measured at two meters above ground and the vapor pressure deficit es−ea, which shows how dry the air is.

When the calculator runs, it evaluates pressure from elevation, uses temperature to determine Δ, and then combines the energy and aerodynamic terms into the ET0 value shown in the result box. If the air is very humid or the site is cool and cloudy, the answer can fall sharply; on hot, breezy days it can rise fast. That is why comparing two weather scenarios is often more useful than looking at a single number in isolation. The result table is designed to make those drivers visible so you can see whether radiation, dryness, or wind is doing most of the work.

Typical ET0 patterns for different climates

Reference ET0 is not fixed by season alone; it changes with cloud cover, humidity, wind, and heat. The table below is a rough check against common daily patterns, not a substitute for station data or a crop-water budget.

Climate TypeTypical ET0 (mm/day)Notes
Humid temperate3–6Mild temperatures and moderate humidity usually keep ET0 in the middle of the range.
Arid desert6–10Strong sun and very dry air tend to push ET0 toward the upper end.
Tropical wet4–8Warm air supports evaporation, but clouds and humidity often restrain it.
High altitude2–5Cooler temperatures can offset intense radiation and keep ET0 lower.
Coastal maritime2–4Persistent cloud cover and moist air usually suppress ET0.

If a computed ET0 seems far outside the table's general pattern, first check the inputs. A warm inland site with strong sun and wind should land higher than a cool coastal site, while misty or overcast days usually suppress ET0 even when temperatures are moderate. The goal is not to force every location into a fixed band, but to give you a quick sense of whether the output matches the weather that was entered.

Why ET0 matters for irrigation planning

Reference evapotranspiration matters because it turns weather into a usable daily water-demand baseline. Irrigation managers use ET0 to time applications, researchers use it to compare climates, and landscape planners use it to estimate how much moisture the atmosphere will pull from grass, soil, and crops after a crop coefficient is applied.

The Penman-Monteith method is powerful because it reflects the physical drivers of evapotranspiration, but it still assumes a uniform reference surface and does not account for crop stress, canopy height differences, or soil moisture shortages. Taller crops, orchards, and stressed fields need their own coefficients or local adjustments before ET0 can be translated into actual demand.

Accurate inputs matter just as much as the formula. Radiation should represent the same day as the temperature, humidity, and wind measurements, wind speed should be adjusted to two meters if needed, and vapor pressure should come from a consistent humidity source. When the input data are clean, the calculator becomes a quick way to see whether the atmosphere is likely to be gentle, average, or thirsty.

Used that way, the calculator is a practical bridge between meteorological data and water management decisions. It lets you compare a calm humid day with a hot windy day, see which term is driving the result, and decide whether ET0 is low enough for a light watering or high enough to justify a closer look at irrigation timing. The result is most useful when it is compared against recent weather, field observations, and local scheduling guidance instead of being read in isolation.