Reference Evapotranspiration Calculator
This calculator estimates daily reference evapotranspiration (ET0) using the FAO Penman‑Monteith method. ET0 represents the water loss from a hypothetical, well‑watered reference grass surface under standard conditions. It is the starting point for irrigation planning, crop water requirement calculations, and hydrological studies.
The Penman‑Monteith equation combines the energy balance (net radiation and soil heat flux) with the aerodynamic drivers of evaporation (wind and vapor pressure deficit). By entering daily‑averaged weather data, you obtain ET0 in units of mm/day when the standard FAO‑856 parameters and unit conventions are followed.
FAO Penman‑Monteith equation
For a daily time step, the FAO‑856 reference ET0 is commonly written as:
ET0 =
where ET0 is in mm/day when:
- Rn is net radiation at the 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)
This tool assumes that Δ and γ are computed internally from T and standard atmospheric pressure for a typical elevation, consistent with FAO‑856 practice. Make sure all inputs use compatible units.
Understanding each input
Use daily‑averaged or daily total weather data that refer to the same 24‑hour period.
- Net Radiation Rn (MJ/m2/day): Net incoming energy at the surface, equal to incoming minus outgoing shortwave and longwave radiation. Typical well‑watered crop values range from about 5–20 MJ/m2/day, with higher values on clear, sunny days.
- Soil Heat Flux G (MJ/m2/day): Daily soil heat storage term. For daily calculations over reference grass, G is usually small and often approximated as 0. Use 0 unless you have a specific estimate.
- Mean Air Temperature T (°C): Daily mean temperature at 2 m height. Many weather data sources provide this directly; otherwise, it can be approximated as the average of daily minimum and maximum temperatures.
- Wind Speed u2 (m/s at 2 m): Mean daily wind speed at 2 m above the ground. If your data are measured at a different height (for example 10 m), they should be adjusted to 2 m using FAO‑856 relationships.
- Saturation Vapor Pressure es (kPa): The vapor pressure that air would have if it were saturated at temperature T. It is a function of temperature only and can be computed from daily minimum and maximum temperatures, or obtained from some weather services.
- Actual Vapor Pressure ea (kPa): The actual moisture content of the air, derived from humidity measurements (for example relative humidity, dew point, or wet and dry bulb temperatures). ea must be in kPa and correspond to the same daily period and location as es.
Ensure that both vapor pressures use the same reference elevation and temperature units, and that wind speed and radiation correspond to the same site and day.
Interpreting the ET0 result
The calculator returns daily reference evapotranspiration, ET0, typically 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 associated with cool, cloudy or humid conditions.
- 3–5 mm/day: Moderate demand, common in many temperate growing conditions.
- 6–10+ mm/day: High demand, typical of hot, dry and windy climates.
To obtain crop evapotranspiration (ETc) for a specific crop and growth stage, multiply ET0 by an appropriate crop coefficient Kc:
ETc = Kc × ET0
Crop coefficients depend on crop type, canopy development, and management. FAO‑856 and local agronomic guides provide typical Kc values.
Worked example
Suppose you have the following daily data for a reference grass surface at a temperate site in mid‑summer:
- Net radiation Rn = 15 MJ/m2/day
- Soil heat flux G = 0 MJ/m2/day (daily time scale)
- Mean air temperature T = 25 °C
- Wind speed u2 = 2 m/s
- Saturation vapor pressure es = 3.17 kPa
- Actual vapor pressure ea = 2.10 kPa
Entering these values in the calculator yields a daily ET0 of roughly 5‑6 mm/day (the exact value depends on the internally computed Δ and γ). This means that the reference crop would lose about 5‑6 mm of water over the day.
If you are growing a crop with a mid‑season crop coefficient Kc of 1.15, then the crop evapotranspiration is approximately:
ETc ≈ 1.15 × ET0
For 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.
Penman‑Monteith vs. other ET methods
The FAO Penman‑Monteith method is widely recommended as the standard approach for estimating reference evapotranspiration where the required weather data are available. Other empirical methods may be used when data are limited, but often at the cost of accuracy or generality.
| Method | Data requirements | Typical use case | Comments |
|---|---|---|---|
| FAO Penman‑Monteith | Radiation (or sunshine), temperature, humidity, wind | Reference standard for ET0 where full weather data exist | Physically based, generally most robust across climates |
| Hargreaves‑Samani | Temperature, extraterrestrial radiation | Regions with only temperature data available | Simpler, but more empirical and less accurate in some climates |
| Blaney‑Criddle | Temperature, daylight hours | Legacy irrigation planning, some arid and semi‑arid regions | Requires local calibration for reliable results |
When you have reliable measurements of radiation, humidity and wind, Penman‑Monteith is usually preferred. Simpler methods are mainly used when weather records are incomplete or for preliminary assessments.
Assumptions and limitations
- Reference surface: ET0 refers to 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 does not represent any specific crop without applying crop coefficients.
- Uniform conditions: The method assumes horizontally uniform conditions (vegetation, soil moisture, and weather) over the area influencing the measurements.
- Daily time scale: Inputs and outputs are for a daily period. Sub‑daily variability (for example hourly peaks in radiation or wind) is not explicitly resolved in this calculator.
- Measurement height and exposure: Wind speed and temperature are assumed at 2 m height over short grass. Weather stations in sheltered or atypical locations can bias ET0 estimates.
- Climatic extremes: In very arid, advective or highly heterogeneous conditions, reference equations may be less representative, and local calibration or lysimeter data may be needed.
- Not a design recommendation by itself: ET0 is one component of irrigation design. System capacity, soil water holding characteristics, rainfall patterns, and management objectives must also be considered.
Use ET0 from this calculator as a technically grounded estimate, but always interpret it together with local experience, field observations and, where available, regional guidelines.
Understanding Reference Evapotranspiration
Evapotranspiration, often abbreviated as ET, merges two vital processes by which water moves from the land surface to the atmosphere. Evaporation is the direct conversion of water to vapor from soils, open water, or wet plant surfaces, while transpiration describes the release of water vapor from plant leaves as part of photosynthesis and plant cooling. When agronomists talk about reference evapotranspiration (ET0), they mean the rate at which a hypothetical, well-watered, short grass surface loses water under given weather conditions. This standardized definition allows researchers and farmers to compare water demand across regions and seasons without the confounding effects of specific crops or management practices. ET0 acts as a benchmark: actual crop water use can be estimated by multiplying ET0 by a crop coefficient that accounts for species and growth stage. Because water scarcity and irrigation efficiency are global concerns, tools that compute ET0 have become indispensable in both high-tech agricultural operations and classroom exercises exploring the water cycle.
The FAO Penman‑Monteith equation is widely regarded as the gold standard for estimating ET0 from routine meteorological observations. It combines energy-balance principles with aerodynamic theory, acknowledging that water loss depends not only on available energy but also on the capacity of air to transport vapor away from the surface. The equation expresses ET0 in millimeters per day, equivalent to liters per square meter. A simplified form for a reference surface reads:
In this equation, is the slope of the saturation vapor pressure curve at temperature in kPa per degree Celsius, and is the psychrometric constant with a value near 0.066 kPa/°C for air at sea level. The net radiation represents the balance of incoming and outgoing shortwave and longwave energy, while captures ground heat flux, often negligible over daily periods. The aerodynamic term uses the wind speed measured at two meters above ground and the vapor pressure deficit , which quantifies how thirsty the air is.
To implement the formula, this calculator first determines Δ from the input temperature using to derive the saturation pressure curve, then combines the energy and aerodynamic terms as shown. All calculations occur instantly in your browser. If you enter a net radiation of 15 MJ/m²/day, temperature of 25°C, wind speed of 2 m/s, and a vapor pressure deficit of about 1.07 kPa, the resulting ET0 is roughly 4.8 mm/day. That means a well-watered reference lawn would lose nearly five liters per square meter that day. By experimenting with the inputs—perhaps raising wind speed or lowering humidity—you can see how ET0 responds to changing weather.
Typical ET0 Values for Different Climates
Because ET0 depends heavily on weather, values vary by climate and season. The table below lists ballpark daily ET0 ranges for several representative climates during peak growing months. These values derive from long-term meteorological records and serve as rough expectations rather than precise forecasts.
| Climate Type | Typical ET0 (mm/day) | Notes |
|---|---|---|
| Humid temperate | 3–6 | Mild temperatures and moderate humidity keep ET modest. |
| Arid desert | 6–10 | High solar radiation and low humidity drive intense water loss. |
| Tropical wet | 4–8 | Abundant sun but frequent clouds and high humidity. |
| High altitude | 2–5 | Cooler temperatures offset strong solar radiation. |
| Coastal maritime | 2–4 | Persistent cloud cover and breezes reduce ET0. |
These ranges help irrigators plan roughly how much water their crops might require. A lettuce farmer in a humid temperate region might expect about 4 mm/day, whereas a desert orchard manager could face demands over 8 mm/day. Such distinctions highlight why a one-size-fits-all irrigation schedule is ineffective. Local weather stations, on-farm sensors, or regional agricultural services often provide daily ET0 updates to guide water application, but having a calculator allows students to explore the underlying physics.
Why ET0 Matters
Reference evapotranspiration plays a central role in sustainable water management. In irrigated agriculture, applying water in line with ET0 prevents both drought stress and wasteful overwatering. Water utilities use ET0 forecasts to schedule deliveries, and conservation agencies rely on the metric to design drought restrictions. Beyond farming, ET0 influences landscape ecology, hydrology, and climate modeling. Urban planners may evaluate how tree planting or green roofs alter ET0 and thereby cool neighborhoods. Hydrologists subtract ET from precipitation to estimate groundwater recharge or streamflow generation. Even climate scientists utilize ET a datasets to validate land-surface models within global circulation simulations. Because the equation integrates radiation, temperature, humidity, and wind, it encapsulates the combined effect of many atmospheric variables, offering a window into how climate change might alter water demand.
Although powerful, the Penman‑Monteith approach carries assumptions. It presumes a uniform reference surface and does not account for soil moisture limitations, advection of hot dry air from surrounding regions, or heterogeneities in canopy structure. In reality, crops taller than grass experience different aerodynamic resistance, and bare soil may have lower albedo, absorbing more energy. Nevertheless, the ET0 concept remains useful precisely because it provides a common baseline. By applying crop coefficients, practitioners tailor ET0 to vineyards, orchards, turfgrass, or any vegetation of interest, while remembering that coefficients themselves vary with growth stage, management, and stress conditions.
The calculator's reliance on user-supplied data underscores the importance of accurate measurements. Net radiation ideally comes from pyranometer readings that capture both shortwave and longwave fluxes. Many stations approximate it from sunshine duration, temperature, and geographical factors using empirical formulas. Wind speed should be measured at two meters height over grass; readings taken near buildings or at different heights require adjustment. Vapor pressure data might derive from humidity sensors or dew point calculations. When high precision is necessary, such as in research or high-value agriculture, each parameter warrants careful calibration. For classroom exploration, however, reasonable estimates provide valuable insight into how weather drives water use.
In conclusion, this Reference Evapotranspiration Calculator offers an accessible gateway to a foundational concept in environmental science and agricultural engineering. By experimenting with parameters, readers can observe how sunny skies, windy afternoons, and dry air conspire to pull moisture from the land. The long explanation and accompanying table aim to demystify the Penman‑Monteith method, empowering students to connect equations with real-world water challenges. Whether planning irrigation, studying hydrology, or simply curious about how the atmosphere drinks from the earth, ET0 is a lens through which the interplay of energy and moisture becomes clear.