Reference Evapotranspiration Calculator (ETo)

Reference Evapotranspiration Calculator (Penman-Monteith)


History

Before the 1960s, farmers relied primarily on visual cues and soil moisture tests to determine when to irrigate. The breakthrough came when scientists recognized that water loss from crops follows predictable patterns based on weather conditions and plant characteristics. This discovery led to the development of the Penman-Monteith equation in 1965, later refined by the FAO in the 1990s, which remains the gold standard for calculating water requirements in agricultural settings.  


Calculating Crop Water Needs And Irrigation System Capacity

The method is taught in agricultural colleges worldwide and represents the culmination of decades of research into plant water needs. Researchers at the University of California and the Food and Agriculture Organization (FAO) sought to standardize irrigation scheduling across different climates and crop types. Eventually, they did it by first calculating how much water a reference surface—specifically, a well-watered grass lawn of uniform height—would lose under given weather conditions. This is what we call Reference Evapotranspiration (ETo).  


Note: In mathematical equations, and formal settings, you would use a subscript zero (₀) in place of the “o” in “ETo”. But in writing, just using a lowercase “o” is sufficient, much easier for writing, communication and doesn’t cause confusion.

Unless your main crop is a short-bladed grass, this baseline value (ETo) is then adjusted using Crop Coefficients (Kc) which are crop-specific multipliers. Combining those two, we end up with Crop Evapotranspiration (ETc) – the actual water needs for different plants at various growth stages. This two-step process allows agricultural professionals to apply consistent methodology across diverse farming operations, from small vegetable gardens to vast wheat fields.  


Why even use ETo?

The reason why you need to know plant water expenditure before doing anything else is so that you know that your water source and chosen method of delivery can handle the requirements when crops need it most (during summer of course) and when water is scarce.


In extreme cases, you might realize that you need to give up on your chosen crop because it requires way too much water, compared to what is available. Or, you could realize that your chosen water delivery method needs to change because you need better efficiency.


Although setting up all those measurements in the field would be pretty cool, just having a tensiometer for daily soil moisture content measurements should be enough. The ETo/ETc values are not that relevant when you already have everything set up, but before you invest your first penny into your farming adventure. They are an estimate, and basically the first “educated guess” used in irrigation system design. An entire cascade of calculations depends on ETo/ETc:

  1. What method of water delivery you choose and thus – irrigation efficiency
  2. Required or recommended irrigation frequency (timing)
  3. Peak water consumption and requirements
  4. Pipe sizing
  5. Water pump volume capacity
  6. And so on…

Reference Evapotranspiration Methodology

Reference evapotranspiration represents the combined water loss from soil evaporation and plant transpiration – the process where water moves through plants from roots to leaves, then evaporates into the atmosphere. The reference surface is defined as a hypothetical grass crop with specific characteristics: 12 centimeters tall, with a fixed surface resistance of 70 seconds per meter and an albedo (reflectivity) of 0.23. These standardized parameters ensure consistency in calculations worldwide.  


Variables

The FAO Penman-Monteith equation, the internationally accepted standard for calculating ETo, incorporates four primary weather variables:

  • solar radiation
  • air temperature
  • humidity
  • wind speed.

IMPORTANT NOTES:

  • Solar Radiation can be obtained through your local meteorological stations, and in this case you should search for Total Radiation, not Net Radiation. Or you could calculate it yourself using online resources. For more information on this, visit the FAO 56 paper, and to get your daily solar radiation figures, visit the Global Solar Atlas calculator. In this awesome tool, the value to look at is “Global Horizontal Radiation” which is the total radiation that hits the earth (they’re just using a different name for it).
  • The ETo equation on our own website automatically calculates Net Radiation using some assumptions like an albedo of 0.23, for example. If you’d like a fully customizable calculator, contact us with a request, although this version provides more than enough precision for everyday users.
  • The GSA calculator uses KWh units, but to get megajoules (MJ), it’s enough to know that 1 KWh = 3.6 MJ. The conversion is easy!

The equation appears complex but essentially balances the energy available for evaporation against the atmospheric demand for water vapor. In practical terms, ETo increases on hot, dry, windy days and decreases during cool, humid, calm conditions. Agricultural colleges teach students to obtain ETo values through these methods.

  1. First, weather stations equipped with appropriate sensors can calculate ETo automatically using the full Penman-Monteith equation.
  2. Second, simplified equations like the Hargreaves method can estimate ETo using only temperature data, though with reduced accuracy.
  3. Third, many regions provide ETo values through agricultural extension services or online databases, eliminating the need for individual calculations.
  4. Fourth, calculate your own using historical climate data for a specific location or nearest weather station.

Typical values of ETo

Daily ETo values typically range from 1 millimeter in winter in temperate climates to over 10 millimeters during summer in arid regions. For context, 1 millimeter of water over 1 square meter equals 1 liter, so a lawn losing 5 mm per day requires 5 liters per square meter daily. These values form the foundation for all subsequent irrigation calculations.  


The Role and Nature of Crop Coefficients (Kc)

Crop coefficients serve as multipliers that adjust reference evapotranspiration to match the water requirements of specific crops. A crop coefficient represents the ratio between the water use of a particular crop and that of the reference grass under identical weather conditions.


For instance, if corn uses 6 mm of water per day when the reference grass uses 5 mm, the crop coefficient equals 1.2. It’s a coefficient so it doesn’t have any unit of measurement. The fundamental principle underlying crop coefficients is that different plants have varying water needs based on their physiological characteristics. Factors influencing these differences include:

  1. leaf area,
  2. plant height,
  3. rooting depth,
  4. stomatal regulation (stomata are microscopic pores on leaves that control gas exchange and water loss).

Deep-rooted crops like alfalfa can maintain higher transpiration rates than shallow-rooted vegetables. Similarly, plants with large leaf areas typically consume more water than those with minimal foliage.


Crop coefficients vary not only between species but also throughout a single plant’s life cycle. This variation reflects changing water demands as plants develop from seedlings to maturity. Agricultural scientists have documented these patterns for virtually all commercial crops, creating detailed tables and graphs that irrigation managers use to schedule water applications throughout the growing season.


The actual crop evapotranspiration (ETc)—the water a specific crop needs—is calculated by multiplying the reference evapotranspiration by the appropriate crop coefficient: ETc = ET₀ × Kc. This simple equation forms the basis for scientific irrigation management taught in agricultural programs worldwide.