What is the Hargreaves equation?

The Hargreaves method estimates reference evapotranspiration as 0.0023 times extraterrestrial radiation times the square root of the daily temperature range times mean temperature plus 17.8. It needs only temperature data, making it useful where humidity, wind, and radiation are unavailable.

What is a crop coefficient (Kc)?

Kc scales reference ET to a specific crop and growth stage. It is near 0.3 to 0.4 at emergence, rises to 1.05 to 1.2 at mid-season full canopy, then falls toward 0.5 to 0.9 at maturity. Multiplying reference ET by Kc gives the actual crop water use.

How do I find extraterrestrial radiation?

Extraterrestrial radiation depends only on latitude and day of year and is tabulated in FAO Irrigation and Drainage Paper 56 in megajoules per square metre per day. The tool converts it internally so reference ET comes out in millimetres per day.

What is effective rainfall?

Effective rainfall is the portion of rain that is actually stored in the root zone and used by the crop, after runoff and deep percolation losses. The net irrigation requirement is crop ET minus effective rainfall over the period.

Is Hargreaves as accurate as Penman-Monteith?

Penman-Monteith is the FAO standard and is more accurate when full weather data is available. Hargreaves is a temperature-only approximation that performs well at monthly timescales and in data-sparse settings, but it can be biased in very humid or very windy locations.

What is the Crop Water Use (ET) Estimator?

Estimates reference evapotranspiration with the Hargreaves temperature method, then multiplies by a crop coefficient (Kc) to give daily crop ET and scales it over a growth stage for seasonal water use. Subtracts effective rainfall to give a net irrigation requirement. An irrigation-scheduling aid for agronomists and irrigation managers. It runs free in your browser on Gera Tools, with nothing uploaded.

Crop Water Use (ET) Estimator

Name: Crop Water Use (ET) Estimator
Creator: Gera Tools
License: https://creativecommons.org/licenses/by/4.0/

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Knowing how much water a crop uses lets you schedule irrigation precisely instead of guessing. This tool estimates reference evapotranspiration from temperature using the Hargreaves method, applies a crop coefficient to get actual crop water use, scales it over a growth stage, and subtracts effective rainfall to give the net irrigation requirement.

How it works

Reference ET is estimated from temperature and extraterrestrial radiation, then scaled by the crop coefficient and the stage length:

ETo (mm/day) = 0.0023 × Ra × (Tmax − Tmin)^0.5 × (Tmean + 17.8)
ETc (mm/day) = ETo × Kc
seasonal ETc = ETc × stage days
net irrigation = seasonal ETc − effective rainfall

Ra is extraterrestrial radiation in millimetres of water equivalent per day (the tool converts your MJ/m²/day input by dividing by 2.45). The crop coefficient Kc rises from emergence to a mid-season peak and then declines, so the same weather gives very different water use depending on growth stage.

Worked example: maize at mid-season

Conditions: Tmax 30 °C, Tmin 16 °C, Tmean 23 °C, Ra 16.5 mm/day (equivalent to approximately 40 MJ/m²/day, typical of a mid-latitude summer).

ETo = 0.0023 × 16.5 × (30 − 16)^0.5 × (23 + 17.8)
    = 0.0023 × 16.5 × 3.74 × 40.8
    ≈ 5.8 mm/day

For maize at mid-season growth (Kc ≈ 1.15):

ETc = 5.8 × 1.15 ≈ 6.7 mm/day
Over 30 days: 201 mm seasonal ETc
Minus 60 mm effective rainfall: net irrigation ≈ 141 mm

That is roughly 14 cm of irrigation water needed for the stage — a meaningful number for planning pump run times or drip-system scheduling.

Understanding crop coefficients (Kc)

The Kc value represents how much more or less water a specific crop uses relative to a reference grass surface. It changes through the growing season in three broadly recognised stages:

Stage	Approximate Kc range
Initial (emergence to 10% cover)	0.3–0.4
Mid-season (full canopy)	0.9–1.2+
Late season (senescence to harvest)	0.5–0.9

Legumes like soybean peak slightly lower than maize; fruit trees have a different seasonal pattern due to canopy and irrigation methods. The FAO Irrigation and Drainage Paper 56 tabulates Kc for dozens of crops and is the standard reference.

When to use Hargreaves vs. Penman-Monteith

The Penman-Monteith equation — the FAO standard — requires solar radiation, wind speed, and humidity alongside temperature. When that data is unavailable (common in remote or data-sparse fields), Hargreaves is the recommended temperature-only alternative. It performs well on a monthly or multi-day basis and is widely used in irrigation planning across Sub-Saharan Africa, South Asia, and other regions with limited weather station networks. For single-day precision or very humid coastal locations, Penman-Monteith should be used if data allows.

Practical notes for irrigation scheduling

Re-run the estimate as temperature and growth stage change through the season. A single estimate for the whole season will be wrong; in practice, updating at least once per growth stage — and more frequently during mid-season — gives the most actionable results. Effective rainfall is site-specific; a standard rule of thumb is to count 80% of rainfall events over 5 mm as effective, but local runoff and soil infiltration rate should inform your figure.