Evapotranspiration Calculator

Calculate daily and monthly reference evapotranspiration (ET0) and crop water use (ETc) using the internationally validated FAO-56 Hargreaves-Samani temperature-radiation model.

Method reviewed by Plant Calculator Team·Updated August 2026

How this is worked out

ET<sub>0</sub> = 0.0023 × R<sub>a</sub> × (T<sub>mean</sub> + 17.8) × (T<sub>max</sub> - T<sub>min</sub>)^{0.5}   ·   ET<sub>c</sub> = ET<sub>0</sub> × K_c

Where R<sub>a</sub> is extraterrestrial solar radiation (mm/day equivalent) computed from geographic latitude and day-of-year solar declination angle, and T is ambient temperature in °C.

Assumptions

Hargreaves-Samani equation provides accurate ET0 estimates using only daily maximum and minimum temperatures and latitude solar geometry.

Diurnal temperature range (Tmax - Tmin) serves as a physical proxy for atmospheric vapor pressure deficit and cloud solar transmission.

Reference ET0 represents water loss from an extensive, uniform, well-watered active green grass surface of 0.12 m height.

Actual crop water consumption (ETc) is calculated by scaling reference ET0 by the crop-specific coefficient (Kc).

Understanding evapotranspiration: Hargreaves-Samani physics & crop ETc

Evapotranspiration is the foundational variable of horticultural water management, quantifying the volume of water lost to the atmosphere through direct soil evaporation and leaf stomatal transpiration. While the full Penman-Monteith equation requires costly meteorological stations (measuring net solar radiation, wind speed, relative humidity, and air temperature), the calibrated FAO-56 Hargreaves-Samani model accurately derives ET₀ from basic daily high and low temperatures and astronomical solar tables.

The Hargreaves-Samani Equation Explained

ET₀ (mm/day) = 0.0023 × R_a × (T_mean + 17.8) × √(T_max - T_min)

Where: R_a = Extraterrestrial Solar Radiation (mm/day equivalent), T_mean = (T_max + T_min)/2 in °C, and T_max/T_min are daily temperatures in °C.

Extraterrestrial Solar Radiation (R_a) Dynamics

Extraterrestrial radiation (R_a) is the theoretical solar energy reaching the top of the Earth's atmosphere, governed strictly by solar declination angle and earth-sun orbital distance. Because atmospheric clarity correlates directly with the daily diurnal temperature range (ΔT = T_max - T_min), the square root term √(ΔT) acts as a physical proxy for cloud cover and solar transmissivity.

Hargreaves Extraterrestrial Solar Radiation across Latitudes
Latitude Zone	Winter Solstice (R_a)	Spring Equinox (R_a)	Summer Solstice (R_a)
25° N (Subtropical)	8.5 mm/day	13.8 mm/day	16.9 mm/day
35° N (Temperate)	6.0 mm/day	12.5 mm/day	17.1 mm/day
45° N (Continental)	3.8 mm/day	11.0 mm/day	17.2 mm/day
55° N (Northern)	1.8 mm/day	9.2 mm/day	17.0 mm/day

Three Worked Evapotranspiration Calculations

1. Mid-Summer Beefsteak Tomato in Richmond, VA (37.5° N, July)

T_max = 90°F (32.2°C), T_min = 66°F (18.9°C). Mean temperature T_mean = 25.55°C. Diurnal range ΔT = 13.3°C. July R_a = 16.8 mm/day. ET₀ = 0.0023 × 16.8 × (25.55 + 17.8) × √(13.3) = 6.11 mm/day (0.24 in/day). Tomato K_c = 1.15 → ET_c = 0.24 × 1.15 = 0.28 in/day (1.96 inches/week).

2. Spring Strawberry Bed in Sacramento, CA (38.5° N, May)

T_max = 80°F (26.7°C), T_min = 50°F (10.0°C). Mean temperature T_mean = 18.35°C, ΔT = 16.7°C. May R_a = 16.5 mm/day. ET₀ = 0.0023 × 16.5 × (18.35 + 17.8) × √(16.7) = 5.60 mm/day (0.22 in/day). Strawberry K_c = 0.85 → ET_c = 0.19 in/day (1.33 inches/week).

3. Autumn Cool-Season Lawn in Chicago, IL (41.8° N, October)

T_max = 62°F (16.7°C), T_min = 44°F (6.7°C). Mean temperature T_mean = 11.7°C, ΔT = 10.0°C. October R_a = 8.5 mm/day. ET₀ = 0.0023 × 8.5 × (11.7 + 17.8) × √(10.0) = 1.82 mm/day (0.07 in/day). Turfgrass K_c = 0.95 → ET_c = 0.07 in/day (0.49 inches/week).

Common Evapotranspiration Calculation Mistakes

Forgetting to convert Fahrenheit to Celsius before formula entry: The empirical constant 0.0023 and the 17.8 baseline are strictly calibrated for temperatures in degrees Celsius. Inputting raw Fahrenheit temperatures inflates calculated ET by over 150%.
Neglecting coastal humidity dampening: In humid coastal regions (marine layer), high relative humidity reduces actual vapor pressure deficit. In humid maritime climates, reduce raw Hargreaves estimates by 10% to 15%.
Ignoring microclimates and wind funnels: Urban courtyard gardens shielded from wind experience 20% lower ET than exposed ridgetop fields where persistent 15 mph winds strip moisture continuously.

Use calculated ET rates to plan irrigation with our Crop Water Requirement Calculator, Irrigation Scheduling Calculator, and Irrigation Run Time Calculator.

Common questions

What is Evapotranspiration (ET)?

Evapotranspiration (ET) is the combined process of water evaporating from the soil surface and plant transpiration from crop leaf stomata into the atmosphere. It represents the total volume of water a crop consumes and loses to the air daily.

How does the Hargreaves-Samani ET0 formula work?

The Hargreaves-Samani method calculates Reference ET (ET0) using extraterrestrial solar radiation (Ra, determined by latitude and day of year) and daily temperature range: ET0 = 0.0023 × Ra × (Tmean + 17.8) × sqrt(Tmax - Tmin). It is the FAO-56 recommended method when solar radiation, relative humidity, or wind speed sensors are unavailable.

Why does daily temperature range (Tmax - Tmin) correlate with solar radiation?

Clear sunny days experience high solar heating during the afternoon (high Tmax) and rapid radiative cooling under clear night skies (low Tmin), creating a wide temperature range. Overcast cloudy days block solar heating and trap night heat, creating a narrow temperature range.

What is the difference between ET0 and ETc?

Reference ET (ET0) is the evaporative demand of an extensive, well-watered green grass surface 0.12 m tall. Crop ET (ETc) is the actual water demand of a specific crop at its current growth stage, calculated as ETc = ET0 × Kc.

Atmospheric & Solar Temperature Data