Hargreaves Reference Evapotranspiration Calculator (ET₀ from Temperature)
Daily water use of a well-watered reference grass in mm per day, from only the day's highest and lowest temperature, the latitude and the date.
Results
The dashed line marks the value you entered.
What this tool does
The Hargreaves–Samani equation is the one FAO-56 offers when humidity, wind and sunshine records are missing: the gap between the day's highest and lowest temperature stands in for cloudiness, since clear days swing more. The sunlight reaching the top of the atmosphere, Ra, is pure geometry of latitude and date, taken from the FAO-56 equations. The result is for short grass, not a crop — multiply by a crop coefficient — and it is less dependable on coasts and islands and in very humid or windy climates, where the temperature range says less about the sun.
Formula
ET₀ = 0.0023 (T_mean + 17.8) √(T_max − T_min) × 0.408 Ra · Ra from FAO-56: dr = 1 + 0.033 cos(2πJ/365), δ = 0.409 sin(2πJ/365 − 1.39), ωs = acos(−tanφ tanδ)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
la | Latitude | ° |
j | Day of the year | — |
tx | Highest air temperature of the day | °C |
tn | Lowest air temperature of the day | °C |
ET | Reference evapotranspiration ET₀ | mm/day |
RA | Extraterrestrial radiation Ra | MJ/m²/day |
RM | Ra as an equivalent depth of evaporation | mm/day |
N | Length of the day (sunrise to sunset) | h |
Worked example
- Latitude40 °
- Day of the year196
- Highest air temperature of the day32 °C
- Lowest air temperature of the day18 °C
- Reference evapotranspiration ET₀6.13 mm/day
- Extraterrestrial radiation Ra40.80 MJ/m²/day
- Ra as an equivalent depth of evaporation16.65 mm/day
- Length of the day (sunrise to sunset)14.6 h
Limitations
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.
- The default values are typical reference figures, not measurements of your situation. Replace them with your own data whenever you have it.