What Hargreaves ET measures
Reference evapotranspiration, or ETo, is the depth of water a standardized, well-watered grass surface loses to evaporation and transpiration in a day. It's the baseline that irrigation scheduling builds on: multiply ETo by a crop or landscape coefficient and you get the actual water use of a lawn, crop or planting bed. Most reference ET calculations, including the FAO Penman-Monteith method, need temperature, humidity, wind speed and solar radiation. The Hargreaves-Samani equation was built for the common case where only daily high and low temperature are available.
It does this by calculating extraterrestrial radiation (Ra), the solar energy reaching the top of the atmosphere at your latitude on a given date, purely from astronomy. The day's temperature range then stands in for how much of that radiation actually made it to the ground through clouds and haze: a wide swing between a hot day and a cool night suggests clear skies and strong solar input, while a narrow range suggests cloud cover holding both numbers closer together.
| Conditions | Typical ETo | Notes |
|---|---|---|
| Cool, cloudy or winter days | 1–3 mm/day (0.04–0.12 in/day) | Short days and a low sun angle keep Ra, and ETo, low. |
| Mild spring or fall weather | 3–5 mm/day (0.12–0.20 in/day) | A common shoulder-season range in temperate climates. |
| Hot, sunny summer weather | 5–8 mm/day (0.20–0.31 in/day) | Typical for a warm growing season at mid-latitudes. |
| Hot, dry, low-humidity climates | 8–11 mm/day (0.31–0.43 in/day) | Large day-night temperature swings often go with these conditions. |
This is reference ET, not crop water use. Multiply the result by a crop coefficient (Kc) for your plant and growth stage to estimate actual water use. The crop evapotranspiration calculator does that step.
How this calculator works
The calculator works in two stages: first it computes extraterrestrial radiation (Ra) from your latitude and date, then it plugs Ra and your temperatures into the Hargreaves-Samani equation.
1. Extraterrestrial radiation (Ra)
Solar declination and Earth-sun distance
dr = 1 + 0.033 × cos(2πJ / 365)
δ = 0.409 × sin(2πJ / 365 − 1.39)
J is the day of the year (1–365/366), taken from the date you enter.
Sunset hour angle and Ra
ωs = arccos(−tan(φ) × tan(δ))
Ra = (24×60/π) × Gsc × dr × [ωs sin(φ) sin(δ) + cos(φ) cos(δ) sin(ωs)]
φ is latitude in radians and Gsc is the solar constant, 0.0820 MJ m-2 min-1. Ra comes out in MJ/m²/day and is converted to an equivalent evaporation depth by multiplying by 0.408.
2. The Hargreaves-Samani equation
Reference ET (ETo)
ETo = 0.0023 × (Tmean + 17.8) × (Tmax − Tmin)0.5 × Ra
Temperatures are in °C and Ra is the equivalent evaporation depth in mm/day, giving ETo in mm/day. If the high and low are equal, the temperature-range term is zero and ETo shows as zero for that day.
Unit conversions
US inputs are converted to Celsius before the formula runs: °C = (°F − 32) ÷ 1.8. The mm/day result is converted back with 1 in = 25.4 mm. Latitude and the calendar date don't change with the unit toggle.
Rounding policy
ETo and its weekly total are shown to 2 decimal places in/day (US) or 1 decimal place mm/day (metric), matching the precision used in the calculation. Ra is shown to 1 decimal place in MJ/m²/day. Temperatures you enter are echoed back to 1 decimal place.
When this calculator isn't the right tool
Hargreaves-Samani is a temperature-only method. Use a different approach when:
- You have humidity, wind and solar radiation data. The reference ET calculator can use a fuller set of weather inputs for a more complete daily estimate.
- You need monthly agricultural water requirements from historical averages. The Blaney-Criddle calculator uses a different temperature-based method built for that purpose.
- You want actual crop or landscape water use, not the grass reference value. See the crop evapotranspiration calculator.
- You're planning a full landscape water budget. The landscape water budget calculator combines ET, area and plant factors over a season.
For other ET and scheduling calculations, browse the full set of scheduling and ET calculators.
Hargreaves ET calculation example
Fresno, CA sits at about 36.8°N. On July 1, the forecast calls for a high of 95°F and a low of 65°F.
- Convert to Celsius: 95°F = 35.00°C, 65°F = 18.33°C. Tmean = 26.67°C, range = 16.67°C.
- Day of year: July 1 is day 182.
- Extraterrestrial radiation: at 36.8°N on day 182, Ra ≈ 41.6 MJ/m²/day, equivalent to about 16.95 mm/day of evaporation.
- ETo: 0.0023 × (26.67 + 17.8) × √16.67 × 16.95 ≈ 7.08 mm/day, shown as about 0.28 in/day.
- Over a week of similar weather: about 0.28 × 7 ≈ 1.95 in.
The same calculation in metric
At 45°N on April 15, with a high of 22°C and a low of 8°C:
- Tmean and range: 15.0°C mean, 14°C range.
- Day of year: April 15 is day 105.
- Extraterrestrial radiation: Ra ≈ 33.2 MJ/m²/day, about 13.6 mm/day equivalent.
- ETo: 0.0023 × (15.0 + 17.8) × √14 × 13.55 ≈ 3.8 mm/day, or about 26.8 mm over the week.
The lower latitude and larger temperature swing in the first example both push Ra and ETo higher; the cooler, higher-latitude spring day in the second example lands well inside the "mild spring" band in the table above.
Getting good inputs
Finding your latitude
Any map application shows coordinates for a location; the first number given is usually latitude. Enter it as a plain decimal degree (36.8, not 36°48') and remember the sign: positive north of the equator, negative south of it.
Reading Tmax and Tmin correctly
Use the high and low for the same 24-hour period, ideally from a station close to the field or landscape you're scheduling for. Airport and official weather-service stations are convenient, but a home weather station or on-site sensor tracks local conditions, such as a cooler microclimate near the coast or a hotter one in a paved area, more closely.
Turning ETo into an irrigation amount
ETo by itself tells you water lost, not water to apply. A typical next step is to multiply ETo by a crop or landscape coefficient to get actual water use, subtract any effective rainfall, and convert the remaining depth to a run time or volume. The effective rainfall calculator and the irrigation water requirement calculator handle those steps.
Common mistakes
- Mixing up the sign of latitude. A Southern Hemisphere latitude entered as positive will compute a Northern Hemisphere season instead.
- Using a monthly average high and low instead of a single day's values. The equation is built for daily data; averaging first changes the range term and the result.
- Treating ETo as the irrigation amount. It's the reference water loss; a crop or landscape coefficient still has to be applied.
- Ignoring very low- or no-range days. A day with almost no difference between the high and low will show a near-zero or zero ETo, which likely understates actual conditions if the sky was in fact clear.
Factors that affect the result
| Factor | Effect on the result | What to check |
|---|---|---|
| Latitude | Sets how much extraterrestrial radiation is possible at a given time of year. | Use the exact coordinate for your site, with the correct sign. |
| Date | Changes day length and sun angle, and therefore Ra. | Use the date the temperatures were recorded, not today's date if entering past data. |
| Temperature range | A wider high-low swing raises the estimate; a narrow one lowers it. | Confirm both readings are from the same day and station. |
| Mean temperature | Higher average temperature raises ETo. | No action needed; this follows directly from your two temperature entries. |
| Wind | Not measured by this method; strong wind can push actual ET above the Hargreaves estimate. | In windy climates, treat the result as a lower-bound estimate. |
| Humidity | Not measured by this method; very dry or very humid air can shift actual ET away from the estimate. | Use a full weather-data method where humidity records are available. |
| Cloud cover | Reduces radiation reaching the ground below the clear-sky Ra value. | The temperature range partly captures this; heavy but short-lived cloud may not. |
Coastal and marine-influenced sites are worth a second look: onshore wind and humidity can narrow the temperature range even on a sunny day, which this method reads as more cloud cover than actually occurred. If your site is exposed to strong sea breezes, compare a few days of Hargreaves results against a nearby ET network station before relying on it for scheduling.
Frequently asked questions
What is the Hargreaves-Samani equation?
The Hargreaves-Samani equation estimates reference evapotranspiration (ETo) using only daily maximum and minimum air temperature, plus extraterrestrial radiation calculated from latitude and date. Hargreaves and Samani published it in 1985 as a simpler alternative to methods that need humidity, wind and solar radiation data. FAO Irrigation and Drainage Paper 56 lists it as an accepted method for locations where only temperature records are available.
Why do I need to enter latitude and date if this only uses temperature?
Latitude and date aren't temperature inputs, but the calculator needs them to work out extraterrestrial radiation (Ra): the solar radiation reaching the top of the atmosphere at your location that day. Ra changes with how high the sun gets and how long the day is, both of which depend on latitude and time of year. The daily temperature range then acts as a stand-in for how much of that radiation actually reached the ground through clouds and haze.
How accurate is the Hargreaves method compared with Penman-Monteith?
FAO-56 recommends the Penman-Monteith equation as the standard reference ET method when temperature, humidity, wind speed and solar radiation are all available, and lists Hargreaves-Samani as an option for sites with only temperature data. Temperature-only methods tend to be less reliable in very windy, very humid or coastal locations, where temperature range doesn't track solar radiation as closely. Treat this as a reasonable estimate, not a substitute for full weather-station data where that exists.
Can I use this calculator for the Southern Hemisphere?
Yes. Enter latitude as a negative number for Southern Hemisphere locations, for example -33.9 for Sydney, Australia. The calculation and seasons simply mirror the Northern Hemisphere, so December falls in high summer at negative latitudes rather than winter.
What's the difference between reference ET and crop ET?
Reference evapotranspiration (ETo), which this calculator gives you, represents a standardized well-watered grass surface. Actual crop water use is ETo multiplied by a crop coefficient (Kc) that varies by crop and growth stage. Use a crop evapotranspiration calculator to apply a coefficient once you have an ETo value.
See the crop evapotranspiration calculator and the crop coefficient table.
Where do I find daily high and low temperature for my location?
A nearby weather station, airport observation or home weather station gives the most direct reading, and national weather services publish daily highs and lows by station. For irrigation scheduling, use temperatures recorded at or near the field or landscape where possible, since local microclimate can shift the numbers from a station a few miles away.
Does this calculator account for wind speed or humidity?
No. The Hargreaves-Samani equation deliberately uses only temperature and calculated radiation, which is what makes it usable when wind and humidity data aren't available. That is also its main limitation: in places with strong, dry winds or unusually high humidity, it can over- or underestimate ETo compared with a method that measures those factors directly.
Can I use Hargreaves ET directly for irrigation scheduling?
It can guide scheduling, especially when it's the only ET estimate available. Multiply the ETo by a crop or landscape coefficient to get water use, then subtract effective rainfall to find how much irrigation to apply. Where a local ET network using more complete weather data covers your area, that source will generally be more accurate than a temperature-only estimate.
See the irrigation scheduling calculator for turning ETo into a watering plan.
Who built and checked this calculator
Licensed Professional Engineer and Irrigation Association Certified Irrigation Designer with more than 20 years in irrigation design, system auditing and landscape water management. Full profile
How this page was checked
- The Ra and Hargreaves-Samani formulas and all five worked test cases were verified by hand against FAO-56.
- Unit conversions were checked both directions (°F ↔ °C, mm ↔ in).
- Edge cases were tested, including equal high and low temperature and latitudes near the polar circles.
Sources
- Allen, R.G., Pereira, L.S., Raes, D. and Smith, M. (1998). Crop Evapotranspiration – Guidelines for Computing Crop Water Requirements. FAO Irrigation and Drainage Paper No. 56. [VERIFY URL]
- Hargreaves, G.H. and Samani, Z.A. (1985). Reference Crop Evapotranspiration from Temperature. Applied Engineering in Agriculture, 1(2), 96–99.
- USDA Natural Resources Conservation Service. National Engineering Handbook, Part 623: Irrigation. [VERIFY URL]
- California Department of Water Resources. California Irrigation Management Information System (CIMIS).