Hargreaves-Samani ET0 calculator
Get reference evapotranspiration from temperature records alone: a day of 12 to 28 °C, mean 20 °C, with radiation of 35 mm/day gives an ET0 of 12.1716 mm/day. No wind or humidity data needed. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- T min
- 12
- T max
- 28
- T mean
- 20
- Ra
- 35
- Temperature range
- 16 mm/day
- Sqrt temperature range
- 4
- Et0
- 12.1716
- Coefficient
- 0.0023
Reference evapotranspiration, written ET0 or ETo, estimates the evaporative demand of the atmosphere over a well-watered short grass surface and is the backbone of crop water requirement calculations, irrigation scheduling, and drought monitoring. The Hargreaves-Samani equation is a temperature-and-radiation method that needs only daily minimum and maximum temperature, a mean temperature, and extraterrestrial radiation for the site and day of year—data that weather stations and climate archives almost always provide even when wind speed, humidity, and net radiation are missing. This reference evapotranspiration Hargreaves calculator applies the classic form ET0 equals 0.0023 times Ra times (Tmean plus 17.8) times the square root of (Tmax minus Tmin), with temperatures in Celsius and Ra and ET0 in millimetres per day water equivalent.
What the Hargreaves–Samani ET0 equation measures and when to use it
Full FAO Penman-Monteith reference evapotranspiration needs net radiation, soil heat flux, vapor pressure deficit, and wind speed at two metres. Many operational networks, historical climate series, and classroom datasets only record temperature extremes and have a way to compute or look up extraterrestrial radiation Ra from latitude and day of year. Hargreaves and Samani closed that gap with an empirical multiplier on Ra that scales demand with the diurnal temperature range and with how warm the day is on average.
The temperature range term acts as a proxy for cloudiness and humidity: clear dry days often show larger Tmax minus Tmin and therefore larger estimated ET0 for the same Ra, while humid or cloudy days compress the range. The (Tmean plus 17.8) factor keeps the estimate positive across cool climates and increases evaporative demand as mean temperature rises. The coefficient 0.0023 is the widely published Hargreaves-Samani constant when Ra is expressed in the same millimetre-per-day water equivalent as ET0.
Use Hargreaves-Samani when you need a transparent, temperature-driven ET0 for irrigation planning, water-balance models, or homework checks and you do not have a full weather suite. Prefer Penman-Monteith when wind, humidity, and radiation observations are reliable and you need the FAO-56 standard for legal or engineering reporting. This capability implements only the Hargreaves-Samani analytic step; it does not compute Ra from latitude or day of year, so you supply Ra already converted to millimetres per day.
Where the Hargreaves method fills the gap
Irrigation consultants and farm management software often need a daily ET0 column for stations that never recorded wind or humidity; feeding Hargreaves-Samani from temperature archives fills that gap without standing up a full micrometeorological stack. Hydrology courses and exam generators need a deterministic oracle that rejects inverted temperature extremes instead of silently returning NaN from a spreadsheet square root. Research notebooks reprocessing twentieth-century climate grids can batch-evaluate ET0 where only monthly or daily temperature extremes and astronomical Ra are available.
Drought monitors and water-balance dashboards sometimes run Hargreaves alongside Penman-Monteith as a temperature-only sensitivity check when secondary sensors drop out.
What you can do with it
Irrigation scheduling from temperature stations
Compute daily Hargreaves-Samani ET0 when only Tmin, Tmax, Tmean, and site Ra are available, then scale by crop coefficients for water budgets.
Climate archive and drought reanalysis
Batch-evaluate reference evapotranspiration from historical temperature extremes and astronomical Ra for water-balance or drought indices.
FAQ
What units should I use for temperatures and Ra?
Temperatures are degrees Celsius. Extraterrestrial radiation Ra must be millimetres per day water equivalent. Convert MJ·m⁻²·day⁻¹ with Ra_mm ≈ 0.408·Ra_MJ before calling.
What happens if maximum temperature is below minimum temperature?
Tmax must be greater than or equal to Tmin; a negative temperature range is not physical for this equation and is not billed.
Does this compute Penman-Monteith ET0 or Ra from latitude?
No. This capability implements only the Hargreaves-Samani temperature-and-radiation formula. You must supply Ra already converted to mm/day; it does not replace full FAO-56 Penman-Monteith.
How do I convert extraterrestrial radiation from megajoules to millimetres per day?
Multiply the value in megajoules per square metre per day by 0.408. That gives the millimetre-per-day water equivalent the formula expects, matching FAO tables; enter that converted figure.
Why does a wider temperature range raise ET0?
The gap between the daily maximum and minimum stands in for cloud and humidity. Clear, dry days show wider ranges and higher evaporative demand for the same radiation, while humid or cloudy days compress the range.
Related tools
For developers — API access
Everything on this page is available programmatically. This section is for teams who want to wire it into their own systems; everyone else can just use the tool above.
API endpoint
Prefer to automate it? One authenticated POST creates the task; the result comes back by webhook or a signed link. The same capability also runs here on the web, by email and from Telegram — and soon from our app too.
Call it from your stack
curl -X POST https://api.kit.forhosting.com/earth/evapotranspiration-hargreaves \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"t_min":12,"t_max":28,"t_mean":20,"ra":35}'const res = await fetch("https://api.kit.forhosting.com/earth/evapotranspiration-hargreaves", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"t_min": 12,
"t_max": 28,
"t_mean": 20,
"ra": 35
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/earth/evapotranspiration-hargreaves",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"t_min": 12,
"t_max": 28,
"t_mean": 20,
"ra": 35
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/earth/evapotranspiration-hargreaves", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"t_min":12,"t_max":28,"t_mean":20,"ra":35}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"t_min":12,"t_max":28,"t_mean":20,"ra":35}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/earth/evapotranspiration-hargreaves", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"t_min": 12,
"t_max": 28,
"t_mean": 20,
"ra": 35
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "earth.evapotranspiration_hargreaves",
"status": "queued",
"_links": {
"result": "/tasks/tsk_…/result"
}
}The API is asynchronous: the call returns a task_id immediately and the result arrives by webhook. Polling is capped at 1 req/s per task.
Pricing
Published price — no tokens, no invented credits. A failed task is never charged.
Errors
| HTTP | Code | Meaning |
|---|---|---|
401 | unauthorized | Missing or invalid API key. |
402 | insufficient_balance | Your balance doesn't cover the task price. |
404 | unknown_type | That task type doesn't exist. |
429 | rate_limited | Too many requests. Use the webhook instead of polling. |
Technical notes
When maximum temperature is below minimum temperature the task fails with invalid_input so automation never silently takes a square root of a negative range.
What the Hargreaves–Samani ET0 equation measures and when to use it
That water-equivalent convention matches FAO tables: if your Ra source is in megajoules per square metre per day, convert first with Ra_mm approximately equal to 0.408 times Ra_MJ before calling this endpoint.
Input contract, units, response shape, and error behaviour
Example: twelve Celsius minimum, twenty-eight Celsius maximum, twenty Celsius mean, and thirty-five millimetres per day of Ra yield a positive ET0 of several millimetres per day typical of a warm mid-latitude growing-season day. Keep temperatures in Celsius, convert energy-based Ra to millimetres per day before calling, and pin the rounded ET0 in tests so goldens stay stable across runtimes. Each field may arrive as a JSON number or a numeric string; missing, blank, or non-finite values fail with invalid_input naming the field. On success the body echoes rounded t_min, t_max, t_mean, and ra; reports temperature_range as Tmax minus Tmin and sqrt_temperature_range as its square root; and returns et0 in millimetres per day under unit mm/day. formula and equation restate the Hargreaves-Samani identity for display, method is hargreaves_samani, coefficient is 0.0023, and steps walks through substitution for teaching UIs. Failed validation is not billed; successful analytic calls use the published $0.002 base price with no model tokens and no outbound network.
Where a Hargreaves reference evapotranspiration API earns its keep
Supply consistent Celsius temperatures, non-negative Ra in millimetres per day, keep t_max at least t_min, pin the rounded millimetre outputs in tests, and you get reproducible Hargreaves-Samani reference evapotranspiration for courses, docs, and automation without shipping a climate library to every edge worker.
Integration use cases
Teaching and exam oracles
Give students a deterministic ET0 check against hand Hargreaves steps and reject inverted Tmax/Tmin as invalid_input.
Technical questions
How do I calculate Hargreaves-Samani reference evapotranspiration?
Send t_min, t_max, and t_mean in °C plus ra in mm/day water equivalent. The API returns ET0 = 0.0023·Ra·(Tmean+17.8)·√(Tmax−Tmin) in mm/day.
What does the Hargreaves ET0 calculator cost?
The browser tool is free. API requests use prepaid KIT balance at $0.002 per successful call; invalid input is not billed.