Reference Evapotranspiration Calculator

ET₀ from latitude, temperature, humidity, wind and sunshine — computed five ways at once, so you can see how far the shortcut methods drift from the FAO-56 standard at your site.

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Free reference evapotranspiration calculator. Computes FAO-56 Penman–Monteith ET0 alongside Hargreaves–Samani, Priestley–Taylor, Turc and Makkink, reports net radiation and day length, and flags when the shortcut methods diverge.
Published

August 10, 2026

✓ Reviewed by a hydrogeologist (Ph.D.) SI units · metric and US wind speeds Method-divergence check Sources: Allen et al. 1998 (FAO-56) · Hargreaves & Samani 1985 · Priestley & Taylor 1972

What to enter for what you want

Latitude and day of year fix the astronomy — how much solar radiation reaches the top of the atmosphere and how long the sun is up — so those two are needed for every method. Everything else describes the weather at the surface.

To find Enter Read it in
ET₀, the reference value All seven inputs Headline
ET₀ where you only have temperature Latitude, day, both temperatures Hargreaves–Samani
ET₀ over a wet surface Add humidity and sunshine Priestley–Taylor
Whether a shortcut is safe here All seven inputs Method spread, and the verdict
Net radiation for an energy budget All except wind Net radiation Rn
Day length at this latitude and date Latitude, day of year Daylight hours N

Wind speed enters the Penman–Monteith estimate only. Increase it and the headline moves while the four bars below stay where they are — which is the whole reason the shortcut methods fail in windy, dry places. Sunshine hours drive everything except Hargreaves–Samani, which infers cloudiness from the daily temperature range instead of being told.

The groundwater question it answers

Evapotranspiration is not groundwater flow, and it sits on this site for a reason: it is the largest term standing between rainfall and recharge, and recharge is what is left after it. In the simplest annual budget,

R = P - ET_a - Q_s

where P is precipitation, ET_a actual evapotranspiration, Q_s surface runoff and R recharge. The arithmetic is unforgiving. Take a temperate site with P = 1200 mm and ET_a = 950 mm and negligible runoff: recharge is 250 mm. Now suppose the evapotranspiration estimate was 10 % too low — a smaller error than the spread between the methods on this page in most climates. ET_a becomes 1045 mm and recharge becomes 155 mm, a 38 % error in the quantity you actually wanted. Recharge is a small residual of two large numbers, so it inherits their absolute errors, not their relative ones.

That is why the divergence between methods is displayed here as prominently as the answer itself. Choosing Turc over Penman–Monteith because the wind data were missing is not a minor methodological preference; in a water balance it can move the recharge estimate by half.

One caution before the residual is taken: this calculator returns reference evapotranspiration, the demand a short, well-watered grass surface would exert. Real land covers do less (or, for phreatophytes with roots in the water table, more). Getting from ET₀ to ET_a requires crop or vegetation coefficients and a soil-moisture accounting the calculator does not attempt.

What the equations say

FAO-56 Penman–Monteith

Penman’s insight in 1948 was that evaporation is driven from two sides at once. Energy must be supplied to break the hydrogen bonds — that is the radiation term — and the vapour must then be carried away, or the air above the surface saturates and the process stalls. That is the aerodynamic term. Monteith added surface resistance so the formulation applied to vegetation rather than open water, and FAO-56 fixed the resistances to those of a hypothetical 0.12 m grass sward so that the result became a reproducible reference.

ET_0 = \frac{0.408\,\Delta\,(R_n - G) + \gamma\,\dfrac{900}{T + 273}\,u_2\,(e_s - e_a)}{\Delta + \gamma\,(1 + 0.34\,u_2)}

The first term in the numerator is energy, the second is drying power. In a humid, calm climate the first dominates and the radiation-only methods work; in an arid, windy one the second can exceed it, and any method that ignores wind and humidity collapses.

The psychrometric constant follows from atmospheric pressure, which follows from elevation:

P = 101.3\left(\frac{293 - 0.0065\,z}{293}\right)^{5.26}, \qquad \gamma = 0.000665\,P

Saturation vapour pressure and its slope come from temperature alone. Note that e_s is the average of the values at T_{max} and T_{min}, not the value at the mean temperature; because the curve is convex, using the mean temperature under-estimates e_s and therefore the drying power.

e^{\circ}(T) = 0.6108\,\exp\!\left(\frac{17.27\,T}{T + 237.3}\right), \qquad \Delta = \frac{4098\,e^{\circ}(T_{mean})}{(T_{mean} + 237.3)^2}

Extraterrestrial radiation is pure geometry — the sun’s distance, its declination, and how long it stays above the horizon:

R_a = \frac{24 \times 60}{\pi}\,G_{sc}\,d_r\,\bigl[\omega_s \sin\varphi \sin\delta + \cos\varphi \cos\delta \sin\omega_s\bigr]

with \omega_s = \arccos(-\tan\varphi \tan\delta), from which daylight hours are N = 24\,\omega_s / \pi. Sunshine hours then convert R_a to the radiation that actually arrives, R_s = (0.25 + 0.50\,n/N)\,R_a, and the long-wave loss is subtracted to give R_n. Daily soil heat flux G is taken as zero, which is standard for periods of a day or longer.

The four shortcuts

Each was built for the data that were available, not out of carelessness.

Hargreaves–Samani needs only temperature. The daily range T_{max} - T_{min} is used as a proxy for cloudiness: clear days heat up and cool off more than overcast ones.

ET_0 = 0.0023\,(T_{mean} + 17.8)\sqrt{T_{max} - T_{min}}\;\frac{R_a}{\lambda}

Priestley–Taylor deletes the aerodynamic term and multiplies the radiation term by an empirical \alpha = 1.26, which was calibrated over extensive wet surfaces where the air is close to saturation.

ET_0 = \alpha\,\frac{\Delta}{\Delta + \gamma}\,\frac{R_n - G}{\lambda}

Turc and Makkink are regressions on solar radiation and temperature, both fitted in humid mid-latitude climates — Turc in France, Makkink in the Netherlands. Turc carries a correction that switches on below 50 % relative humidity, an admission that the fit was never meant for dry air.

ET_{0,\text{Turc}} = 0.013\,\frac{T_{mean}}{T_{mean} + 15}\,(23.88\,R_s + 50), \qquad ET_{0,\text{Makkink}} = 0.65\,\frac{\Delta}{\Delta + \gamma}\,\frac{R_s}{\lambda}

The latent heat of vaporisation \lambda is taken as 2.45 MJ kg⁻¹, its value at 20 °C; dividing an energy flux in MJ m⁻² day⁻¹ by it converts to mm of water per day.

The variables

Symbol Quantity SI unit Note
ET0 Reference evapotranspiration mm day⁻¹ For 0.12 m grass, not for your land cover
Rn Net radiation at the surface MJ m⁻² day⁻¹ Short-wave gain minus long-wave loss
Ra Extraterrestrial radiation MJ m⁻² day⁻¹ Astronomy only; no weather in it
Rs Solar radiation at the surface MJ m⁻² day⁻¹ From sunshine hours via Ångström
G Soil heat flux MJ m⁻² day⁻¹ Taken as 0 for daily and longer periods
Δ Slope of the vapour pressure curve kPa °C⁻¹ Rises steeply with temperature
γ Psychrometric constant kPa °C⁻¹ ≈ 0.067 at sea level; falls with elevation
es − ea Vapour pressure deficit kPa The drying power of the air
u2 Wind speed at 2 m m s⁻¹ Measurements at 10 m must be reduced first
N Daylight hours h Not the same as sunshine hours n

Typical values

Reference evapotranspiration for grass, as a rough sanity check on the headline.

Climate ET₀, cool season ET₀, warm season Annual
Humid temperate (NW Europe, N Japan) 0.5–1.5 3–5 500–700
Warm humid subtropical (S Japan, SE China) 1.5–2.5 4–6 900–1200
Mediterranean 1–2 5–7 1100–1400
Semi-arid continental 0.5–2 6–9 1200–1700
Hot desert 2–4 8–12 1800–2600

Daily values in mm day⁻¹, annual totals in mm. Ranges after Allen et al. (1998), Chapter 1, and are indicative only.

When it breaks down

The shortcuts fail where the aerodynamic term matters. This is the failure mode the calculator watches. It computes all five estimates and reports their spread as a percentage of the Penman–Monteith value. Below about 25 % the methods are telling the same story; above 40 % they are not, and in that regime the divergence is almost always advective — dry air, strong wind, or both — which the radiation-based methods have no way to see. The verdict line states which regime you are in.

Reference is not actual. ET₀ is defined for a specific hypothetical surface. A pine forest, a paddy field and a bare gravel plain in identical weather have quite different actual evapotranspiration, and only the paddy comes close to ET₀.

Sub-daily periods are outside the formulation. The FAO-56 daily equation assumes G = 0 and uses daily mean quantities. For hourly work the coefficients change.

Near the poles the geometry degenerates. Above roughly 66.5° latitude the sun does not set (or rise) at midsummer, \arccos runs out of domain, and the day length is clamped at 24 hours. Treat high-latitude summer results as approximate.

Wind must be at 2 m. Standard meteorological stations often measure at 10 m, where speeds are roughly 30 % higher. Feeding a 10 m speed in directly will inflate ET₀.

Worked example

Problem. Naha, Okinawa, on 15 July. Latitude 26.2 °N, elevation 28 m, Tmax = 32 °C, Tmin = 27 °C, mean relative humidity 78 %, wind 3.5 m s⁻¹ at 2 m, 7.0 hours of bright sunshine. How large is the difference between methods in a warm, humid, moderately windy maritime climate?

  1. Mean temperature: (32 + 27)/2 = 29.5 °C
  2. Pressure and psychrometric constant: P = 100.97 kPa, γ = 0.0671 kPa/°C
  3. Vapour pressures: es = (4.759 + 3.561)/2 = 4.160 kPa, ea = 0.78 × 4.160 = 3.245 kPa, so the deficit is only 0.915 kPa
  4. Slope: Δ = 0.2374 kPa/°C
  5. Astronomy for day 196: δ = 0.3746 rad, ωs = 1.7655 rad, so N = 13.49 h and Ra = 40.18 MJ/m²/day
  6. Radiation: Rs = (0.25 + 0.50 × 7.0/13.49) × 40.18 = 20.47, Rns = 15.76, Rnl = 2.05, hence Rn = 13.72 MJ/m²/day
  7. Penman–Monteith: ET0 = 5.12 mm/day
  8. The others: Hargreaves 3.99, Priestley–Taylor 5.50, Turc 4.64, Makkink 4.23 mm/day

The spread is 29 % of the reference value, and the verdict flags it. Hargreaves–Samani is the outlier at 22 % low, and the reason is visible in the inputs: the daily temperature range is only 5 °C, because the sea keeps the nights warm. Hargreaves reads a small range as heavy cloud and reduces its estimate accordingly, when in fact the sky was half clear. On small maritime islands the temperature-range proxy misfires, and using it for a recharge budget would inflate recharge by roughly the same 1.1 mm/day it lost from evapotranspiration — some 400 mm a year, which on a limestone island is the difference between a sustainable and an over-drawn lens.

Frequently asked

Which method should I use if I only have monthly climate normals?

Penman–Monteith, still. FAO-56 is explicit that the equation may be applied to monthly mean data, and doing so is far better than switching to a temperature-only method. If humidity is missing, estimate e_a from T_{min} (dewpoint ≈ T_{min} in humid climates) rather than abandoning the equation.

Why does Hargreaves–Samani need latitude if it only uses temperature?

Because it does not only use temperature. It uses R_a, which is astronomy, and scales it by the temperature range. The name is misleading — it is a radiation method wearing a thermometer.

My station reports solar radiation directly. Can I skip sunshine hours?

Not in this version. The calculator derives R_s from sunshine hours via the Ångström relation with the default coefficients (0.25, 0.50). If you have measured R_s, back out the equivalent sunshine hours: n = N\,(R_s/R_a - 0.25)/0.50.

Is α = 1.26 in Priestley–Taylor universal?

No. It was calibrated over extensive saturated surfaces. Values from 1.05 for dry canopies to 1.7 for advective conditions appear in the literature. Treating 1.26 as a constant is exactly the assumption that fails when the spread on this page grows.

Read further

The water balance this calculator feeds is set out in The Water Cycle Explained: Where Does the Rain Go?, the opening article of the Groundwater Science series, which follows a raindrop from precipitation through the unsaturated zone to the water table.

References

  1. Allen, R.G., Pereira, L.S., Raes, D. & Smith, M. (1998) Crop Evapotranspiration — Guidelines for Computing Crop Water Requirements. FAO Irrigation and Drainage Paper 56, Rome. Chapters 1–4.
  2. Penman, H.L. (1948) Natural evaporation from open water, bare soil and grass. Proceedings of the Royal Society of London A 193, 120–145.
  3. Monteith, J.L. (1965) Evaporation and environment. Symposia of the Society for Experimental Biology 19, 205–234.
  4. Hargreaves, G.H. & Samani, Z.A. (1985) Reference crop evapotranspiration from temperature. Applied Engineering in Agriculture 1, 96–99.
  5. Priestley, C.H.B. & Taylor, R.J. (1972) On the assessment of surface heat flux and evaporation using large-scale parameters. Monthly Weather Review 100, 81–92.
  6. Turc, L. (1961) Évaluation des besoins en eau d’irrigation, évapotranspiration potentielle. Annales Agronomiques 12, 13–49.
  7. Makkink, G.F. (1957) Testing the Penman formula by means of lysimeters. Journal of the Institution of Water Engineers 11, 277–288.

HY

Reviewed by Heejun Yang, Ph.D.

Hydrogeologist working on groundwater time-series analysis and water–rock interaction modelling. Equations, unit conversions, and reference values on this page were checked against the primary sources listed above.