Evapotranspiration Calculator: A Worked Guide

An evapotranspiration calculator estimates reference evapotranspiration, known as ET0, from temperature, latitude and date. Enter your latitude, the date, and the high and low temperature for the day, and it returns a daily ET0 figure in millimetres or inches per day. That figure describes water loss from a reference grass surface, not from a named crop.

The verified example on the calculator page makes the idea concrete. At 40 degrees N on 1 July, with a high of 30 degrees C and a low of 18 degrees C, ET0 is about 5.7 mm per day, roughly 40 mm per week. This guide walks through that example step by step.

What evapotranspiration means in plain words

Evapotranspiration is water leaving the land and plants in two ways at once. Evaporation is water leaving soil and plant surfaces directly into the air. Transpiration is water moving through a plant and leaving through its leaves. The calculator combines those two losses into one number, ET0.

ET0 is a reference figure, not a measurement from your own garden. It describes water loss from a reference grass surface. A lawn, a vegetable bed and a flower bed in the same place on the same day share the same ET0, even though the plants lose water at different rates. The difference between crops comes later, when ET0 is multiplied by a crop coefficient for a specific crop.

What the evapotranspiration calculator asks for

The calculator asks for four things only. It estimates ET0 without wind, humidity, sunshine hours or soil inputs, because it uses temperature as a stand in for sunshine and humidity. Clear dry days usually have a wide gap.

Input	What to enter	Why it matters
Latitude	Your latitude in degrees, negative in the southern hemisphere	Latitude sets day length and sun angle, and so sets Ra
Date	The date for the estimate	Date sets the day of year, and so sets Ra
Daily high	The maximum temperature for the day, or a monthly average maximum	The high sets the mean temperature and the temperature range
Daily low	The minimum temperature for the day, or a monthly average minimum	The low sets the mean temperature and the temperature range

Latitude needs care with its sign. In the northern hemisphere, enter a positive number, such as 40 for 40 degrees N. In the southern hemisphere, enter a negative number. Do not enter 30 for 30 degrees S.

Temperature inputs can be a single day or a monthly average. For a single day, enter that day high and low. For planning, enter the monthly average high and monthly average low instead. Use monthly averages for planning, and daily values for scheduling. The output is a daily ET0 figure.

The Hargreaves formula, term by term

The calculator uses the Hargreaves equation. The formula as printed on the calculator page is ET0 equals 0.0023 times Ra times Tmean plus 17.8 times the square root of Tmax minus Tmin. Ra is extraterrestrial radiation. It comes from latitude and day of year, using FAO 56.

Tmean is the mean temperature for the day, the high plus the low, divided by 2. In the worked example, Tmean is 24 degrees C. The formula adds 17.8 to Tmean. Tmax minus Tmin is the daily temperature range. In the worked example, 30 minus 18 gives a range of 12 degrees C. The square root of 12 is 3.464. A wider range gives a larger ET0.

The number 0.0023 is a fixed coefficient. Ra in FAO 56 Table 2.6 is given in MJ per m2 per day. Divide it by 2.45 to convert it to mm per day equivalent. If Ra is taken straight from the table without dividing by 2.45, the ET0 result will be about 2.45 times too high.

The worked example step by step

At 40 degrees N on 1 July, with a high of 30 degrees C and a low of 18 degrees C, ET0 is about 5.7 mm per day, roughly 40 mm per week. The steps below recompute that result.

Step 1 is the mean temperature. 30 plus 18 is 48, divided by 2 is 24 degrees C. Step 2 is the temperature term. 24 plus 17.8 is 41.8. Step 3 is the temperature range. 30 minus 18 is 12 degrees C. The square root of 12 is 3.464.

Step 4 is Ra for the exact date. Ra on exact 1 July at 40 degrees N, from FAO 56 Equation 21, day of year 182, is 41.66 MJ per m2 per day. Divide by 2.45 to get 17.00 mm per day. Label it Ra on 1 July.

Step 5 is the final multiplication. 0.0023 times 17.00 times 41.8 times 3.464 gives 5.66 mm per day, or 5.7 mm per day rounded to one decimal place. Step 6 is the weekly figure. 5.66 times 7 is 39.6 mm per week, roughly 40 mm per week. Proposed only: 5.7 mm per day is 0.22 in per day.

Why the date on Ra matters

The difference between a table Ra and an exact date Ra is small here, but it is real. FAO 56 Table 2.6 gives Ra for the 15th day of each month only. The table value for 15 July at 40 degrees N is 40.8 MJ per m2 per day, or 16.65 mm per day. Put that table Ra into the same steps, with the same temperatures, and ET0 is 5.55 mm per day, not 5.7 mm per day. The weekly figure is 38.8 mm per week, not 39.6 mm per week.

The gap between 5.55 and 5.66 is 0.11 mm per day, from the Ra choice only. Label every Ra value with its date.

Daily ET0 and weekly ET0

A daily ET0 figure answers a question about one day. A weekly ET0 figure answers a question about seven days at the same daily rate. The page gives the weekly figure by multiplying the daily figure by 7. That assumes the same daily ET0 on each day. In real weather, daily ET0 changes from day to day, so a weekly figure from one day is a simple projection, not a measured weekly total.

The table below shows how ET0 changes through the year at one latitude. All four rows use Ra from FAO 56 Table 2.6 for the 15th day of the named month at 40 degrees N. All four temperature pairs are example inputs only, not observed weather. Every ET0 figure is recomputed from the formula.

Month and date	Example high and low	Ra in mm per day	ET0 in mm per day	ET0 in mm per week
15 January	10 and 2 degrees C	6.12	0.95	6.6
15 April	22 and 10 degrees C	14.16	3.81	26.7
15 July	30 and 18 degrees C	16.65	5.55	38.8
15 October	20 and 9 degrees C	9.18	2.26	15.8

ET0 follows Ra, from 0.95 mm per day in January to 5.55 mm per day in July. The July row is the 15 July table calculation, not the exact 1 July calculation, which is why it shows 5.55 mm per day instead of 5.7 mm per day.

What a normal result looks like

The calculator page gives a typical summer range for many temperate regions. ET0 is about 4 to 7 mm per day, shown on the page as 0.15 to 0.28 in per day, with more in hot dry climates. If your result falls inside it on a summer day in a temperate region, it is in the expected range. If it falls well outside it, check your inputs first.

One rounding point is worth noting. 4 mm divided by 25.4 is 0.16 in to two decimal places, while the page shows 0.15 in. 7 mm divided by 25.4 is 0.28 in, which matches the page. The low end is therefore 0.01 in lower than the value rounded to two decimal places. That is a rounding difference only. If a result looks far too high, the most likely cause is the Ra unit error. Using Ra without dividing by 2.45 gives about 13.9 mm per day in the worked example instead of 5.7 mm per day.

What to do with your ET0 result next

ET0 is a starting point, not a watering instruction on its own. The next step on the calculator page is to multiply ET0 by a crop coefficient in the crop water requirement calculator. That step turns reference ET0 into crop ET, known as ETc, for a specific crop. This guide gives no Kc values, because this calculator gives none.

Once you have a crop water figure, you can plan watering with the other calculators on the site. The garden watering schedule calculator works from weekly need and rain to plan sessions. The irrigation scheduling calculator works from daily ET and soil water to set the gap between waterings. The irrigation run time calculator turns a depth of water into minutes per zone. Use ET0 first, then the crop step, then scheduling.

Common mistakes

First, using Ra in the wrong unit. Ra from FAO 56 Table 2.6 is in MJ per m2 per day. Divide by 2.45 first. Second, using a 15th day table Ra as if it were the Ra for another date. Label it with the 15th day date.

Third, entering a southern latitude as a positive number. Latitude is negative in the southern hemisphere. Fourth, treating ET0 as crop water need. ET0 is for a reference grass surface. A named crop needs ET0 multiplied by its crop coefficient.

Fifth, using a monthly average as a daily scheduling figure on an extreme day. Use daily values for scheduling, and monthly averages for planning. Sixth, reading a weekly ET0 figure as a volume in litres. ET0 is a depth, in mm per day or mm per week. A depth becomes a volume only with an area.

FAQs

Q: What does an evapotranspiration calculator do?
A: It estimates reference evapotranspiration, known as ET0, from temperature, latitude and date, and returns a daily ET0 figure in mm per day or inches per day.

Q: What is the Hargreaves formula used by the evapotranspiration calculator?
A: ET0 equals 0.0023 times Ra times Tmean plus 17.8 times the square root of Tmax minus Tmin. Ra must be in mm per day equivalent, so divide a table value in MJ per m2 per day by 2.45 first.

Q: What is the worked example result for the evapotranspiration calculator?
A: At 40 degrees N on 1 July, with a high of 30 degrees C and a low of 18 degrees C, ET0 is about 5.7 mm per day, roughly 40 mm per week. The exact recomputation gives 5.66 mm per day.

Q: Why does the 15 July table value give a different result from the worked example?
A: FAO 56 Table 2.6 gives Ra for the 15th day of each month only. At 40 degrees N, Ra on 15 July is 16.65 mm per day, which gives ET0 of 5.55 mm per day. Ra on exact 1 July is 17.00 mm per day, which gives 5.66 mm per day.

Q: What is a typical ET0 in summer?
A: About 4 to 7 mm per day, shown on the calculator page as 0.15 to 0.28 in per day, in many temperate regions, with more in hot dry climates. Winter ET0 is lower.

Q: What do I do with the ET0 result next?
A: Multiply ET0 by a crop coefficient in the crop water requirement calculator to get crop ET for a specific crop.