Dual Crop Coefficient Calculator
The dual crop coefficient approach of FAO-56 (Allen et al. 1998) splits the crop coefficient into two parts, Kc = Kcb + Ke. This calculator covers the soil evaporation part: it computes the evaporation reduction coefficient Kr, the soil evaporation coefficient Ke, the resulting Kc, the crop evapotranspiration ETc and the depletion De of the top soil layer, either for one day or for a run of drying days.
It is written for agronomists and irrigation consultants who need to check a daily water balance of the evaporating layer. Every value is computed in double precision without rounding inside the chain; results are shown to 4 decimals, and in drying-days mode each day starts from the previous day's De at full precision. The formulas are printed with the values you typed so each step can be checked by hand.
Calculator
Results
Formulas
Kc max = max(1.2 + (0.04 × (u2 − 2) − 0.004 × (RHmin − 45)) × (h/3)^0.3, Kcb + 0.05)
fc = ((Kcb − Kc min)/(Kc max − Kc min))^(1 + 0.5 × h)
few = min(1 − fc, fw); for drip, fw × (1 − 2/3 × fc) replaces fw
Kr = 1 if De ≤ REW, otherwise Kr = (TEW − De)/(TEW − REW)
Ke = min(Kr × (Kc max − Kcb), few × Kc max)
E = Ke × ETo
Kc = Kcb + Ke; ETc = Kc × ETo
De end = min(max(De + E/few, 0), TEW)
Drying days
| Day | De start (mm) | Kr (dimensionless) | Ke (dimensionless) | E (mm/day) | De end (mm) | ETc (mm/day) |
|---|
How to use the calculator
- Enter Kcb (dimensionless, 0 or more) and ETo in mm/day (above 0).
- Type Kc max, or leave it empty and enter u2 in m/s, RHmin in % and the plant height h in m so that Kc max = max(1.2 + (0.04 × (u2 − 2) − 0.004 × (RHmin − 45)) × (h/3)^0.3, Kcb + 0.05) is computed.
- Type fc from 0 to 0.99, or leave it empty and enter Kc min (and h) so that fc = ((Kcb − Kc min)/(Kc max − Kc min))^(1 + 0.5 × h) is computed.
- Enter fw from 0.01 to 1 and choose the wetting type: sprinkler or furrow, or drip.
- Enter TEW and REW in mm (REW above 0 and below TEW) and De at the start of the day in mm, from 0 to TEW.
- Choose one day, or drying days and the number of days from 2 to 30.
- Read Kc max, fc, few, Kr, Ke, E, Kc, ETc and De end, check the formulas with your values, and in drying-days mode read the table with one row per day.
Frequently asked questions
When does Kr fall below 1?
Kr stays at 1 while the depletion De at the start of the day is at most REW. Once De exceeds REW, Kr = (TEW − De)/(TEW − REW), so it falls in a straight line and reaches 0 when De equals TEW. With TEW 20 mm and REW 9 mm, De 9 mm gives Kr 1 and De 20 mm gives Kr 0.
Why is few smaller for drip than for sprinkler or furrow wetting?
few is the smaller of 1 − fc and fw. For drip, fw is first multiplied by (1 − 2/3 × fc). With Kcb 0.9, ETo 7 mm/day, u2 3 m/s, RHmin 20 %, h 1 m, Kc min 0.15 and fw 0.3, furrow wetting gives few 0.3000 and Ke 0.3902, while drip gives few 0.1948 and Ke 0.2533.
What happens when Kc max or fc is left empty?
An empty Kc max is computed as max(1.2 + (0.04 × (u2 − 2) − 0.004 × (RHmin − 45)) × (h/3)^0.3, Kcb + 0.05); this equation is meant for usual field conditions. An empty fc is computed as ((Kcb − Kc min)/(Kc max − Kc min))^(1 + 0.5 × h), which needs Kcb − Kc min of at least 0.01 and a result below 0.99.
How does the drying-days mode work?
ETo is held constant and no water is added. De at the end of each day becomes De at the start of the next day at full precision, never a rounded value. De is capped at TEW, so once it reaches TEW, Kr and Ke are 0 and ETc equals Kcb × ETo.
This calculator gives an estimate only and is not a substitute for a qualified agronomist. Source: FAO Irrigation and Drainage Paper 56, chapter 7 (1998), and the Rev.1 edition of 2025.