Crop Coefficient Calculators

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The crop coefficient (Kc) is a dimensionless factor that relates actual crop evapotranspiration (ETc) to reference evapotranspiration (ET₀) calculated from weather data for a well-watered reference grass. ETc = Kc × ET₀. Kc accounts for differences in crop physiology, canopy cover, and soil surface characteristics that make actual crop water use different from the reference surface. Kc values change through the crop growth season — typically low at planting (sparse cover), increasing to a maximum at full canopy, and declining at senescence. The FAO Irrigation and Drainage Paper No. 56 (FAO-56) is the global standard for Kc values and the Penman-Monteith ET₀ method.

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Crop Coefficient Equation

ETc = Kc × ET₀

ETc = actual crop evapotranspiration (mm/day); Kc = crop coefficient (dimensionless); ET₀ = reference evapotranspiration for well-watered grass (mm/day, from Penman-Monteith equation).

Example: ET₀ = 6 mm/day, Kc = 1.15 (corn at mid-season): ETc = 1.15 × 6 = 6.9 mm/day of water demand.

Kc Growth Stage Values (FAO-56 examples)

  • Corn (maize): Kc_ini = 0.30; Kc_mid = 1.20; Kc_end = 0.60
  • Wheat: Kc_ini = 0.30; Kc_mid = 1.15; Kc_end = 0.40
  • Tomato: Kc_ini = 0.60; Kc_mid = 1.15; Kc_end = 0.80
  • Alfalfa: Kc_mid = 1.20
  • Grass (turf): Kc ≈ 0.85–1.05

FAO-56 Dual Crop Coefficient

The dual Kc approach separates ETc into transpiration (Kcb × ET₀) and soil evaporation (Ke × ET₀): ETc = (Kcb + Ke) × ET₀. Kcb (basal Kc) describes crop transpiration when soil surface is dry; Ke accounts for evaporation from the wet soil surface after rain or irrigation. The dual approach is more accurate for drip-irrigated crops where only a fraction of the soil surface is wetted.

Irrigation Scheduling Application

Net irrigation requirement (NIR) = ETc − effective rainfall − soil moisture available. Irrigation is applied when soil moisture depletion reaches a management allowed depletion (MAD) fraction (typically 40–50% of plant-available water).

Glossary

Crop Coefficient (Kc)
A dimensionless factor converting reference ET₀ to actual crop evapotranspiration: ETc = Kc × ET₀; varies by crop type and growth stage; standardized in FAO-56.
Reference Evapotranspiration (ET₀)
Evapotranspiration from a hypothetical well-watered reference grass; calculated from weather data using the Penman-Monteith equation; represents atmospheric evaporative demand.
Basal Crop Coefficient (Kcb)
The transpiration component of the dual Kc approach: evapotranspiration from the crop canopy when the soil surface is dry; used with Ke (soil evaporation) in FAO-56 dual Kc method.

Frequently Asked Questions

The crop coefficient (Kc) converts reference ET₀ (evapotranspiration of well-watered grass) to actual crop water use: ETc = Kc × ET₀. Kc varies by crop type and growth stage: low at emergence (sparse canopy), maximum at full canopy (Kc_mid), and declining at senescence. FAO-56 tabulates Kc values for hundreds of crops. Example: if ET₀ = 5 mm/day and wheat is at mid-season (Kc = 1.15): wheat needs ETc = 5.75 mm/day. This is the basis for irrigation scheduling and water budget calculations.

Reference evapotranspiration (ET₀) is the evapotranspiration rate from a reference surface — well-watered short grass with specific height, albedo, and aerodynamic resistance properties. It is calculated from weather data using the FAO Penman-Monteith equation, which accounts for net radiation, air temperature, humidity, and wind speed. ET₀ represents atmospheric evaporative demand, removing crop-specific factors. Multiplying ET₀ by crop-specific Kc gives actual crop water use. ET₀ typically ranges from 1–2 mm/day in winter to 8–12 mm/day in hot, dry summers.

FAO-56 defines four crop growth stages: initial (sparse cover, Kc_ini often 0.3–0.4); crop development (Kc increases as canopy develops); mid-season (Kc_mid = maximum, 1.0–1.25 for most crops at full cover); and late season (Kc declines as leaves senesce and crop matures, Kc_end often 0.3–0.9). The Kc curve is plotted against days after planting or cumulative growing degree days. Irrigators use these curves to adjust irrigation frequency and volume throughout the season.

The single Kc averages transpiration and soil evaporation into one coefficient — simpler and sufficient for surface irrigation where the whole soil is wetted. The dual Kc separates ETc = (Kcb + Ke) × ET₀, where Kcb is basal transpiration and Ke is soil evaporation. Dual Kc is more accurate for drip and micro-irrigation (where only a fraction of soil is wetted), mulched crops, or when tracking soil water in the top layer separately. Most irrigation scheduling software and research use the dual Kc approach from FAO-56.