What is a crop coefficient, and what is Kc on a given date?
A crop coefficient (Kc) compares a crop's water use with that of a reference grass surface under the same weather. FAO Irrigation and Drainage Paper 56 (FAO-56) gives each crop a curve with four parts: a flat initial stage while the crop is small, a straight-line rise through development, a flat mid-season value at full cover, and a straight-line change through the late season to harvest. Kc on any date is read from that curve.
| Crop | Kc ini | Kc mid | Kc end | Stage lengths (days) | Height |
|---|---|---|---|---|---|
| Maize (grain) | 0.30 | 1.20 | 0.60 | 20 / 35 / 40 / 30 | 2.0 m |
| Tomato | 0.60 | 1.15 | 0.80 | 30 / 40 / 45 / 30 | 0.6 m |
| Green beans | 0.50 | 1.05 | 0.90 | 20 / 30 / 30 / 10 | 0.4 m |
| Onion, dry | 0.70 | 1.05 | 0.75 | 15 / 25 / 70 / 40 | 0.4 m |
| Cabbage | 0.70 | 1.05 | 0.95 | 40 / 60 / 50 / 15 | 0.4 m |
Real stage lengths depend on variety, planting date and temperature, so use local figures when you have them. The crop coefficient table lists more crops, and the agriculture calculators cover the steps that follow.
How this crop coefficient calculator works
The calculator counts the day of the season, finds the stage that day falls in, and interpolates between the stage Kc values. If you turn on the climate adjustment, it first adjusts Kc mid and Kc end.
1. Day of the season
Day of season
Day = (date to check − planting date) + 1
Planting day is day 1. Season length = initial + development + mid-season + late-season days.
2. Interpolate along the stage curve
Kc by stage (FAO-56 straight-line interpolation)
Initial (day ≤ Lini): Kc = Kc ini
Development: Kc = Kc ini + (Day − Lini) ÷ Ldev × (Kc mid − Kc ini)
Mid-season: Kc = Kc mid
Late season: Kc = Kc mid + (Day − Lini − Ldev − Lmid) ÷ Llate × (Kc end − Kc mid)
L is the length of each stage in days. Dates after the last day of the late season have no Kc, so the calculator asks for an earlier date.
3. Climate adjustment for Kc mid and Kc end
FAO-56 adjustment (equations 62 and 65)
Kc = Kc(table) + [0.04 × (u2 − 2) − 0.004 × (RHmin − 45)] × (h ÷ 3)0.3
u2 is wind speed at 2 m in m/s, RHmin is minimum relative humidity in %, and h is crop height in m. It is applied to Kc mid and to Kc end only when the table value is 0.45 or more. FAO-56 gives it for u2 of 1–6 m/s, RHmin of 20–80% and h of 0.1–10 m, and the calculator warns outside those ranges.
Kc initial is left as entered. FAO-56 sets it from how often the soil surface is wetted, which needs a separate calculation.
Unit conversions and rounding
Wind and height are converted to metric for the math: 1 mph = 0.44704 m/s and 1 ft = 0.3048 m. Kc is calculated without rounding and shown to 2 decimals. Your own entries are shown as typed.
When this calculator isn't the right tool
- Water use in mm or gallons. Kc is only a ratio. The crop evapotranspiration calculator multiplies it by ETo, and the crop water requirement calculator takes it further.
- Reference ET itself. Use the reference ET calculator.
- Lawns and ornamental landscapes. Use the landscape coefficient calculator.
- Separate soil evaporation and transpiration. That needs the FAO-56 dual crop coefficient, which this page doesn't calculate.
- Sparse crops such as young orchards or vineyards, where ground cover and canopy size change Kc. Table values assume the crop covers the ground.
Crop coefficient calculation examples
US units, standard climate. Grain maize planted May 1, 2026, checked on June 10, 2026, using the maize preset (Kc 0.30 / 1.20 / 0.60, stages 20 / 35 / 40 / 30 days).
- Day of season: May 1 to June 10 is 40 days later, so the day is 41 of 125.
- Stage: Day 41 is after the initial stage (day 20) and before day 55, so it is in development.
- Interpolate: Kc = 0.30 + (41 − 20) ÷ 35 × (1.20 − 0.30) = 0.30 + 0.60 × 0.90 = 0.84.
- Also shown: development runs through June 24, 2026, and the season ends September 2, 2026.
The same method in metric, with the climate adjustment
Tomato planted April 15, 2026, checked on June 20, 2026 (Kc 0.60 / 1.15 / 0.80, stages 30 / 40 / 45 / 30 days, height 0.6 m). Minimum humidity is 30% and wind is 3 m/s.
- Day of season: April 15 to June 20 is 66 days later, so the day is 67 of 145.
- Adjustment: [0.04 × (3 − 2) − 0.004 × (30 − 45)] × (0.6 ÷ 3)0.3 = 0.10 × 0.6170 = 0.0617.
- Kc mid: 1.15 + 0.0617 = 1.2117, shown as 1.21. Kc end: 0.80 + 0.0617 = 0.8617, shown as 0.86.
- Interpolate (development, day 30 to day 70): Kc = 0.60 + (67 − 30) ÷ 40 × (1.2117 − 0.60) = 0.60 + 0.925 × 0.6117 = 1.17.
Without the adjustment the same date gives 1.11, so climate matters most in windy, dry seasons and for tall crops.
How do I use the Kc I get?
Crop water use is Kc multiplied by reference evapotranspiration (ETo) for the same period, so a Kc of 0.84 with an ETo of 5 mm per day is 4.2 mm per day. Take ETo from a local weather network or calculate it, and use the same time step for both numbers.
Getting good stage dates
FAO-56 describes the initial stage as ending at roughly 10% ground cover and the development stage as ending at effective full cover. Local extension services often publish stage lengths for local planting dates, and those beat a table example from another region. If you plant in stages, run each planting date separately.
Common mistakes
- Counting from emergence when the stage lengths start at planting, or the reverse.
- Using unadjusted table values for a season that is much windier or drier than the table climate.
- Entering wind in mph while the field is set to m/s. Check the unit label beside the field.
- Reading Kc after harvest. The curve ends on the last day of the late season.
What changes the crop coefficient?
| Factor | Effect on Kc | What to adjust |
|---|---|---|
| Wind speed | Higher wind raises Kc mid and Kc end by 0.04 per m/s above 2 m/s, before the height factor. | Turn on the climate adjustment and enter average wind at 2 m. |
| Minimum humidity | Lower humidity raises Kc mid and Kc end by 0.004 per percentage point below 45%, before the height factor. | Enter average daily minimum humidity for the mid- and late-season stages. |
| Crop height | Taller crops get a larger adjustment through the (h ÷ 3)0.3 factor. | Enter the mid-season height, not the final or seedling height. |
| Planting date and temperature | Shift stage lengths, so the same calendar date falls in a different stage. | Use stage lengths for your planting date. |
| Soil wetting frequency | Changes the initial Kc, which is not adjusted here. | Enter your own Kc initial if the surface is wetted much more or less often than the table assumes. |
| Ground cover | Sparse plantings use less than full-cover table values. | Use a method built for orchards or vineyards. |
Frequently asked questions
What is a crop coefficient (Kc)?
A crop coefficient is the ratio of a crop's water use to the water use of a reference grass surface under the same weather. FAO-56 describes each crop with a curve of Kc values through the season. Multiply Kc by reference evapotranspiration (ETo) to estimate the crop's water use on a given day.
How do you calculate Kc for a given date?
Count the days from planting to the date, with planting day as day 1. Kc equals the initial value until the initial stage ends, rises in a straight line through the development stage, holds at the mid-season value, then changes in a straight line to the end value over the late season. This calculator does that interpolation for you.
When should I adjust Kc for climate?
FAO-56 publishes its mid-season and end-season Kc values for a sub-humid climate with minimum relative humidity near 45% and wind near 2 m/s. In a windier or drier climate those values are too low, and in a calmer or more humid one they are too high. FAO-56 adjusts them with wind speed, humidity and crop height, and only when the table value is 0.45 or more.
Why is the initial Kc not adjusted for climate here?
FAO-56 sets the initial Kc mainly from how often the soil surface is wetted and how much water the weather can evaporate from it. This calculator uses the initial value you enter or the table value. If your soil surface is wet much more or less often than the table assumes, enter your own value.
What can I enter if my crop is not in the list?
Choose the enter-your-own option and type the Kc and stage lengths for your crop. FAO-56 publishes them for many more crops, and local extension services often publish stage lengths for local planting dates.
See the crop coefficient table for more crops.
How do I turn Kc into water use?
Multiply Kc by the reference evapotranspiration for the same period. For example, a Kc of 0.84 and an ETo of 5 mm per day gives 4.2 mm per day of crop water use. Irrigation also has to cover losses and any rain, which the calculators for those steps handle.
Start with the crop evapotranspiration calculator.
Who built and checked this calculator
Licensed Professional Engineer and Irrigation Association Certified Irrigation Designer with more than 20 years in irrigation design, system auditing and landscape water management. Full profile
How this page was checked
- Interpolation and climate-adjustment formulas checked against FAO-56 by hand.
- Both worked examples traced through the calculator code, in US and metric units.
- Preset Kc values and heights compared with FAO-56 Table 12.
Sources
- Allen, R.G., Pereira, L.S., Raes, D. and Smith, M. (1998). Crop evapotranspiration: Guidelines for computing crop water requirements. FAO Irrigation and Drainage Paper 56. Chapter 6 (single crop coefficient, Tables 11 and 12, equations 62, 65 and 66) [VERIFY URL].
- USDA Natural Resources Conservation Service. National Engineering Handbook, Part 623 Irrigation, Chapter 2, Irrigation Water Requirements [VERIFY URL].
- ASCE Environmental and Water Resources Institute (2005). The ASCE Standardized Reference Evapotranspiration Equation [VERIFY URL].