Growth potential equation

Growth potential equations and formulas for cool- and warm-season turfgrass
FormatCool-season grass (C3)Warm-season grass (C4)
Equation Cool-season grass (C3) GP = e−½((T − 68)/10)² Warm-season grass (C4) GP = e−½((min(T, 88) − 88)/12)²
Excel Cool-season grass (C3) Warm-season grass (C4)
R Cool-season grass (C3) Warm-season grass (C4)
Python Cool-season grass (C3) Warm-season grass (C4)

GP ranges from 0 to 1 (or 0 to 100%). T (shown as temp_f in the formulas) is average air temperature in °F. Warm-season GP stays at 1 above 88°F.

How to use growth potential

  1. Choose the grass and temperature. Decide whether you are calculating GP for cool-season (C3) or warm-season (C4) grass. Find the average air temperature for the day or month you want to assess.
  2. Use the matching constants. With Fahrenheit temperatures, the optimum and scaling constant are 68°F and 10 for C3, or 88°F and 12 for C4. With Celsius temperatures, use 20°C and 50/9 for C3, or 31°C and 7 for C4.
  3. Calculate GP. Subtract the optimum temperature from the average temperature, divide by the scaling constant, square that result, multiply by −0.5, and raise e to that power. For C4 grass, use the optimum temperature when average temperature is above the optimum temperature; GP remains at 1 when C4 grass is grown in high temperatures.
  4. Read the result. GP runs from 0 to 1 (or express on a scale of 0 to 100%). A value of 0.5 represents half of the maximum temperature-based growth potential; a value near 1 indicates temperatures near the model's optimum.
GP equals e to the power of negative 0.5 times the square of the fraction T minus T nought over var

where,

GP
Growth potential, on a scale from 0 to 1.
e
The mathematical constant, approximately 2.71828.
T
Average air temperature, in °F or °C. Use the matching unit for T, Topt, and var.
Topt
Optimum temperature: 68°F for C3 or 88°F for C4; 20°C for C3 or 31°C for C4.
var
Temperature scaling constant, which controls how quickly GP falls as temperature moves away from the optimum: 10 for C3 or 12 for C4 with °F; 50/9 for C3 or 7 for C4 with °C.

C4 growth does not have the same photorespiration-driven decline above its optimum as C3 growth, so C4 GP remains at 1 above the optimum temperature. Temperature-based GP is a planning estimate: actual growth also depends on factors such as water, nitrogen, light, and the grass variety.

About growth potential

We developed the growth potential model to explain the many ways that temperature impacts turf growth. The model considers turf growth to be good when the growth potential (GP) is between 50% and 100% (the best possible growth occurs at a GP of 100%). However, when weather conditions are either too hot or too cold for optimal turf growth, the GP falls below 50%, and turf becomes progressively more stressed. When the GP falls to 10% or lower, growth is extremely limited.

Growth potential gallery

Season length by summed growth potential
Optimum overseeding and grow-in window
Estimated nutrient use by GP
Wichita spring green-up

Growth potential calculator

Growth potential

100% 80% 60% 40% 20% 0% Growth potential Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 100% 80% 60% 40% 20% 0% Jan Mar May Jul Sep Nov

Monthly values

Monthly values, January through December
JanFebMarAprMayJunJulAugSepOctNovDec
Avg. temp °C
Cool GP %
Warm GP %

Temperature averages from 2021 to 2025 (ERA5-Land)

Documents

Case studies

Sudbrook Moor Golf Club Grantham, United Kingdom

James Sergeant used GP to set clipping volume targets, then measured clippings to guide nitrogen applications. Annual nitrogen use fell from about 15 g/m² under the previous years' program to nearly 5 g/m². The bent-Poa greens continued to perform well.

PACE Turf report
Pender Harbour Golf Club British Columbia, Canada

After catastrophic winter kill in 2017, Jason Haines used GP to show members why greens recovery was slow: spring temperatures were poor for growth compared with previous years. During the summer, growth potential showed short dips, telling him when to ease off stressful maintenance and giving him the data to explain why. Jason suggests posting GP alongside green speed to explain conditions.

Jason Haines blog
Alabama golf course Alabama, United States

An Alabama golf course used GP to help decide which month to aerify creeping bentgrass greens and optimize recovery time. The golf course also looked at GP ahead of an April tournament, because they considered fertilizing a bermudagrass rough to make it more challenging. GP graphs showed growth would be below 20% at that time of year and that made enough new rough growth unlikely.

USGA Green Section Record
Comparing season length

Summing daily GP over a year gives a proxy for growing-season length, which makes it easy to compare locations on temperature. For example, one year works out to about 138 days for Minneapolis and 165 for New York City. You can scale inputs by that ratio: 8 mm of sand topdressing in New York would be about 6.7 mm in Minneapolis. The same approach works for nitrogen rates and mowing frequency.

Asian Turfgrass Center article

FAQs

How does growth potential relate to nitrogen use?

GP shows how favorable the temperature is for growth. We use GP value with a standard daily nitrogen amount to estimate nitrogen demand at your location. This gives you a starting point for planning. Compare the estimate with actual growth before adjusting nitrogen applications. See Standard nitrogen for how our weather report uses GP.

How does growth potential relate to clipping volume?

GP estimates growth conditions from temperature, and clipping volume measures how much grass you actually harvested. High GP does not guarantee high clipping volume because nitrogen supply, water, growth regulators, and other conditions also affect growth. Comparing measured clippings with the amount expected from recent GP can help you decide whether to adjust nitrogen. We call this comparison Turf GvX.

Is there a separate growth potential model for kikuyugrass?

Yes. Kikuyugrass GP peaks at an average air temperature of 24°C. Its equation is:

Here T is average air temperature in °C. Use var = 6.1 when T is 24°C or lower, and var = 3.9 when it is above 24°C.

R
gpk <- function(temp_c) {
  var <- ifelse(temp_c <= 24, 6.1, 3.9)
  exp(-0.5 * ((temp_c - 24) / var)^2)
}

Further reading