Photothermal Quotient & Read Your Yield Potential
Weighs radiation
Grain number — and so cereal yield potential — is set by radiation per degree-day during the grain-set window. Enter the mean radiation and temperature to get the photothermal quotient, the yield-potential band, the grains/m² estimate and whether heat or radiation is capping you.
Grain-set window
Runs in your browser — nothing uploaded. PTQ & grain-number relationship per Fischer (1985).
Next: a workable balance — yield potential of about 8.3 t/ha is realistic if agronomy is sound. If you can shift sowing so the grain-set window falls in cooler, brighter conditions, PTQ and grain number rise.
Photothermal Quotient and the grains/m² relationship after Fischer, R.A. (1985), 'Number of kernels in wheat crops and the influence of solar radiation and temperature', J. Agric. Sci. 105:447–461, plus the PTQ grain-number physiology literature. Grain-number coefficients and the yield-potential conversion are representative; actual grain number also depends on water, nitrogen and frost during the window.
Photothermal quotient — key facts
- PTQ formula
- radiation ÷ (mean temp − base)
- Units
- MJ m⁻² d⁻¹ per °C
- Wheat base temp
- 4.5 °C
- Rice base temp
- 10 °C
- Heat-capped
- PTQ below ≈ 1.0
- High potential
- PTQ above ≈ 1.5
- Sets
- grains/m², then yield
- Source
- Fischer (1985), J. Agric. Sci.
- Privacy
- Runs in your browser; nothing uploaded
Crop photothermal-quotient reference
Base temperatures, grain-set windows and the grain-number response coefficients this tool uses, with each cereal's typical good PTQ range. Source: Fischer (1985) and the PTQ grain-number physiology literature.
| Cereal | Base temp (°C) | Grain-set window | Grains/m² = a + b × PTQ | Grain wt (mg) | Typical good PTQ |
|---|---|---|---|---|---|
| Wheat | 4.5 | ≈ 30 days before anthesis (Fischer critical period) | 2,000 + 13,800 × PTQ | 38 | 0.8–1.7 |
| Barley | 4.5 | ≈ 20–30 days bracketing awn emergence / anthesis | 3,000 + 12,000 × PTQ | 42 | 0.8–1.8 |
| Rice | 10 | ≈ panicle initiation to heading (spikelet-number window) | 5,000 + 9,000 × PTQ | 24 | 0.6–1.4 |
| PTQ band | Range | What it means |
|---|---|---|
| Low — heat-capped | below 1.0 | Warm conditions burn through development fast with little radiation per degree-day; grain number and yield potential are limited. |
| Moderate | 1.0 – 1.5 | A workable balance of radiation and temperature; yield potential is solid but not maximal. |
| High potential | above 1.5 | Plenty of radiation per degree-day during grain set; conditions support a high grain number and yield potential. |
Radiation per degree-day is what sets the grain
Cereal yield is dominated by grain number, and grain number is set in a short window around anthesis. The photothermal quotient explains that window in one number: how much radiation the crop captures for every degree-day of development. When skies are bright and temperatures are cool, each stage of floret development is bathed in light, more carbohydrate is built, and more florets survive to set grain. When the window is hot, development races, fewer days of radiation are captured per stage, and grain number falls — even if the total sunlight looks generous.
That is why summing heat alone, as growing-degree-day tools do, misses the picture. Two seasons with identical degree-day totals can carry very different yield potentials depending on how much radiation arrived per degree. This tool computes the quotient live, places it on the grains/m² response curve from Fischer's work, and tells you whether heat or radiation is the binding constraint — so the lever you reach for (earlier sowing, an earlier variety, canopy cooling) is the one that actually moves your potential.
Pair it with the Crop Heat Unit Phenology, Heat Stress Degree Days and Growing Degree Days tools for a complete picture of how temperature drives both the timing and the potential of your cereal crop.
How to use it — five steps
- 1
Pick the cereal
Choose wheat, barley or rice so the right base temperature and grain-set window are applied.
- 2
Enter the radiation
Use the mean daily solar radiation (MJ/m²/day) averaged over the grain-set window — not the whole season.
- 3
Enter the temperature
Enter the mean daily air temperature over the same window; the tool subtracts the base temperature for you.
- 4
Read the PTQ
Read the quotient, its yield-potential band, and the grains/m² it implies, marked on the response curve.
- 5
Act on the limiter
If heat is the limiter, shift the window earlier; if radiation is, push agronomy to fill the high potential.
Frequently Asked Questions
What is the photothermal quotient (PTQ)?+
The photothermal quotient is the ratio of growth energy to development speed during a crop's grain-set window: PTQ = mean daily solar radiation ÷ (mean temperature − base temperature). It captures how much radiation the crop captures per unit of thermal development. A high PTQ means plenty of light per degree-day, which builds more carbohydrate per stage of development and lets more florets survive to set grain. Fischer (1985) showed grains per m² in wheat rises strongly with PTQ over the roughly 30 days before anthesis.
How is PTQ calculated?+
PTQ = radiation ÷ (mean temp − base temp). For example, wheat with a 4.5°C base temperature, 18 MJ/m²/day of radiation and a 17°C mean over the window gives 18 ÷ (17 − 4.5) = 18 ÷ 12.5 = 1.44 — a moderate-to-high value. The denominator is the thermal driving rate of development; the numerator is the energy available for growth. The tool does this live as you type and marks your value on the grains/m² response curve.
What is a good PTQ for wheat?+
For wheat, a PTQ below about 1.0 is heat-capped (warm conditions burn through development fast with little radiation per degree-day), roughly 1.0–1.5 is a moderate, solid potential, and above 1.5 is high — plenty of radiation per degree-day supporting a high grain number. Typical good environments sit around 0.8–1.7. The figure to chase is a high PTQ during the critical window, not just warm, sunny weather overall.
Why does temperature lower yield potential through PTQ?+
Warmer temperatures speed development, so the crop spends fewer days in the critical pre-anthesis window. Fewer days means less total radiation captured per stage of floret development, so fewer florets survive to set grain. Because temperature is in the denominator of PTQ, higher heat directly pulls the quotient down — which is why a hot grain-set period caps yield even when total sunlight looks ample.
What is the base temperature in the formula?+
The base temperature is the threshold below which development effectively stops, so only degrees above it drive the crop forward. This tool uses 4.5°C for wheat and barley and 10°C for rice, in line with the crop-physiology literature. The denominator of PTQ is the mean temperature minus this base, which is why a cool-but-not-cold window with bright skies produces the highest quotients.
Which window does PTQ apply to?+
PTQ matters most over the crop's grain-number-setting window. For wheat that is roughly the 30 days before anthesis (Fischer's critical period); for barley it brackets awn emergence and anthesis; for rice it spans panicle initiation to heading, when spikelet number is set. Use the average radiation and average temperature over that window — not the whole season — because that is when grain number is decided.
Is my yield potential limited by heat or by radiation?+
When PTQ falls below about 1.0 the tool flags heat as the dominant limiter: development is racing and there is too little radiation per degree-day. When PTQ is at or above 1.0, radiation becomes the practical ceiling on how much more grain you could set. The widget shows both ingredients side by side so you can see which lever — cooler timing or brighter conditions — would move your potential most.
How does PTQ translate into grains per m²?+
Grain number rises roughly linearly with PTQ over the relevant range: this tool uses grains/m² = intercept + slope × PTQ, with crop-specific coefficients drawn from the Fischer-type relationship (for wheat, around 2,000 + 13,800 × PTQ). So a wheat PTQ of 1.44 implies roughly 21,900 grains/m². Yield potential then follows grain number multiplied by a representative single-grain weight.
How is the yield-potential figure in t/ha derived?+
Yield potential = grains/m² × single-grain weight. The conversion is grains/m² × grain weight (mg) × 1e-5 to land in tonnes per hectare. For wheat at 38 mg per grain and ~21,900 grains/m², that is about 8.3 t/ha of potential — the ceiling the canopy could fill if water, nitrogen and frost do not intervene. It is a potential, not a guarantee.
Can I raise a low PTQ?+
Yes — the main lever is timing. Sowing earlier, or choosing an earlier-maturing variety, can move the grain-set window into cooler, brighter weather, lifting the quotient and the grain number it supports. Irrigation that cools the canopy helps in hot, dry environments. You cannot add radiation, but you can place the critical window where the radiation-to-temperature balance is most favourable.
Does PTQ work for barley and rice too?+
Yes. The same radiation-to-thermal-time logic applies; only the base temperature, the window definition and the grain-number coefficients change. Barley uses a 4.5°C base around awn emergence; rice uses a 10°C base from panicle initiation to heading, where the spikelet number is set. Pick the crop and the tool applies the right coefficients and bands.
How is PTQ different from growing degree days (GDD)?+
GDD sums heat only — it tells you how fast the crop is developing, not how much yield potential it has. PTQ adds the radiation term that GDD ignores, so it captures the radiation-per-degree-day that actually decides grain number. Two seasons with identical GDD can have very different PTQ and therefore very different yield potentials, which is exactly the gap this tool fills.
Will a high PTQ guarantee high yield?+
No — PTQ sets the grain-number potential, but realising it still needs non-limiting water and nitrogen through grain set and freedom from frost or disease during the window. Treat a high PTQ as permission to push agronomy: it tells you the ceiling is high, so protecting the crop pays off. A high PTQ wasted on a stressed crop still yields poorly.