Fire Growth Rate Calculator (t² Model)
Calculate Heat Release Rate (HRR) and Total Energy based on standard fire growth curves.
Time since ignition (t)
Slow (α = 0.0029 kW/s²)
Medium (α = 0.0117 kW/s²)
Fast (α = 0.0469 kW/s²)
Ultra-Fast (α = 0.1876 kW/s²)
Custom Alpha Value
Calculation Results
Growth Coefficient (α):
–
Heat Release Rate (HRR):
–
Total Energy Released:
–
Interpretation: At 0 seconds, the fire has reached a peak intensity of 0 kW.
Understanding Fire Growth Rate
In fire safety engineering and performance-based design, predicting how quickly a fire will grow is crucial for designing suppression systems, smoke control strategies, and egress routes. The most common method for modeling the pre-flashover phase of a fire is the t-squared (t²) fire growth model.
The t-Squared Formula
The model assumes that the heat release rate (HRR) of a fire increases with the square of time. The fundamental formula is:
Q = α × t²
Where:
- Q is the Heat Release Rate (HRR) in kilowatts (kW).
- α (Alpha) is the fire growth coefficient in kW/s².
- t is the time since effective ignition in seconds (s).
Standard Growth Classifications
The National Fire Protection Association (NFPA) and other standards bodies classify fires into four main growth rates based on the value of Alpha (α). These classifications help engineers estimate the threat level of different fuel loads.
| Growth Mode | Alpha (α) (kW/s²) | Time to reach 1055 kW (1000 BTU/s) | Typical Fuel Examples |
|---|---|---|---|
| Slow | 0.00293 | ~600 sec (10 min) | Densely packed paper products, floor coverings. |
| Medium | 0.01172 | ~300 sec (5 min) | Traditional mattresses, upholstered furniture (cotton). |
| Fast | 0.0469 | ~150 sec (2.5 min) | Polyurethane mattresses, light wood pallets, plastic bins. |
| Ultra-Fast | 0.1876 | ~75 sec (1.25 min) | High-rack storage, flammable liquids, upholstered furniture (modern synthetics). |
Total Heat Released
While the HRR tells you the intensity of the fire at a specific moment, the Total Heat Released (THR) tells you the total energy generated up to that point. This is calculated by integrating the HRR over time:
Energy (E) = (α × t³) / 3
This result is typically expressed in kilojoules (kJ) or Megajoules (MJ). This metric is vital for determining the total thermal load on structural elements.
Limitations of the Calculator
This calculator models the "growth phase" of a fire. It does not account for:
- Decay phase: When fuel begins to run out.
- Sprinkler activation: Which would cap or reduce the HRR.
- Oxygen starvation: In a sealed room, the fire may become ventilation-controlled rather than fuel-controlled.