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t² Fire Growth
Heat release rate at a given time, or the time to reach a given rate, using the growth curve Q̇ = α·t².
Direction of the calculation
Growth rate
The growth rate is defined by t_g — the time to reach 1,055 kW. The growth coefficient α follows from it and is not chosen directly.
α = 1,055 / 150² = 0.04689 kW/s²
The time in question
If a peak or a ventilation limit is known, enter it to get a warning when the curve passes it. The tool assumes no peak of its own.
Validity range
Validity range
The conditions that determine whether the correlation applies. Crossing them changes the state of the result.
- The correlation describes the growth phase only. It has no peak, no decay, and it is not valid after flashover. With no external limit the curve rises without bound.
- A negative time, a non-positive t_g or a non-positive target Q̇ are not points on the curve. In those cases no number is shown.
Model limits
What the model does not describe, even within its validity range. These always hold.
- The tool does not decide where flashover occurs — that depends on the compartment, the fire load and the ventilation. If you know a peak, enter it and you will be warned when the curve passes it.
The equation
Q̇ = α · t², α = 1055 / t_g²
0.04689 · 150²
- Q̇ [kW]
- Heat release rate
- α [kW/s²]
- Growth coefficient — derived from t_g
- t [s]
- Time from ignition
- t_g [s]
- Growth time — to 1,055 kW
The t² growth curve — SFPE Handbook 5th ed.
Result
ResultThe calculation completed within the model's range of validity.
- Heat release rate Q̇
- 1,055 kW
- Growth coefficient α
- 0.04689 kW/s² (t_g = 150 s)
- The reference heat release rate1000 BTU/s × 1055.05585262 J/BTU ÷ 10001,055 kW
The convention was framed as 1,000 BTU/s — a round number in imperial units. 1055 is not a physical constant but the result of that conversion, so it is derived here from the definition of the BTU rather than written down as a number.
- Growth coefficient — α = Q̇_ref / t_g²1,055 / 150²0.04689 kW/s²
- Heat release rate — Q̇ = α · t²0.04689 · 150²1,055 kW
About the reference rate
1,000 BTU/s = 1,055 kW
The convention was framed as the time to reach 1,000 BTU/s — a round number in imperial units. 1055 is not a physical constant but the result of a unit conversion, and it is derived here from the exact definition of the BTU.
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