Fire Growth Rate Calculator

t-squared Growth Framework

The calculator applies the t-squared fire growth model, where heat release rate increases with the square of time from ignition. In preliminary engineering, this approximation supports quick scenario ranking, detector response timing checks, and conservative smoke-control screening when detailed fuel package data is unavailable. Because Q(t) is smooth and monotonic, it is also useful for sensitivity studies across several time points.

Selecting a Growth Coefficient

Preset categories represent common development speeds used in fire protection engineering practice. Slow growth can approximate limited-fuel ignition or sheltered burning, while medium and fast can represent typical office or retail contents under favorable conditions. Ultra-fast can reflect rapid flaming of light contents or highly exposed arrays. Custom α lets you calibrate the curve to test data, to a hazard analysis point, or to a project inventory assumption.

Interpreting Outputs and Units

Heat release rate Q is reported in kW, time t in seconds, and α in kW/s². The instantaneous growth rate dQ/dt (kW/s) indicates how sharply conditions are changing at the calculated time. Higher dQ/dt implies faster deterioration of tenability and shorter available decision time. Comparing dQ/dt across scenarios helps identify which hazards deserve more detailed modeling.

Using Results in Engineering Workflows

Use “Heat release at time” to estimate Q at selected times for tenability checks, smoke layer calculations, or early ventilation sizing. Use “Time to reach target” to estimate when a design limit is reached, such as a chosen Q for sprinkler activation sensitivity, fan startup objectives, or structural heat flux screening. Use “Coefficient from Q and time” to back-calculate α from a known point, then apply it to extend the curve consistently.

Quality Checks and Limitations

The model describes growth only and does not represent decay, ventilation-limited burning, sprinkler control, or compartment feedback effects. Confirm that α and the time horizon match the scenario basis, and avoid extrapolating far beyond the intended design period. Keep inputs realistic, document the chosen category, and treat results as screening values. Exported tables provide traceable calculations for reviews and reports. If multiple scenarios are assessed, store each export with a clear filename, and note assumptions beside drawings or calculation packages for future traceability.

FAQs

1) What does “fire growth rate” mean in this calculator?

It represents how the heat release rate increases over time in the t-squared model. The calculator reports both Q(t) and the instantaneous slope dQ/dt at the calculated time.

2) When should I use a preset category instead of custom α?

Use presets for early design or screening when you need a reasonable, documented assumption. Use custom α when you have test data, a scenario basis, or a hazard analysis point that should control the curve.

3) Can I compute the time to reach 1,000 kW?

Yes. Select “Time to reach target,” enter the target Q value in kW, select a category or α, and the calculator returns the corresponding time in seconds.

4) What does dQ/dt tell me for engineering decisions?

dQ/dt is the instantaneous growth rate at time t. It helps compare scenarios and indicates how rapidly conditions may worsen, which can inform detection timing, response planning, and sensitivity checks.

5) Are the results suitable for final design?

They are best used for preliminary sizing, scenario ranking, and documentation. Final design may require compartment modeling, ventilation limits, suppression effects, and project-specific fuel characterization beyond a simple growth curve.

6) Why export CSV and PDF outputs?

Exports provide consistent, traceable records of inputs and outputs for review packages, calculation notes, and audits. They also simplify comparing multiple scenarios using the same table format.