WILDFIRE ENGINEERING TOOL · BYRAM RELATIONSHIP
Flame Length Calculator
Translate fireline intensity into estimated flame length—or work backwards from an observed flame length. See the equation, unit conversions and operational context in one reproducible view.
Range: 0–10,000 kW/m. You may type a larger value.
Relationship used
L = 0.0775 × I0.46L in metres · I in kW/mCALCULATED ESTIMATE
4.44 ft flame length
Historical suppression interpretation
Lower flame-length class
Within the lowest flame-length band used in historical fire-behaviour guidance.
READ THE RESULT CORRECTLY
An empirical relationship, not a fire forecast.
This calculator applies the Byram relationship to a single value. It does not model wind, slope, fuel arrangement, flame tilt, spotting, crown fire or changing conditions.
Do not use the result as a safety distance, evacuation threshold or substitute for local incident information. Observed flame length and calculated flame length are not interchangeable in every fire environment.
Interpretation bands
Lowest historical band.
Direct attack becomes more difficult.
Serious control problems may occur.
High-intensity behaviour; direct head attack historically described as ineffective.
Method and sources
Forward: L = 0.0775 I0.46. Inverse: I = (L / 0.0775)1/0.46. Conversion: 1 Btu/(ft·s) = 3.46147 kW/m; 1 m = 3.28084 ft.
The relationship is a compact empirical estimate. Recent experimental work shows flame-zone geometry can affect the intensity–length relationship, so treat the output as context, not ground truth.
USDA Forest Service: SI reformulation · NWCG interpretation guidance
Flame length vs flame height: what is the difference?
Flame length follows the flame from its base toward its tip. Flame height describes its vertical reach. A tilted flame can therefore have a greater length than vertical height. The calculator above estimates length; it does not calculate flame tilt or vertical height.
As a simple geometric illustration, a straight 2 m segment tilted 60° from vertical has a vertical projection of 1 m: 2 × cos(60°). This illustrates the distinction; a real fluctuating flame is not a rigid straight segment, and this is not a fire-behaviour model.
Flame length examples from fireline intensity
These are calculated examples using L = 0.0775 × I0.46, with I in kW/m and L in metres. They are not field measurements or predictions for a particular fire.
| Fireline intensity | Estimated flame length |
|---|---|
| 100 kW/m | 0.64 m |
| 500 kW/m | 1.35 m |
| 1,000 kW/m | 1.86 m |
| 2,000 kW/m | 2.56 m |
| 5,000 kW/m | 3.90 m |
Why does the coefficient matter?
The linked USDA research note contains an errata sheet correcting the SI flame-length equation to use 0.0775. Use the corrected equation rather than copying the superseded coefficient from the original page. Source: Wilson (1980), USDA Forest Service, INT-292, errata sheet.
Can I calculate intensity from flame height?
The inverse mode expects flame length. Substituting vertical height treats a different quantity as the input. Keep the measurement definition and the model’s assumptions with any reported result.
Flame length concept · Flame height concept · Calculate fireline intensity from fuel and spread inputs