Calculate the Fire Weather Index (FWI) from ISI and BUI, or from FFMC, DMC, DC and wind speed, with the fire danger class and Daily Severity Rating.
Fire Weather Index Formula
The Fire Weather Index (FWI) is the final output of the Canadian Forest Fire Weather Index System. It combines the Initial Spread Index (ISI) and the Buildup Index (BUI) using the official Van Wagner (1987) equations:
If you start from the three fuel moisture codes instead, the calculator first derives ISI and BUI:
- FWI is the Fire Weather Index, a unitless rating of fire intensity potential
- ISI is the Initial Spread Index, a rating of expected rate of fire spread
- BUI is the Buildup Index, a rating of the total fuel available for combustion
- f(D) is the duff moisture function and B is an intermediate intensity value
- FFMC is the Fine Fuel Moisture Code (0 to 101), m is the equivalent fine fuel moisture content in percent
- W is the wind speed at noon in km/h (the calculator converts mph and m/s for you)
- DMC is the Duff Moisture Code and DC is the Drought Code
- DSR is the Daily Severity Rating, used to average fire danger over time
The calculator has two modes. In the first mode you enter ISI and BUI directly and it applies the piecewise equations above. In the second mode you enter FFMC, DMC, DC, and the noon wind speed; the calculator derives ISI and BUI first, then computes the FWI. In both modes it also reports the intermediate values f(D) and B, assigns a fire danger class, and converts the FWI into the Daily Severity Rating. Note that the true FWI equation is piecewise, so simple one-line approximations you may find elsewhere will not match official published FWI values.
Fire Danger Classes and Moisture Code Reference
The European Forest Fire Information System (EFFIS) maps the FWI to six danger classes. These are the thresholds the calculator uses:
| FWI value | Danger class | Meaning |
|---|---|---|
| Below 5.2 | Very low | Fires ignite poorly and spread little |
| 5.2 to 11.2 | Low | Limited ignition and slow spread |
| 11.2 to 21.3 | Moderate | Fires start readily and spread at moderate rates |
| 21.3 to 38.0 | High | Vigorous surface fire, control becomes difficult |
| 38.0 to 50.0 | Very high | Intense fire behavior, crowning possible |
| 50.0 and above | Extreme | Fast spreading, high intensity fires, suppression at the head unlikely |
Each input code tracks moisture in a different fuel layer, and each layer dries out on a different timescale. This is why a single rain event can lower FFMC quickly while DC stays high for weeks:
| Code | Fuel layer | Approx. drying time lag | Typical range |
|---|---|---|---|
| FFMC | Surface litter, top 1 to 2 cm | About 16 hours | 0 to 101; fires ignite readily above about 74, high danger above 90 |
| DMC | Loosely compacted duff, 5 to 10 cm deep | About 12 days | Open-ended; values above about 60 indicate deep burning is possible |
| DC | Deep compact organic layer, 10 to 20 cm | About 52 days | Open-ended; above about 300 signals seasonal drought and stubborn smoldering |
Example Problems
Example 1: FWI from ISI and BUI. A weather station reports an ISI of 10 and a BUI of 50. Since BUI is at most 80, f(D) = 0.626*50^0.809 + 2 = 16.83. Then B = 0.1 * 10 * 16.83 = 16.83. Because B is greater than 1, FWI = e^(2.72*(0.434*ln(16.83))^0.647) = 22.24. That falls in the 21.3 to 38.0 band, so the fire danger class is High. The Daily Severity Rating is DSR = 0.0272 * 22.24^1.77 = 6.59.
Example 2: FWI from the moisture codes. Suppose FFMC = 90, noon wind = 20 km/h, DMC = 40, and DC = 300. The fine fuel moisture is m = 147.2*(101 - 90)/(59.5 + 90) = 10.83, which gives ISI = 0.208 * e^(0.05039*20) * 91.9*e^(-0.1386*10.83)*(1 + 10.83^5.31/(4.93*10^7)) = 11.75. Since DMC (40) is less than 0.4*DC (120), BUI = 0.8*40*300/(40 + 120) = 60. Running ISI = 11.75 and BUI = 60 through the FWI equations gives f(D) = 19.18, B = 22.53, and FWI = 27.27, again a High danger class, with a DSR of about 9.5.
FAQ
What is considered a dangerous Fire Weather Index value?
On the EFFIS scale, anything above 21.3 is High danger and above 50 is Extreme. There is no upper cap on the FWI; values above 30 are generally taken as a signal of serious fire intensity potential, and historic extreme fire events have produced FWI values well above 50. Keep in mind that regional agencies calibrate their own danger class thresholds to local fuels and climate, so the same FWI value can carry a different official rating in different regions.
Why does this result differ from other online FWI calculators?
Many simple web calculators use a one-line approximation such as 0.434*ln(ISI) + 0.537*ln(BUI) - 1.233, which does not reproduce the official index. This calculator implements the full piecewise Van Wagner (1987) equations used by the Canadian Forest Fire Danger Rating System and EFFIS, including the duff moisture function f(D) and the conditional final transformation, so its output matches values published by fire weather agencies.
What is the Daily Severity Rating and how is it different from the FWI?
The DSR is a power-law transformation of the FWI (DSR = 0.0272 * FWI^1.77) that scales the index to better reflect the expected difficulty of fire control and the effort needed for suppression. Because of the exponent, high FWI days are weighted much more heavily. Unlike the FWI, the DSR is designed to be averaged over time or over stations, which is why seasonal and monthly severity summaries are built from DSR rather than from raw FWI values.