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 Van Wagner and Pickett (1985) equations, retaining the printed 147.2 coefficient in the FFMC-to-moisture conversion:
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 noon wind speed measured at 10 m in the open, 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 reports ISI, BUI and DSR, with intermediate values f(D) and B in Calculation details and a current EFFIS reference class. It uses moisture codes already calculated for the same day and location; it does not derive daily moisture codes from weather history. BUI is clamped to zero when needed, and DMC = DC = 0 gives BUI = 0. 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 current European Forest Fire Information System (EFFIS) reference uses six classes: Low below 11.2, Moderate from 11.2, High from 21.3, Very High from 38, Extreme from 50 through 70, and Very Extreme above 70. Middle ranges use their lower bound and exclude the next threshold. These regional classes are not local fire warnings:
| FWI value | Danger class | Meaning |
|---|---|---|
| Below 11.2 | Low | Lower relative intensity potential on this reference scale |
| 11.2 to below 21.3 | Moderate | Moderate relative intensity potential |
| 21.3 to below 38.0 | High | High relative intensity potential |
| 38.0 to below 50.0 | Very high | Very high relative intensity potential |
| 50.0 through 70.0 | Extreme | Extreme relative intensity potential |
| Above 70.0 | Very Extreme | Very extreme relative intensity potential |
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; local ignition interpretation depends on fuels and conditions |
| DMC | Loosely compacted duff, 5 to 10 cm deep | About 12 days | Open-ended; a relative index of drying in this fuel layer |
| DC | Deep compact organic layer, 10 to 20 cm | About 52 days | Open-ended; a relative index of long-term drying |
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 current EFFIS reference scale, the High band begins at 21.3, Extreme begins at 50 and Very Extreme is above 70. FWI is open-ended and is an intensity index, not an ignition probability or a guarantee of fire behavior. 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 printed 1985 piecewise equations for this educational implementation, including the duff moisture function f(D) and the conditional final transformation, but agreement with a particular agency requires the same moisture codes, wind exposure, inputs, equation version and rounding. This calculator is an educational calculation, not an operational bulletin.
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.
