NWS 2001 felt-temperature formula with frostbite risk bands.
NWS 2001 formula: WC(°F) = 35.74 + 0.6215·T − 35.75·V^0.16 + 0.4275·T·V^0.16, with T in °F and V in mph. Valid for T ≤ 50 °F (10 °C) and V ≥ 3 mph (4.8 km/h).
A windless cold day at −5 °C is uncomfortable; the same temperature at 40 km/h wind feels viciously cold and can cause frostbite in tens of minutes. The reason is the boundary layer of warm air your skin generates, which the wind strips away — the heat your body can produce locally is no longer enough to maintain skin temperature. The wind-chill index quantifies this as a "feels-like" temperature: the air temperature in still conditions that would produce the equivalent rate of heat loss from exposed skin. The calculation is non-trivial — the relationship is non-linear in both temperature and wind — and the formula has been revised twice. The current standard, the NWS 2001 formula (jointly adopted by the U.S. National Weather Service and Environment Canada), is more conservative than the older 1939 Siple-Passel index it replaced. This calculator uses the NWS 2001 formula and bands the result against frostbite-onset times for unprotected skin.
NWS 2001, with T in °F and V in mph:
WC(°F) = 35.74 + 0.6215 · T − 35.75 · V^0.16 + 0.4275 · T · V^0.16
Valid for T ≤ 50 °F (10 °C) and V ≥ 3 mph (4.8 km/h). Below the wind threshold, the boundary-layer effect is negligible and the formula returns nonsensical results — the calc detects this and falls back to the actual temperature with a note. Conversion: input may be °C/°F and km/h/mph in any combination; the calc normalizes internally to the formula's native units, then reports the result back in both °C and °F. The frostbite-risk bands (NWS, exposed skin): - WC ≥ 0 °F (−18 °C): cold but no frostbite risk. - WC 0 to −18 °F (−18 to −28 °C): frostbite in 30 min. - WC −18 to −32 °F (−28 to −36 °C): frostbite in 10–30 min. - WC −32 to −46 °F (−36 to −43 °C): frostbite in 5–10 min. - WC < −46 °F: frostbite in under 5 min — extreme exposure protocols.
Enter the air temperature and pick the temperature unit (°C/°F). Enter the wind speed and pick the wind unit (km/h or mph). The calc shows the felt temperature in both °C and °F, the drop versus actual, the actual values for confirmation, the wind speed, and a frostbite-risk verdict. If your conditions fall outside the formula's valid range, an italic note explains why the felt temperature equals the actual.
Cold and windy: T = −15 °C (5 °F), wind 40 km/h (24.85 mph). - V^0.16 = 24.85^0.16 ≈ 1.660. - WC(°F) = 35.74 + 0.6215 × 5 − 35.75 × 1.660 + 0.4275 × 5 × 1.660 = 35.74 + 3.108 − 59.345 + 3.548 = −16.95 °F ≈ −27.2 °C. - Drop vs actual: 12.2 °C (or 22.0 °F). - Risk band: WC ≈ −17 °F → frostbite in 30 min — bundle up.
Mild winter: T = 0 °C, wind 20 km/h. WC ≈ −5 °C. Risk: cold but no frostbite.
Threshold below which the formula breaks. The NWS formula assumes a measurable wind. At V < 3 mph, V^0.16 is too small and the affine combination overshoots. The calc detects this and returns the actual temperature instead of a misleading number. Likewise above 10 °C the formula was never meant to apply — wind cools you only because skin is warmer than air, and at warm temperatures the dynamic shifts to evaporative cooling, which is a separate phenomenon (the "heat index" handles that side, in summer).
Skin-only. The index is for exposed skin. A balaclava, gloves, and a ski jacket dramatically reduce effective wind exposure — the perceived chill while properly dressed is nowhere near the WC number. The risk bands are worst-case for unprotected skin, not for a fully-clothed person.
Older formulas. The pre-2001 Siple-Passel formula ran much more aggressive: a same-input WC could be 10–15 °F lower (colder) than NWS 2001. If you are reading historical weather records, check which formula was in use; "feels like −60" in a 1990s newspaper is not the same number as "feels like −60" today.
Humidity ignored. The wind-chill formula does not include humidity — it's purely a heat-loss-from-skin calculation in dry air. In practice, very humid cold air (rare; cold air is usually dry) can feel slightly different, but the effect is small compared to wind.
Wind speed measurement height. The formula was fit to wind speeds at ~10 m above ground (the standard meteorological height). Wind at 1.5 m (face height) is typically lower; if you have a face-height anemometer your "felt" temperature will be milder than the report.
Wet skin / sweat. Wet skin chills faster than dry skin because of evaporation. The WC formula doesn't account for this — wet conditions effectively shift the risk band up by one tier. Stay dry in the cold.