WBGT calculator: estimate wet bulb globe temperature

What WBGT measures

Wet bulb globe temperature (WBGT) is the heat-stress index athletic associations, the military and OSHA guidance use for people working or training outdoors. Unlike the heat index, which is calculated for shade, it accounts for four things: air temperature, humidity, wind and the sun’s radiant load. A WBGT meter measures it with three thermometers: a natural wet-bulb, a black globe and a dry bulb.

WBGT = 0.7 × Tnwb + 0.2 × Tg + 0.1 × Ta

Tnwb is the natural wet-bulb temperature, Tg the black-globe temperature and Ta the air temperature. The wet-bulb carries 70% of the weight, which is why a humid 88 °F afternoon can band higher than a dry 95 °F one.

How this calculator estimates WBGT

Without the instruments, the calculator estimates the two readings it cannot take, then combines them with the formula above. This is the approach behind the National Weather Service’s experimental WBGT product.

1. Wet-bulb, from temperature and humidity

Stull (2011) fits the psychrometric wet-bulb to air temperature (°C) and relative humidity (%), valid for 5–99% humidity and −20 to 50 °C. The NWS method uses it in place of the natural wet-bulb.

Tw = Ta·atan(0.151977·√(RH + 8.313659)) + atan(Ta + RH)
     − atan(RH − 1.676331)
     + 0.00391838·RH^1.5·atan(0.023101·RH) − 4.686035

2. Black globe, from sun and wind

Dimiceli and Piltz (NWS Tulsa) solve the heat balance of a black globe and linearise it, so the globe temperature follows from solar irradiance S (W/m²), its direct and diffuse fractions, the sun’s zenith angle z, wind speed u (metres per hour) and the air’s emissivity. Temperatures are in °C, as in the paper.

Tg = (B + C·Ta + 7,680,000) / (C + 256,000)
B  = S·( fdb / (4σ·cos z) + 1.2·fdif / σ ) + εa·Ta⁴
C  = 0.315·u^0.58 / 5.3865×10⁻⁸
εa = 0.575·ea^(1/7),   σ = 5.67×10⁻⁸

In the paper’s three field tests in Tulsa, the estimate came within about 0.5 °F of a measured globe. Wind is limited to 1–40 mph, the range the authors examined, so calm air is treated as 1 mph.

3. The sky choices

The sun buttons stand in for an irradiance reading. Each assumes a midsummer early afternoon, with the sun about 30° from overhead:

For comparison: the simplified WBGT

The Australian Bureau of Meteorology publishes a one-line approximation from temperature and humidity alone. It ignores wind and sun and assumes moderately strong sun in light wind, and studies have found it overestimates heat stress in hot, humid weather. The calculator shows it as a cross-check, not as the answer.

sWBGT = 0.567·Ta + 0.393·e + 3.94
e = (RH/100) · 6.105 · exp(17.27·Ta / (237.7 + Ta))   (hPa)

The full physical model is Liljegren et al. (2008), which iterates the energy balance of each instrument and needs the sun’s position and measured radiation. It is the reference model in research, and needs more than a four-input calculator can honestly feed.

WBGT estimates in full sun

Worked out with the method above for full sun and a 5 mph breeze. Each cell is the estimated WBGT in °F, with its GHSA band.

What the number means for practice

Each state association sets its own WBGT bands. Georgia’s GHSA By-Law 2.67 is the worked example the calculator uses; the full rules for each band, including rest breaks and equipment, are on the Georgia heat policy page.

• Under 82.0 °FNormal activities
• 82.0–86.9 °FUse discretion; watch at-risk players closely
• 87.0–89.9 °FPractice limited to 2 hours, more rest breaks
• 90.0–92.0 °FPractice limited to 1 hour, no conditioning
• Over 92.0 °FNo outdoor workouts

Other states use different numbers. Find yours in state heat policies for athletics:

• Georgia heat policy
• Texas heat policy
• Florida heat policy
• Arizona heat policy
• Arkansas heat policy
• Colorado heat policy
• Hawaii heat policy
• Illinois heat policy
• Kansas heat policy
• Massachusetts heat policy
• Mississippi heat policy
• Missouri heat policy
• Nevada heat policy
• New Hampshire heat policy
• New Mexico heat policy
• North Carolina heat policy
• Ohio heat policy
• West Virginia heat policy

An estimate, not a reading

Most state policies decide practice by a WBGT reading taken on site, at the practice location, with an instrument. This calculator is not that reading. It assumes a sky rather than measuring the sun, uses the psychrometric wet-bulb in place of the natural one (which can read low in humid, still air), and knows nothing about the turf, the bleachers or the building that blocks the breeze.

Use it to understand the number and to sanity-check a forecast. For why the field and the town forecast disagree, read WBGT on the field vs the town forecast and WBGT forecast vs on-site reading.

Sources

1. 01Dimiceli, V. E. and Piltz, S. F. — Estimation of Black Globe Temperature for Calculation of the WBGT Index (NWS Tulsa)weather.gov/media/tsa/pdf/WBGTpaper2.pdf (opens in a new tab)
2. 02Stull, R. (2011) — Wet-Bulb Temperature from Relative Humidity and Air Temperature, J. Appl. Meteor. Climatol. 50, 2267–2269doi.org/10.1175/JAMC-D-11-0143.1 (opens in a new tab)
3. 03Australian Bureau of Meteorology — Thermal comfort observations: approximation to the WBGTbom.gov.au/info/thermal_stress/ (opens in a new tab)
4. 04Liljegren, J. C. et al. (2008) — Modeling the Wet Bulb Globe Temperature Using Standard Meteorological Measurements, J. Occup. Environ. Hyg. 5(10), 645–655doi.org/10.1080/15459620802310770 (opens in a new tab)
5. 05OSHA Technical Manual, Section III, Chapter 4: Heat Stress (WBGT with and without solar load)osha.gov/otm/section-3-health-hazards/chapter-4 (opens in a new tab)
6. 06GHSA By-Law 2.67, Practice Policy for Heat and Humidity (as summarised on our Georgia page)

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