Heat Adjusted Pace Calculator — WBGT and What Heat Really Costs

Start With What Is Wrong Everywhere Else

Almost every online WBGT calculator uses this:

WBGT = 0.567·Ta + 0.393·e + 3.94

attributed to the Australian Bureau of Meteorology. Lemke and Kjellstrom evaluated the published methods for deriving WBGT from ordinary weather data (*Industrial Health* 2012;50:267–278) and could not trace that formula to the reference the Bureau cited for it. They tracked it to a Gagge and Nishi relation from 1976, found the Bureau's version differed from it, and noted the original was fitted for indoor conditions with no solar radiation and no wind term.

Their conclusion: the Bureau's published formula is incorrect, and research built on it needs re-evaluating. For outdoor WBGT they recommend Liljegren et al. (2008) — a thermodynamic model requiring solar irradiance and wind speed, which no weather app gives you.

So this page does not use it. It builds the number from the definition instead, and shows you every substitution it makes.

How the Number Here Is Built

ISO 7243 defines WBGT as a weighted sum of three thermometers:

WBGT = 0.7·T_nwb + 0.2·T_g + 0.1·T_a — outdoors, in sun WBGT = 0.7·T_nwb + 0.3·T_g — in shade or indoors

Where T_nwb is a naturally ventilated wet bulb, T_g is a black globe, and T_a is ordinary air temperature. Two substitutions turn that into something you can compute from a forecast:

The wet bulb.** With air moving over it — which running guarantees — the naturally ventilated wet bulb approaches the psychrometric wet bulb. That one is not approximated here, it is **solved: the psychrometric relation e_s(T_wb) = e + A·p·(T_a − T_wb) has exactly one root, and this page finds it by bisection.

The globe. In shade it sits at air temperature. In sun it runs well above it, and how far above depends on the solar load — so instead of hiding that in a fitted coefficient, it is the one input you set. Each sun setting adds a stated number of degrees to the globe, and because the globe carries a weight of only 0.2 outdoors, you can see in the breakdown table exactly what your choice cost in WBGT. Full sun adds about 3 °C to the final figure, not 15.

The breakdown also prints a cross-check: Stull's published 2011 single-expression fit for wet-bulb temperature, and how far it sits from the solved value. Stull states his fit accurate to within −1 to +0.65 °C with a mean absolute error under 0.3 °C. Across the range runners race in — 0 to 40 °C, 20 to 99% humidity — the two methods here agree to within 0.73 °C. Where they would disagree badly is the cold, dry corner, which Stull explicitly excludes from his own validity range, and which this calculator declines to enter.

The Flag System

Two notes on this table. Sources differ on whether the yellow/red boundary is 72 or 73 °F, so 72 is used here and the discrepancy stated rather than quietly picked. And the ACSM deliberately avoided making these a strict cancellation standard — they are recommendations, and a race director weighing them has more to consider than one number.

What Heat Measurably Cost

This is the part where most calculators invent something. There is no validated per-runner heat pace adjustment formula, so what this page gives you instead is measurement.

Ely, Cheuvront, Roberts and Montain (*Med Sci Sports Exerc* 2007;39(3):487–493) took results from seven marathons — Boston, New York, Twin Cities, Grandma's, Richmond, Hartford and Vancouver — covering up to 36 years each, and grouped the races into WBGT quartiles. For the top male finishers, times relative to the course record were:

Read the standard deviations. They are the same size as the differences between the bands, which is the honest summary: the trend is real and consistent, and any single race could land anywhere.

The adjustment this page offers is the gap between your band and the coolest one the paper measured — about 2.8% from the coolest band to the warmest. For a three-hour marathon that is five minutes.

Three things that figure is not:

It is not a personal prediction. It is what happened to the front of real marathon fields, averaged over decades.

It understates it for most people. The paper found slower runners are affected more than faster ones. The per-quartile numbers for the 25th, 50th, 100th and 300th finishers exist in the paper, but the only versions available to this page came from a secondary blog rather than the source, so they are not reproduced here. If you are a three-hour-plus marathoner, the real cost to you is larger than the table above.

It stops at the edge of the data. Outside 5 to 25 °C WBGT this page offers no adjustment at all. Extrapolating a measured relationship past its data is exactly how the numbers on other calculators get invented.

What Actually Changes on Race Day

The arithmetic is the least useful thing on this page. What matters:

Run by effort, not by pace. Heart rate rises for the same work as temperature climbs, and your goal pace was set in different air. The runners who blow up in hot marathons are almost always the ones who held goal pace through halfway.

Humidity is the hidden half. At 30 °C and 30% humidity you can still evaporate sweat. At 30 °C and 85% you cannot, and that is a physiological difference, not a comfort one. This is why dew point tells you more than temperature — and why the number this page leads with is a wet bulb rather than a thermometer reading.

Acclimation is worth more than any pacing adjustment. Ten to fourteen days of heat exposure produces measurable adaptation: more plasma volume, earlier sweating, lower sweat sodium. It is the only intervention here that changes the physiology rather than managing it.

The flag can understate the risk. This calculator computes a globe temperature from your sun setting, and a real black globe in a real race can be hotter than any of the options offered — a windless road with reflective surfaces being the worst case.

Where This Sits Against the Other Tools Here

The heat index calculator covers the apparent-temperature side of heat, which is about comfort and general risk rather than exercise. The sweat rate calculator is where to go for how much to drink — the fluid question is separate from the pacing one, and conditions that slow you down are also the conditions that make your sweat rate hardest to estimate. For an unadjusted goal pace, the running pace calculator does the arithmetic.