Heat & Altitude Adjustment Calculator

Every constant below traces to a published study. Where the literature disagrees, the disagreement is preserved as the width of the band rather than averaged into a single number. Sample sizes are given because most of this rests on laboratory studies of fewer than thirty athletes.

Why the result is a range

• The between-athlete spread is larger than the effect being estimated. Chapman and colleagues timed 27 elite runners over 3,000 m at 2,100 m: the mean slowing was 48.5 s with a standard deviation of 12.7 s. Gore's group found individual responses at just 580 m ranging from +1.2% to −12.3%. Arterial oxygen desaturation explains part of it, but only about 14% of the variance in performance — so even a tested athlete cannot honestly be given a point estimate. The band shown is roughly ±1 SD, covering about two-thirds of athletes.
• Read the band, not the midpoint. If you have raced at altitude or in heat before, you already know which end of it you sit at. That personal history is better evidence than this model.

Altitude

• VO₂max decline. Wehrlin & Hallén tested eight endurance athletes in a hypobaric chamber from 300 m to 2,800 m and found VO₂max falling 6.3% per 1,000 m, with a range of 4.6–7.5% — a linear decline that had already begun between 300 m and 800 m. The tool fits a mild quadratic through this and three other datasets, with a threshold at 300 m.
  Wehrlin JP, Hallén J. Eur J Appl Physiol. 2006;96(4):404–12. PMID 16311764 — PubMed · DOI
• Performance falls less than VO₂max. This is the key modelling step, and it is why the earlier version of this tool over-stated the altitude penalty. Clark and colleagues measured both in the same ten cyclists: VO₂peak fell 8.2 / 13.9 / 22.5% at 1,200 / 2,200 / 3,200 m, but five-minute time-trial power fell only 5.8 / 10.3 / 19.8%. The anaerobic contribution is unaffected by hypoxia, so the shortfall is partly absorbed. The tool applies a coupling factor of 0.78 for efforts under eight minutes, rising toward 0.90 for longer ones as the anaerobic share shrinks.
  Clark SA, Bourdon PC, Schmidt W, et al. Eur J Appl Physiol. 2007;102(1):45–55. PMID 17882451 — PubMed · DOI
• The 0.90 coupling factor for efforts over twenty minutes is reasoned, not measured. No study has measured it. It follows from the observation that hypoxic impairment scales with both elevation and duration, but it is the least evidenced number in the altitude model.
  Fulco CS, Rock PB, Cymerman A. Aviat Space Environ Med. 1998;69(8):793–801. PMID 9715971 — PubMed
• Running benchmark. The model returns about 10% at 2,100 m for an unacclimatised runner, which matches Chapman's measured 3,000 m field result.
  Chapman RF, Stager JM, Tanner DA, Stray-Gundersen J, Levine BD. Med Sci Sports Exerc. 2011;43(9):1649–56. PMID 21311361 — PubMed · DOI
• Acclimatisation recovers part of the loss, never all of it. Pooled estimates put the attenuation at 8–37%; Bassett's hour-record modelling gives 27% at 2,338 m. Above roughly 2,000–2,500 m, VO₂max itself is largely not restored even after weeks. Confidence in the day-tiers is low and they are deliberately coarse.
  Salgado RM, et al. Exerc Sport Sci Rev. 2024. PMID 39262050 — PubMed · DOI · Pühringer R, et al. High Alt Med Biol. 2022;23(1):37–42. PMID 34939827 — PubMed · DOI
• Runners get a small credit from thinner air. Davies measured the energy cost of overcoming air resistance in still conditions at about 2% at marathon speed, 4% at middle-distance speed and 7.8% when sprinting; the model applies the middle-distance figure, which is generous for a long event and still amounts to under 1% of the total. For sprinters thin air is a net benefit, and Péronnet's model puts the break-even for 400 m at roughly 2,400 m of elevation.
  Péronnet F, Thibault G, Cousineau DL. A theoretical analysis of the effect of altitude on running performance. J Appl Physiol. 1991;70(1):399–404. PMID 2010398 — PubMed · DOI · Davies CTM. Effects of wind assistance and resistance on the forward motion of a runner. J Appl Physiol. 1980;48(4):702–9. PMID 7380693 — PubMed · DOI
• For cyclists, power is not speed. The figure shown is watts. Because air density falls with elevation, drag falls too — at 2,000 m a rider roughly 10% down on power is about 2.4% faster on a flat time trial, which is why Bassett's group identified 2,000–2,500 m as the optimal elevation for the hour record. On a sustained climb, where gravity dominates, the full power loss lands on the clock.
  Bassett DR Jr, Kyle CR, Passfield L, Broker JP, Burke ER. Med Sci Sports Exerc. 1999;31(11):1665–76. PMID 10589872 — PubMed · DOI

Heat — running

• Two published models, kept apart. The lower bound follows Mantzios and colleagues, whose analysis of 1,258 races across 42 countries found a broad optimum plateau (10–17.5°C dry bulb) and a shallow decline outside it of 0.3–0.4% per °C. The upper bound follows the steeper Ely and Vihma parameterisation, with a single optimum near 11°C. These are genuinely different models, not one model with noise, so they are shown as the two edges of the band rather than averaged.
  Mantzios K, Ioannou LG, Panagiotaki Z, et al. Effects of weather parameters on endurance running performance: discipline-specific analysis of 1258 races. Med Sci Sports Exerc. 2022;54(1):153–61. PMID 34652333 — PubMed · DOI · Full text · Ely MR, Cheuvront SN, Roberts WO, Montain SJ. Med Sci Sports Exerc. 2007;39(3):487–93. PMID 17473775 — PubMed · DOI · Vihma T. Int J Biometeorol. 2010;54(3):297–306. PMID 19937453 — PubMed · DOI
• Calibre is the largest moderator — and it is disputed. Vihma found that raising the temperature from 10°C to 25°C cost an elite man about 5 minutes but a four-hour runner about 23. Several large studies agree that slower runners suffer two to five times more. El Helou's analysis of 1.79 million finishers, the largest of the lot, found no calibre effect at all. The tool takes the majority position but the disagreement is real.
  El Helou N, et al. PLoS One. 2012;7(5):e37407. PMID 22649525 — PubMed · DOI · Full text
• Above 25°C the curve steepens by half again. This rests on only two field observations — elite women 6.2% slower at 32°C in Doha, and amateurs about 13.5% slower at 31.4°C in São Paulo. It is the weakest element in the whole model. Above 33°C the tool says so on the page.
• Distance scaling is weaker than the folklore. Sprints are faster in the heat; ultras are hit hardest. Between 5 km and the marathon, though, the elite coefficients are non-monotonic, so the tool applies one curve across that range rather than inventing an exponent.

Heat — cycling

• Cycling gets its own curve, and the reason is air density, not airflow. The obvious argument — that cyclists move faster and so cool better — turns out to be capped: the benefit of airflow plateaus around 16 km/h, which an elite runner already exceeds. The genuinely cycling-specific mechanism is that warm air is thinner. A 20°C rise cuts air density about 7%, repaying roughly 6% in speed for a given power. So in cycling, heat costs watts but hands some back as speed. Running has no equivalent.
  Racinais S, Alonso JM, Coutts AJ, et al. Consensus recommendations on training and competing in the heat. Br J Sports Med. 2015;49(18):1164–73. PMID 26069301 — PubMed · DOI · Full text · Bright FM, Clark B, Jay O, Périard JD. Influence of air velocity on self-paced exercise performance in hot conditions. Med Sci Sports Exerc. 2023;55(8):1382–91. PMID 36989528 — PubMed · DOI
• The curve is anchored, not fitted. Values are interpolated between measured points: Peiffer & Abbiss found 40 km time-trial power essentially flat from 17°C to 27°C and only significantly down at 32°C; Racinais recorded −16% at 36°C in unacclimatised riders; Ely found 16.6% less work at 40°C than 21°C.
  Peiffer JJ, Abbiss CR. Influence of environmental temperature on 40 km cycling time-trial performance. Int J Sports Physiol Perform. 2011;6(2):208–20. PMID 21725106 — PubMed · DOI · Ely BR, Cheuvront SN, Kenefick RW, Sawka MN. Aerobic performance is degraded, despite modest hyperthermia, in hot environments. Med Sci Sports Exerc. 2010;42(1):135–41. PMID 20010120 — PubMed · DOI
• Indoors, on a trainer, or grinding up a climb below 16 km/h, subtract a further 6–7%. Still air removes most of the evaporative advantage. The tool does not model this automatically — it does not know where you are riding.
• Full sun is not modelled and it is not small. At a constant 30°C air temperature, adding 800 W/m² of solar load roughly halved time to exhaustion in one study.
  Otani H, et al. Eur J Appl Physiol. 2016;116(4):769–79. PMID 26842928 — PubMed · DOI

Acclimatisation, and what the model cannot see

• Heat acclimatisation is well evidenced for cycling. Racinais measured −3 ± 4% at 36°C after fourteen days, against roughly −16% on arrival. Most adaptation appears within a week; two weeks is needed to optimise time-trial performance. For running the same retention band is an inference — no field study has ever compared acclimatised and unacclimatised runners in the same race.
  Guy JH, Deakin GB, Edwards AM, Miller CM, Pyne DB. Adaptation to hot environmental conditions. Sports Med. 2015;45(3):303–11. PMID 25380791 — PubMed · DOI · Tyler CJ, Reeve T, Hodges GJ, Cheung SS. The effects of heat adaptation on physiology, perception and exercise performance in the heat: a meta-analysis. Sports Med. 2016;46(11):1699–724. PMID 27106556 — PubMed · DOI
• Humidity is not modelled, and it matters. Only dry-bulb temperature is used. Holding temperature at 30°C and raising humidity from 24% to 80% cut time to exhaustion by 32% in one controlled study. Wet-bulb globe temperature predicts marathon performance roughly twice as well as air temperature alone. Treat humid conditions as materially warmer than the thermometer says.
  Maughan RJ, Otani H, Watson P. Eur J Appl Physiol. 2012;112(6):2313–21. PMID 22012542 — PubMed · DOI
• Altitude and heat are combined multiplicatively — the two performance fractions are multiplied rather than the losses added, which is slightly less punitive than simple addition. No study has measured the interaction directly, so this is a modelling assumption, not a finding. The previous version's 1.15× compounding factor had no source and has been removed.
• Your weather forecast is the binding constraint on precision. Course-measured conditions differ from the nearest weather station by around 2°C on average, and in 45% of paired comparisons by more than 3°C. A tool that gave you different targets for 21°C and 22°C would be claiming precision the input cannot carry. This is a second reason the output is a band.
  Cheuvront SN, Caruso EM, Heavens KR, et al. Effect of WBGT index measurement location on heat stress category classification. Med Sci Sports Exerc. 2015;47(9):1958–64. PMID 25628176 — PubMed · DOI
• Enter the average elevation of the course, not the summit. A course that sits low with one high pass behaves much closer to its mean than its peak.
• There is no systematic review of the temperature–performance dose response. Every recent meta-analysis in this area concerns an intervention — cooling, menthol, acclimation — rather than the dose–response itself. The curves here are a synthesis of primary studies, not a settled consensus.

How to use this. The value is the direction and rough size of the adjustment, not the decimal place. Set out nearer the starting target than the average, expect to converge on the finishing target as the day warms, and let perceived effort and heart rate arbitrate. If the model says four per cent and you feel fine, that is useful; if it says four and you are struggling at eight, that is more useful still. Over a season, logging where you actually fall inside these bands will tell you more about the athlete than any published curve can.