Heat & Altitude Adjustment Calculator

• Step one, VO₂max. Bassett and colleagues fitted two curves giving percent of sea-level VO₂max against altitude in kilometres: y = −1.12x² − 1.90x + 99.9 acclimatized (R² = 0.973) and y = 0.178x³ − 1.43x² − 4.07x + 100 unacclimatized (R² = 0.974). These are the same equations the TrainingPeaks altitude article uses. They reproduce Bassett's own Mexico City figures to a tenth of a point, and they track Wehrlin and Hallén's independently measured 6.3% per 1,000 m closely up to about 3,000 m — two models from different data agreeing across the range that matters.
• Step two, power rather than VO₂max. Sustained power falls less than VO₂max does, and this is where most calculators go wrong. Clark and colleagues measured both in well-trained cyclists under acute hypoxia: at 1,200, 2,200 and 3,200 m, VO₂peak fell 8.2, 13.9 and 22.5% while five-minute time-trial power fell 5.8, 10.3 and 19.8%. The ratio is close to 0.88, and that factor is applied here. The TrainingPeaks article applies the VO₂max curves straight to power, which overstates the loss by two to three points.
• At 10,000 ft this gives about 18% unacclimatized and 14% acclimatized. Expect an athlete-to-athlete spread of roughly ±5 percentage points either way — that is the inter-individual standard deviation Bassett reports. Highly trained athletes who desaturate more sit at the worse end, which is counter-intuitive but well documented.
• What this replaced. The previous version used an unattributed power law, altitude_km^1.6 × 4.2, with hard caps at 35% and 30%. It overstated the loss by about seven points at 10,000 ft and went perfectly flat above roughly 13,000 ft. Both the formula and the caps are gone.
• Limits. Bassett fitted to data reaching about 4,300 m, which is why the altitude slider stops there rather than extrapolating — beyond that the polynomials cross over and the acclimatized curve implausibly overtakes the unacclimatized one. No study has measured 20–60 minute power at 3,000 m directly, so these figures are interpolated from five-minute time trials, which lean harder on VO₂max than an FTP effort does. Acclimatization recovers submaximal endurance substantially by about day 15 but does little for VO₂max itself.

• Each band recovers a fixed fraction of the initial decrement: nothing at 0–2 days, then 8%, 18% and 22%. Bassett reports only two states — unacclimatized (1–7 days) and acclimatized (several weeks) — so the first and last bands are anchored to his endpoints and the middle two interpolate between them. At 10,000 ft the 15+ band returns 14.2% against the 14.3% his acclimatized curve gives, so the schemes agree where it matters most.
• A deliberate departure at the extremes, and why. Bassett's two curves are separately fitted polynomials, so the recovery they imply is not constant — it runs about 42% at 3,000 ft, 21% at 10,000 ft, and collapses to 3% by 14,100 ft, where the two curves converge and then cross. A recovery that shrinks to nothing as altitude rises is an artefact of fitting rather than a physiological finding, so this tool holds the fraction constant instead. The practical effect is that it is slightly more conservative than Bassett below about 9,000 ft and considerably less pessimistic above 12,000 ft, and it cannot produce the crossover.
• The shape is well supported; the middle magnitudes are not. Two independent datasets agree that recovery is monotonic from day one and plateaus at about two weeks: Horstman found no further gain from day 15 to day 22, and Schuler none from day 14 to day 21. But the day-3 to day-14 numbers come from converting time-to-exhaustion gains into power, and time to exhaustion amplifies a power change several-fold — a 1% power change can move it 4 to 15 times as much. Convert Horstman's +59% endurance time at a middling multiplier and you get roughly +6% power, about a fifth of the decrement, which is exactly where Bassett's acclimatized curve sits. That convergence is reassuring, but the 8–14 day band could defensibly be anywhere from 10% to 30% recovered. The figures are shown as whole numbers for that reason.
• There is no dip at days two to five, and racing off the plane has no advantage. This is worth stating plainly because the opposite is widely believed. No study measuring performance on successive days after arrival shows a decline below day-one values, and a controlled trial at 2,500 m found no difference in 20 km time-trial performance between arriving 2 hours and 14 hours beforehand, despite measurably greater plasma volume loss in the longer group. What is real is that mood disturbance peaks around 24 hours and settles by roughly 48 — which is probably where the belief comes from. So the practical read is a fork: either commit to a fortnight or accept the full hit, because three to seven days costs a week of good training and clears very little.
• VO₂max barely recovers; submaximal endurance does. Fulco's review concluded VO₂max does not improve meaningfully with extended exposure while submaximal performance improves without it, and that remains broadly the consensus. There is some evidence of small VO₂max gains at moderate altitude — Schuler measured about 4% per week at 2,340 m — so Bassett's implied ~20% recovery is mid-range rather than generous.
• This is not altitude training. The input asks how many days you have spent at or near the race altitude immediately before racing there. Live-high train-low is a different question with a different mechanism — it targets sea-level performance through haematological adaptation over about four weeks at 12–16 hours a day. Below two weeks, none of the gain in these bands is from making red cells. And days at altitude are not free fitness: training quality is lower up there.

• The spread is athlete-to-athlete variation, not model error. Clark measured five-minute time-trial power loss in well-trained cyclists at three altitudes and reported standard deviations of 2.9, 4.3 and 3.5 percentage points at 1,200, 2,200 and 3,200 m. Notably those are flat rather than growing with altitude — unlike the VO₂max standard deviations in the same study, which do scale — so the band here is a fixed ±4 points rather than a percentage of the estimate. It tapers below about 8,000 ft only because half of a very small decrement is a more honest spread than ±4 — that taper reproduces Clark's lowest measured point, where a 5.8% loss carried an SD of 2.9.
• That is one standard deviation, so roughly two thirds of athletes fall inside it and a third fall outside. Treat it as a typical spread rather than a confidence interval — it comes from a single study with a small sample.
• Highly trained athletes tend to sit at the worse end, which is counter-intuitive. The mechanism is exercise-induced arterial hypoxaemia: a big cardiac output moves blood through the lung fast enough that it does not fully saturate, and that gets worse when the air is thin. One study found athletes prone to it lost 22% of VO₂max at 2,150 m against 16% in those who were not.
• The only way to narrow the range is to measure yourself. A single threshold effort at altitude tells you more than any model here.

• It is now fitted, not invented. The previous version was an unattributed power law with hard caps at 15% and 8%, no humidity term, and nothing below 10 °C. This one is a least-squares fit to fourteen reference points drawn from seven studies, all published between 1997 and 2023 and plotted in the figure above. The form is loss = a × (Teff − 9)² above the optimum and b × (9 − Teff)² below it, with a = 0.0145 and b = 0.0040.
• Humidity is now an input, and it was the largest missing piece. Sweat only cools you when it evaporates, so the same air temperature costs far more in saturated air. Humidity enters as a shift in effective temperature, calibrated so that going from 30% to 80% is worth about 5.7 °C at 20 °C and 8.3 °C at 35 °C — which is what shade wet-bulb globe temperature gives. Jenkins's study is the useful independent check here: holding air temperature at 36 °C and raising vapour pressure from 2.0 to 4.0 kPa cost a further 3.4 percentage points of 20 km time-trial power, implying about 0.14 points per point of humidity, against the 0.17 this model returns.
• The optimum moved to 9 °C, and the cold side is no longer flat. Galloway measured the longest cycling time to exhaustion at 10.5 °C, with capacity falling on both sides; El Helou fitted a quadratic to 1,791,972 marathon finishes and put the optimum between 3.8 and 9.9 °C depending on ability, again two-sided. The cold-side coefficient here is carried from that shape rather than from our own fit, because the reference set contains no cold conditions — treat sub-zero figures as indicative.
• What changed in practice. At 50% humidity the new curve returns 1.8% at 20 °C, 3.7% at 25, 6.4% at 30, 9.8% at 35 and 13.9% at 40, against the old 2.3, 4.2, 6.5, 9.1 and 12.0. So it is slightly gentler in the twenties and materially harsher above 35, which is the direction the data demanded — and the old 15% ceiling is gone, so 45 °C now reads 18.8% rather than being clipped.
• Acclimation now recovers a constant 55% rather than being a separate linear cap. The old shape recovered 13% of the decrement at 20 °C but 45% at 35 °C purely as an artefact of laying a straight line over a curve. Individual studies range from almost no benefit to complete recovery — Racinais found 14 days of natural acclimatization returned a hot time trial to its cool-condition time outright, while others recovered under half — and meta-analytic estimates cluster at 50 to 75%. Fifty-five percent is a mid-range reading of a genuinely wide literature.

• The residual spread is 3.4 percentage points, and it is not random. The two largest misses are the two lowest-airflow protocols: Racinais's road time trial at 37 °C and Ely's laboratory trial at 40 °C, both of which lost six to nine points more than the curve predicts. Look at the orange points in the figure — laboratory work in still air sits systematically above everything raced outdoors.
• Airflow is a first-order moderator that this model does not take as an input. Junge's pooled analysis of fourteen prolonged cycling time trials found that temperature, humidity and wind speed together explain 77% of the variance in power decrement, with wind entering as 1/√WS. The same cohort at the same 39 °C lost 16% at one airflow and 2% at another. Practically: a cyclist moving at 35 km/h gets far more convective cooling than a runner at 12 km/h or a rider on a turbo, so this model — anchored to outdoor time trials — will understate the cost of indoor training and probably understates it for slower athletes too.
• No duration term. Heat plainly costs a four-hour event more than a twenty-minute one, but no published continuous function exists for it, and in the pooled data the spread is dominated by airflow and acclimation rather than duration. Adding a scaler would be invention, so there is none.
• Elite marathon runners lose less than this curve says. The three open circles sit below it throughout. Some of that is selection — those are the fastest finishers in the field, who are self-selected for heat tolerance — but if you are modelling a strong runner in moderate heat, read the lower half of the band.
• The 1.15 multiplier when altitude and heat are both severe is inherited and unvalidated. It is plausible that the two stressors compound rather than simply add, but nothing in the reference set constrains its size.

• Moving air is the single biggest thing standing between you and heat strain. Junge's pooled analysis of fourteen prolonged cycling time trials found that temperature, humidity and wind speed together explain 77% of the variance in power decrement, with wind entering as 1/√WS. The same cohort at the same 39 °C lost 16% of power in one trial and 2% in another, largely on convective cooling.
• The model is calibrated on outdoor time trials, so "outdoors, moving" is the fitted case and applies no multiplier. The other two settings scale up from it: still-air laboratory protocols lose roughly two to four times what outdoor time trials lose at matched temperature, so indoors with a fan applies ×1.4 and indoors with still air ×2.2. Those are a deliberately coarse mid-range reading of a wide spread, not fitted coefficients — the underlying studies differ in acclimation status and protocol as well as airflow.
• The practical case this exists for is the hot garage. A rider at 35 km/h has perhaps 10 m/s of airflow; the same rider on a trainer with no fan has almost none, and will find a session that reads as comfortable outdoors becomes unmanageable indoors at the same air temperature. If you coach anyone doing summer intervals inside, this is the setting that matters.
• Runners sit between the two ends and closer to the outdoor case. The tool does not split by sport here, because in the source data airflow and population are confounded — the marathon studies are elite fields who are self-selected for heat tolerance, so their smaller decrements are not purely an airflow effect.

• Only two numbers here are solid enough to encode, and both are stated with their limits. Maximum heart rate falls with altitude at about 1.7 bpm per 1,000 m, roughly linearly and detectable from as low as 600–700 m, from Mourot's pooled regression across studies. Submaximal heart rate rises about 1 bpm per °C of air temperature at a fixed workload, from Jenkins's fourteen trained cyclists riding 45 minutes at 70% of VO₂peak at 18, 27 and 36 °C with absolute humidity matched. Outside 18–36 °C, or at much lower airflow, that slope is extrapolation.
• The spread on the altitude figure is as large as the effect. In the 2,500–3,500 m band the reported decrement is about 4 bpm with a standard deviation of nearly 4, so per-athlete prediction is close to useless. It is shown because knowing the direction and rough size prevents a specific mistake — an athlete deciding they are unfit because they cannot reach their usual maximum.
• What deliberately is not here: a threshold heart rate rule. The usable heart-rate range compresses at altitude from both ends, since maximum falls while heart rate at a given power rises. That much is well established. But no source I could find quantifies the compression or supports a "your threshold heart rate becomes X" rule, so the tool does not offer one.
• The failure mode worth naming. In the heat, heart rate overstates metabolic intensity — the usual heart-rate to percent-VO₂max relationship does not hold once you are hot. So an athlete holding a heart-rate cap on a hot day works easier than intended and under-doses the session. The asymmetry matters: heat makes heart rate a poor intensity target but an excellent adaptation monitor. A falling heart rate at a fixed submaximal workload across days is the accepted marker that heat acclimation is taking hold, worth about 17 bpm at the end of a standard bout and 5 bpm at rest after 10 to 14 days.
• Sweat rate rises about 0.04 L/h per °C over the same range, from the same study. Plan fluid on that rather than on thirst, which lags.

• These are targets for the same relative effort, not a prediction of finishing time. Terrain, drafting, pacing discipline and how well you sleep at altitude all move the result independently.
• The adjustment applies to sustained aerobic efforts. Short, anaerobic efforts are far less affected by altitude — sprint power is nearly unchanged — so do not apply this to a 20-second attack.
• Descending and flat riding at altitude are faster for the same power because the air is thinner. This tool adjusts what you can produce, not what that production buys you against the wind.

Altitude model sources.

• Bassett DR Jr, et al. Comparing cycling world hour records, 1967–1996: modeling with empirical data. Med Sci Sports Exerc 1999;31(11):1665–76. PMID 10589872
• Clark SA, et al. Time to exhaustion at 100% peak power output, and V̇O₂ kinetics, following acclimatisation to normobaric hypoxia. Eur J Appl Physiol 2007;102(1):45–55. doi:10.1007/s00421-007-0554-0
• Wehrlin JP, Hallén J. Linear decrease in V̇O₂max and performance with increasing altitude in endurance athletes. Eur J Appl Physiol 2006;96(4):404–12. doi:10.1007/s00421-005-0081-9
• Fulco CS, Rock PB, Cymerman A. Maximal and submaximal exercise performance at altitude. Aviat Space Environ Med 1998;69(8):793–801. PMID 9715971
• Burtscher M, et al. Effects of living at higher altitudes on mortality. Front Physiol 2018;9:1504. doi:10.3389/fphys.2018.01504
• Chapman RF, Laymon AS, Levine BD. Timing of arrival and pre-acclimatization strategies for the endurance athlete competing at moderate to high altitudes. High Alt Med Biol 2013;14(4):319–24. doi:10.1089/ham.2013.1022
• Foss JL, Constantini K, Mickleborough TD, Chapman RF. Short-term arrival strategies for endurance exercise performance at moderate altitude. J Appl Physiol 2017;123(5):1258–65. doi:10.1152/japplphysiol.00314.2017
• Horstman D, Weiskopf R, Jackson RE. Work capacity during 3-wk sojourn at 4,300 m: effects of relative polycythemia. J Appl Physiol 1980;49(2):311–18. doi:10.1152/jappl.1980.49.2.311
• Mourot L. Limitation of maximal heart rate in hypoxia: mechanisms and clinical importance. Front Physiol 2018;9:972. doi:10.3389/fphys.2018.00972
• McDonald T, et al. Physiological adaptations to heat acclimation: a Bayesian meta-regression. Comprehensive Physiology 2025. PMC12122934
• Jenkins EJ, Campbell HA, Lee JKW, Mündel T, Cotter JD. Delineating the impacts of air temperature and humidity for endurance exercise. Exp Physiol 2023;108(2):207–20. doi:10.1113/EP090969
• Junge N, Jørgensen R, Flouris AD, Nybo L. Prolonged self-paced exercise in the heat — environmental factors affecting performance. Temperature 2016;3(4):539–48. doi:10.1080/23328940.2016.1216257
• Arngrímsson SA, Petitt DS, Borrani F, Skinner KA, Cureton KJ. Hyperthermia and maximal oxygen uptake in men and women. Eur J Appl Physiol 2004;92(4–5):524–32. doi:10.1007/s00421-004-1053-1
• Peiffer JJ, Abbiss CR. Influence of environmental temperature on 40 km cycling time-trial pacing. Int J Sports Physiol Perform 2011;6(2):208–20. PMID 21725106
• Tatterson AJ, et al. Effects of heat stress on physiological responses and exercise performance in elite cyclists. J Sci Med Sport 2000;3(2):186–93. doi:10.1016/S1440-2440(00)80080-8
• Racinais S, et al. Effect of heat and heat acclimatization on cycling time trial performance and pacing. Med Sci Sports Exerc 2015;47(3):601–6. doi:10.1249/MSS.0000000000000428
• Ely BR, et al. Aerobic performance is degraded, despite modest hyperthermia, in hot environments. Med Sci Sports Exerc 2010;42(1):135–41. PMID 20010120
• Ely MR, Cheuvront SN, Roberts WO, Montain SJ. Impact of weather on marathon-running performance. Med Sci Sports Exerc 2007;39(3):487–93. PMID 17473775
• El Helou N, et al. Impact of environmental parameters on marathon running performance. PLoS One 2012;7(5):e37407. doi:10.1371/journal.pone.0037407
• Galloway SD, Maughan RJ. Effects of ambient temperature on the capacity to perform prolonged cycle exercise in man. Med Sci Sports Exerc 1997;29(9):1240–9. PMID 9309637
• Racinais S, et al. Consensus recommendations on training and competing in the heat. Scand J Med Sci Sports 2015;25(S1):6–19. doi:10.1111/sms.12467
• Maher JT, Jones LG, Hartley LH. Effects of high-altitude exposure on submaximal endurance capacity of men. J Appl Physiol 1974;37(6):895–98. doi:10.1152/jappl.1974.37.6.895

Estimates for planning, not medical guidance. Altitude illness is a real risk above about 2,500 m and is not modelled here.