Atmospheric Pressure & Altitude Calculator

Atmospheric Pressure Guide

What should I know about The Barometric Formula?

P(h) = P₀ × (1 − Lh/T₀)^(gM/RL). Simplified for the troposphere (up to ~11km): P ≈ P₀ × exp(−h/H), where H = scale height ≈ 8,400m. Standard sea level: P₀ = 101,325 Pa = 1013.25 hPa = 1 atm. Pressure decreases by about 12% per 1,000m near sea level. At 5,500m (Everest base camp): pressure ≈ 500 hPa, half sea level. At 8,848m (Everest summit): pressure ≈ 314 hPa, about one-third sea level. The 'death zone' begins at approximately 8,000m, where oxygen partial pressure becomes too low to sustain human life without supplemental oxygen for more than brief periods, which is why climbers above this altitude typically use bottled oxygen.

What's the key thing to understand about Boiling Point and Altitude?

Water boils when vapour pressure equals atmospheric pressure. At sea level (101kPa): water boils at 100°C. At 1,500m altitude (84kPa): water boils at approximately 94.5°C. At 3,000m (70kPa): 89.8°C. At 5,500m (53kPa): 83°C. Higher altitude cooking implications: water boils at lower temperature → food takes longer to cook. Baking requires adjustment — reduce leavening, increase liquids, increase temperature. Pressure cookers solve this — they seal and increase internal pressure, raising the boiling point of water above 100°C and cooking food faster as a result.

What should I know about Air Density at Altitude?

Air density ρ = P / (RT). Where R = specific gas constant for air = 287 J/(kg·K), T = temperature in Kelvin. At sea level, 15°C: ρ = 101325 / (287 × 288.15) = 1.225 kg/m³. At 3,000m, 5°C: ρ ≈ 0.91 kg/m³. Reduced air density at altitude affects: aircraft performance (lower lift, reduced engine output). Athletic performance — distance running requires more breaths per minute; sprinting is slightly faster due to reduced drag. Aerobic capacity drops approximately 1% per 100m above 1,500m. Altitude training camps for endurance athletes exploit this effect deliberately, using the body's adaptation to thinner air to boost red blood cell production before returning to sea level to compete.

What's the key thing to understand about Effective Oxygen Percentage?

Sea level air composition: 21% oxygen. This does NOT change with altitude. What changes is the partial pressure: total pressure × 21%. At sea level: pO₂ = 21.3 kPa. Mount Everest: pO₂ ≈ 6.6 kPa (about 31% of sea level oxygen availability). This is why oxygen masks are needed above approximately 4,500m for many people. Altitude sickness: typically appears above 2,400m. Acute mountain sickness (AMS): headaches, nausea, fatigue. Resolves in 24-48 hours with acclimatisation or descent. High altitude pulmonary or cerebral oedema are much more serious complications that can develop from AMS if a climber continues ascending rather than resting or descending.

How does atmospheric pressure relate to weather systems?

High-pressure systems (anticyclones) form where air sinks and spreads out, which suppresses cloud formation and typically brings settled, calmer weather. Low-pressure systems (depressions/cyclones) form where air rises, cools, and condenses, which is why they're associated with cloud, rain, and stronger winds — the steeper the pressure gradient between a low's centre and its surroundings, the stronger the wind. Meteorologists read these patterns from isobars (lines of equal pressure) on weather charts; closely spaced isobars indicate rapidly changing pressure over a short distance, and therefore strong winds. A rapidly falling barometer reading at a fixed location is one of the oldest and still-reliable signs that a storm or significant weather change is approaching, which is why household barometers remain a simple, functional forecasting tool even though they only measure pressure at one point.

Why do aircraft altimeters need a pressure setting?

An aircraft altimeter is essentially a barometer calibrated to read altitude instead of pressure, using the same barometric relationship this calculator applies. Because sea-level pressure varies day to day with weather systems, pilots must periodically update the altimeter's reference pressure setting (QNH) from air traffic control to get an accurate height above sea level — flying on yesterday's setting in today's weather can introduce a real altitude error of 100 feet or more per 1 hPa of pressure change missed. Above a certain transition altitude (18,000 feet in the US, commonly lower in other countries), aircraft switch to a standard reference pressure of 1013.25 hPa for all aircraft, called a 'flight level', so that every aircraft at a given level is using the same reference and remains vertically separated from others regardless of the actual local sea-level pressure that day.

What should I know about Altitude Sickness and Pressure?

Altitude sickness (acute mountain sickness) is driven by the drop in oxygen partial pressure as atmospheric pressure falls with altitude, not by the thinner air 'feeling' different in any other way — the percentage of oxygen in air stays at 21% all the way up, but each breath delivers fewer oxygen molecules because overall pressure is lower. Symptoms (headache, nausea, fatigue, dizziness) commonly begin above roughly 2,500m and become more likely the faster you ascend, which is why mountaineers and trekkers follow a 'climb high, sleep low' acclimatisation strategy and limit net sleeping-altitude gains to around 300-500m per day above 3,000m. Supplemental oxygen used by high-altitude climbers above 7,000-8,000m works by restoring effective oxygen partial pressure closer to what the body is adapted to at lower altitude, rather than changing the actual atmospheric pressure around the climber.

Pressure vs Altitude Reference Table

The barometric formula predicts how fast pressure falls as altitude increases, and seeing the standard-atmosphere figures for a handful of familiar altitudes side by side makes the relationship concrete.

The sharp drop between sea level and cruising altitude is exactly why airliner cabins are pressurised — at 11,000m the outside air is far too thin to breathe normally, so the cabin is maintained at an equivalent pressure altitude of roughly 1,800-2,400m (about 800 hPa) instead of the true outside pressure, which still causes mild discomfort for some passengers but is far safer and more comfortable than the unpressurised outside air.

Pressure Units Compared: atm, Pa, hPa, psi, mmHg, inHg

Atmospheric pressure is reported in several different units depending on the field — meteorology, physics, engineering, and aviation each have their own convention — and converting between them is a frequent source of errors because the numbers look completely different for the same real pressure.

hPa and mbar are numerically identical (1 hPa = 1 mbar exactly), which is why UK and European weather forecasts quote pressure in either unit interchangeably, while US aviation and weather reports almost always use inHg instead — so a UK pilot reading a US METAR report needs to convert, and 29.92 inHg is the figure to recognise as 'standard sea-level pressure' in that system, equivalent to the 1013.25 hPa used everywhere else.

Temperature Lapse Rate and Why the Barometric Formula Is an Approximation

The simplified exponential form of the barometric formula used elsewhere on this page, P ≈ P₀ × exp(−h/H) with scale height H ≈ 8,400m, assumes a constant temperature throughout the atmosphere — which isn't actually true, but is close enough for most everyday estimates up to a few kilometres. In reality, the International Standard Atmosphere (ISA) model used by meteorologists and aviation defines a standard temperature lapse rate of about 6.5°C of cooling for every 1,000m of altitude gained in the troposphere (the lowest ~11km of atmosphere, where almost all weather and human activity happens), starting from a sea-level reference of 15°C. Because both temperature and pressure are falling together with altitude — rather than pressure falling against a constant background temperature — the true pressure–altitude relationship curves slightly differently from the simple exponential approximation, which is why professional-grade altimeter and atmospheric models use the full ISA equations rather than the single-exponential shortcut. For a concrete comparison: the simplified exponential formula predicts a pressure of roughly 752 hPa at 2,500m (101,325 × exp(−2500/8400) ≈ 75,242 Pa), which is within about 1% of the ISA model's more precise figure for the same altitude — close enough for hiking, weather, and general-science purposes, but not precise enough for aviation-grade altimetry, which is exactly why real aircraft altimeters are built around the full ISA model rather than this page's simplified version.