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Air Pressure at Altitude - Barometric Formula and ISA Model

Calculate atmospheric pressure at any altitude using the barometric formula, exponential approximation, or ISA model. Essential for aviation, mountaineering, and atmospheric physics.

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Pressure drops ~1% per 100 m in troposphere. ISA is the global aviation standard reference. Scale height H ≈ 8.4 km for exponential decay. Everest summit has ~33% of sea-level pressure.

Key quantities
1013.25 hPa
Sea Level
Key relation
~507 hPa
At 5.5 km
Key relation
~8.4 km
Scale Height
Key relation
~337 hPa
Everest
Key relation

Ready to run the numbers?

Why: Atmospheric pressure decreases with altitude, affecting aviation performance, human physiology, and weather systems. The barometric formula is fundamental to atmospheric science.

How: Uses barometric formula P = P₀(1 - Lh/T₀)^(gM/RL) for troposphere, exponential P = P₀exp(-h/H) for quick estimates, and ISA model for aviation standard.

Pressure drops ~1% per 100 m in troposphere.ISA is the global aviation standard reference.
Sources:ICAO Standard AtmosphereNASA Glenn - Atmospheric Properties

Run the calculator when you are ready.

Calculate Pressure at AltitudeEnter altitude to compute atmospheric pressure using barometric or ISA model

Enter Parameters

Basic Inputs

The altitude above sea level
Pressure at reference level (usually sea level)

Units & Settings

Unit for altitude measurement
Unit for pressure measurement

Advanced Options

Temperature model to use
Custom sea level temperature in Kelvin (only used if Temperature Model is Custom)
Use International Standard Atmosphere model
Include stratosphere corrections for altitudes above 11 km

For educational and informational purposes only. Verify with a qualified professional.

🔬 Physics Facts

🏔️

Mount Everest has only 33% of sea-level pressure.

— ICAO

✈️

Aircraft cabins are pressurized to ~8,000 ft equivalent.

— NASA

📉

Pressure decreases exponentially with altitude.

— NOAA

🔬

Scale height is altitude where pressure drops by factor e.

— NIST

📋 Key Takeaways

  • • Atmospheric pressure decreases approximately 1% per 100 meters of altitude gain in the troposphere
  • • At 5,500 m (18,000 ft), pressure is about 50% of sea level; at 11,000 m (36,000 ft), it's only 25%
  • • The barometric formula is most accurate for altitudes 0-11 km, accounting for temperature changes
  • • The ISA model is the aviation industry standard, providing consistent reference conditions worldwide

💡 Did You Know?

🏔️Mount Everest (8,849 m) has only 33% of sea level pressure — climbers need supplemental oxygen above 8,000 mSource: ICAO
✈️Commercial aircraft cruise at 35,000-40,000 ft where pressure is only 23% of sea level — cabins are pressurized to ~8,000 ft equivalentSource: NASA
🌡️The barometric formula was first derived in the 17th century by Blaise Pascal and Evangelista TorricelliSource: AMS
📉Pressure decreases exponentially with altitude — doubling altitude doesn't halve pressure, it reduces it by ~75%Source: NOAA
🌍The International Standard Atmosphere (ISA) was established in 1924 and remains the global aviation standardSource: ICAO
🔬The scale height (8,434 m) represents the altitude where pressure drops by a factor of e (2.718)Source: NIST
🌪️Pressure differences drive weather — low pressure systems bring storms, high pressure brings clear skiesSource: WMO

📖 How Barometric Pressure Calculation Works

The barometric formula calculates atmospheric pressure at altitude by accounting for the weight of air above and temperature variations. The calculation involves several steps:

Step 1: Determine Atmospheric Layer

Identify whether the altitude is in the troposphere (0-11 km) or stratosphere (11-20 km), as each has different temperature profiles.

Step 2: Calculate Temperature at Altitude

For troposphere:

T(h)=T0−L×hT(h) = T_0 - L \times h
where L = -0.0065 K/m (lapse rate).

Step 3: Apply Barometric Formula

For troposphere:

P=P0×(1−L×hT0)g×MR×LP = P_0 \times \left(1 - \frac{L \times h}{T_0}\right)^{\frac{g \times M}{R \times L}}
where g = 9.80665 m/s², M = 0.0289644 kg/mol, R = 8.31447 J/(mol·K).

Step 4: Stratosphere Correction

Above 11 km, temperature is constant, so pressure follows:

P=P11×exp⁡(−g×M×(h−11000)R×T11)P = P_{11} \times \exp\left(-\frac{g \times M \times (h-11000)}{R \times T_{11}}\right)

🎯 Expert Tips for Accurate Calculations

💡 Use ISA Model for Aviation

The ISA model provides standardized conditions for comparing aircraft performance. Always use ISA when working with aviation applications or comparing data across different locations.

💡 Barometric Formula for Troposphere

The barometric formula is most accurate for altitudes 0-11 km (troposphere). For higher altitudes, use the ISA model with stratosphere corrections.

💡 Exponential Approximation Quick Estimate

The exponential approximation (P = P₀ × exp(-h/H)) is simpler but less accurate. Use it for quick estimates or when temperature data isn't available.

💡 Verify Reference Pressure

Always use sea level pressure (1013.25 hPa ISA standard) as reference. If using local pressure, correct it to sea level first for accurate altitude calculations.

⚖️ Calculation Methods Comparison

MethodAccuracyAltitude RangeBest For
Barometric FormulaExcellent0-11 kmTroposphere, most accurate
Exponential ApproximationGood0-8 kmQuick estimates
ISA ModelExcellent0-20 kmAviation standard
Stratosphere ModelExcellent11-20 kmHigh altitude

❓ Frequently Asked Questions

Why does atmospheric pressure decrease with altitude?

Atmospheric pressure is caused by the weight of air above. As altitude increases, there's less air above pushing down, so pressure decreases. The relationship follows the barometric formula, accounting for decreasing air density and temperature with altitude.

What is the difference between barometric formula and exponential approximation?

The barometric formula accounts for temperature changes with altitude (lapse rate), making it more accurate. The exponential approximation assumes constant temperature, simplifying calculations but reducing accuracy, especially at higher altitudes.

How accurate is the ISA model compared to actual conditions?

The ISA model provides standardized reference conditions. Actual conditions vary with weather, location, and time. ISA is accurate for comparing aircraft performance but may differ from actual conditions by ±10-15% depending on weather patterns.

What is the International Standard Atmosphere (ISA)?

ISA is a standardized atmospheric model: sea level temperature 15°C, pressure 1013.25 hPa, density 1.225 kg/m³, with a temperature lapse rate of -6.5°C per 1000m up to 11 km. It provides a consistent reference for aviation worldwide.

How does pressure affect human physiology at high altitudes?

Lower pressure means less oxygen available. Above 2,500 m, some people experience altitude sickness. Above 5,500 m, supplemental oxygen is typically needed. Above 8,000 m (death zone), humans cannot survive long without oxygen support.

Can pressure be negative at high altitudes?

No, atmospheric pressure is always positive. It represents the weight of air above, which cannot be negative. However, pressure approaches very small values at extreme altitudes (e.g., 0.001 hPa at 100 km altitude).

How does the barometric formula account for temperature changes?

The barometric formula includes the temperature lapse rate (L = -0.0065 K/m), which describes how temperature decreases with altitude. This makes the formula more accurate than assuming constant temperature, especially in the troposphere where most weather occurs.

What is scale height and why is it important?

Scale height (H ≈ 8,434 m) is the altitude where pressure decreases by a factor of e (2.718). It represents the characteristic height of the atmosphere and is used in the exponential approximation formula. It provides insight into how quickly pressure decreases with altitude.

📊 Atmospheric Pressure by the Numbers

1013.25
hPa at Sea Level
506.6
hPa at 5.5 km
226.3
hPa at 11 km
8434
m Scale Height

⚠️ Disclaimer: This calculator provides estimates based on standard atmospheric physics models. Actual atmospheric pressure varies with weather conditions, geographic location, and time. For critical applications (aviation, mountaineering), always verify calculations with official sources and consider local weather conditions. Not a substitute for professional meteorological or aviation analysis.

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