Standard Atmosphere Calculator
Calculate temperature, pressure, density, and speed of sound at any altitude using the International Standard Atmosphere (ISA) model. Includes a full density altitude calculator, pressure altitude converter, and ISA reference table from sea level to 80 km.
This density altitude calculator and standard atmosphere tool implements the ICAO ISA model across all seven atmospheric layers — from the troposphere at sea level up to 86 km in the mesosphere. Enter any altitude for complete ISA properties, or provide station pressure and temperature to find your exact density altitude using the full bisection method — not an approximation. The ISA lapse rate of −6.5°C per 1,000 m governs the troposphere; above 11,000 m the tropopause is isothermal at −56.5°C. Standard sea-level conditions: T = 288.15 K (15°C), P = 101,325 Pa (1013.25 hPa), ρ = 1.225 kg/m³, speed of sound = 340.29 m/s.
The temperature profile shows the characteristic tropopause kink (minimum at 11 km), stratosphere warming from ozone UV absorption, and mesosphere cooling. Your entered altitude is highlighted in amber.
Density altitude is the altitude in the standard atmosphere where air density equals the actual air density at your location. It accounts for both pressure and temperature effects. Select your input mode:
The simplified approximate formula (education mode) — compare against the precise ISA bisection result:
Density Altitude
— ft
Physical Interpretation
—
Pressure altitude is the altitude in the ISA at which the standard pressure equals your station pressure. It is independent of temperature — temperature affects density altitude, not pressure altitude.
Pressure Altitude
— ft
Complete ISA properties from −1,000 m to 80,000 m. Rows are colour-coded by atmospheric layer. All values computed from the ISA equations and hardcoded here for instant reference — no JavaScript required. The lapse rate is −6.5°C per 1,000 m through the troposphere; the tropopause at 11,000 m is isothermal at −56.5°C; the stratosphere warms from 20–47 km.
| Alt (m) | Alt (ft) | T (°C) | P (hPa) | ρ (kg/m³) | c (m/s) | Layer |
|---|---|---|---|---|---|---|
| −1,000 | −3,281 | 21.5 | 1,139.3 | 1.3470 | 341.2 | Troposphere |
| 0 | 0 | 15.0 | 1,013.25 | 1.2250 | 340.3 | Troposphere |
| 1,000 | 3,281 | 8.5 | 898.7 | 1.1120 | 336.4 | Troposphere |
| 2,000 | 6,562 | 2.0 | 795.0 | 1.0070 | 332.5 | Troposphere |
| 3,000 | 9,843 | −4.5 | 701.2 | 0.9090 | 328.6 | Troposphere |
| 5,000 | 16,404 | −17.5 | 540.5 | 0.7360 | 320.5 | Troposphere |
| 8,000 | 26,247 | −37.0 | 356.0 | 0.5260 | 308.1 | Troposphere |
| 11,000 | 36,089 | −56.5 | 226.3 | 0.3640 | 295.1 | Tropopause |
| 15,000 | 49,213 | −56.5 | 121.1 | 0.1950 | 295.1 | Tropopause |
| 20,000 | 65,617 | −56.5 | 54.75 | 0.0880 | 295.1 | Tropopause |
| 25,000 | 82,021 | −51.6 | 25.49 | 0.04010 | 298.0 | Stratosphere |
| 30,000 | 98,425 | −46.6 | 11.97 | 0.01840 | 301.7 | Stratosphere |
| 40,000 | 131,234 | −22.8 | 2.871 | 0.003850 | 317.2 | Stratosphere |
| 47,000 | 154,199 | −2.5 | 1.109 | 0.001400 | 329.8 | Stratopause |
| 50,000 | 164,042 | −2.5 | 0.6694 | 0.000861 | 329.8 | Mesosphere |
| 60,000 | 196,850 | −26.1 | 0.2196 | 0.000288 | 315.1 | Mesosphere |
| 70,000 | 229,659 | −53.6 | 0.05529 | 0.0000828 | 299.7 | Mesosphere |
| 80,000 | 262,467 | −74.5 | 0.01052 | 0.0000185 | 282.5 | Mesosphere |
★ 20% column is highlighted. All values use ISA lapse rate −6.5°C per 1,000 m in the troposphere. Speed of sound c = √(γ·R·T) with γ = 1.4, R = 287.058 J/(kg·K).
What Is Density Altitude? — Definition and Formula
Density altitude is the altitude in the International Standard Atmosphere (ISA) at which the air density equals the actual air density at your location. It is a performance-equivalent altitude, not your actual elevation. Crucially, density altitude ≠ actual elevation — it is affected by both temperature and (to a lesser extent) humidity, in addition to pressure.
The density altitude formula derives from the ISA model and the ideal gas law. The actual air density at any station is:
The density altitude equation is then the altitude h in the standard atmosphere where ρ_ISA(h) = ρ_actual. In the troposphere, there is a commonly used approximate density altitude formula:
The precise density altitude calculator above uses numerical bisection — finding the exact altitude where ISA density equals the computed actual density — valid at all altitudes and ISA layers, not just the troposphere.
What does density altitude mean in practice?
- High density altitude means lower air density — the air behaves as if you were at a higher altitude in standard conditions. Engines produce less power, propellers generate less thrust, aerodynamic lift is reduced.
- Low density altitude means denser air — the air behaves as if you were at a lower altitude. Performance is better than your actual elevation would suggest.
- A hot day at sea level (35°C, 101,325 Pa) produces a density altitude of approximately 1,200 m (3,940 ft) — significantly above sea level in terms of air density.
- A cold winter at 2,000 m (−20°C) produces a density altitude of approximately 1,200 m — the cold dense air lowers DA well below the actual elevation.
Define density altitude simply: It is the altitude at which a standard-day aircraft performance table would give the same values as your actual conditions. If your density altitude is 2,500 m, the aircraft performs as if it were at 2,500 m on a standard day — regardless of your actual elevation.
As air temperature increases, density altitude will increase — this is the single most important rule for understanding density altitude. Warmer air expands (from the ideal gas law ρ = P/RT), making it less dense, which corresponds to a higher equivalent ISA altitude.
Pressure Altitude vs Density Altitude — The Difference
Understanding pressure altitude vs density altitude is fundamental to both aviation and aerospace engineering. They are related but distinct.
| Altitude Type | Determined By | Formula Basis | Affected By Temperature? |
|---|---|---|---|
| Indicated Altitude | Altimeter reading (baro-set) | Pressure + altimeter setting | No (pressure only) |
| Pressure Altitude | Ambient pressure alone | ISA pressure inversion: P→h | No — temperature-independent |
| Density Altitude | Ambient pressure + temperature | ρ = P/(RT) → find ISA h where ρ_ISA = ρ_actual | Yes — this is the key difference |
| True Altitude | Actual height above mean sea level | Surveyed or GPS | Indirectly (refraction effects) |
When is pressure altitude equal to density altitude? Only when the actual outside air temperature (OAT) equals the ISA standard temperature at that pressure altitude. In the troposphere, ISA temperature at altitude h is T_ISA = 288.15 − 0.0065×h (K). At sea level (PA = 0 m), they are equal when OAT = 15°C. At 2,000 m pressure altitude, they are equal when OAT = 288.15 − 0.0065×2000 − 273.15 = 2.0°C. On any warmer day, density altitude exceeds pressure altitude; on any colder day, density altitude is lower.
The key insight on pressure altitude vs density altitude: pressure altitude tells you about pressure only — it is what your altimeter reads with the standard QNH of 1013.25 hPa set. Density altitude adds the temperature correction. In hot conditions, density altitude can exceed pressure altitude by hundreds or thousands of feet.
How Temperature Changes With Altitude — The ISA Lapse Rate
The ISA lapse rate in the troposphere is −6.5°C per 1,000 m (−3.56°F per 1,000 ft). This means for every 1,000 metres of altitude gained from sea level, temperature decreases by 6.5°C. This temperature change with altitude governs the density altitude formula and all atmospheric property calculations in the troposphere.
The lapse rate of −6.5°C per 1,000 m reflects the dry adiabatic and moist adiabatic cooling of rising air parcels — as air rises, it expands (pressure decreases), doing work against its surroundings and cooling in the process. The ISA uses a standard value that represents average global conditions.
Temperature profile by layer — what happens to temperature as altitude increases:
- Troposphere (0–11 km): Temperature decreases from 15°C at sea level to −56.5°C at 11,000 m at the ISA lapse rate of −6.5°C per 1,000 m. This is why speed of sound decreases with altitude here.
- Tropopause (11–20 km): Isothermal at −56.5°C. Temperature does not change with altitude. Speed of sound is constant at 295.1 m/s throughout this layer.
- Stratosphere (20–47 km): Temperature increases — from −56.5°C at 20 km to −2.5°C at 47 km — because the ozone layer absorbs ultraviolet radiation and converts it to heat. This temperature inversion is one of the most important features of Earth's atmosphere.
- Stratopause (47–51 km): Isothermal at −2.5°C — peak stratospheric temperature.
- Mesosphere (51–86 km): Temperature decreases again from −2.5°C to −74.5°C at 80 km. The mesosphere has no ozone heating and no tropospheric solar absorption — it is the coldest region of the atmosphere.
The ISA lapse rate of −6.5°C per 1,000 m means that at 5,000 m (16,404 ft), the standard temperature is 288.15 − 0.0065×5000 = 255.65 K = −17.5°C. This temperature change per 1,000 feet equivalent is −3.56°F per 1,000 ft — a useful rule of thumb for flight planning.
Speed of Sound vs Altitude
The speed of sound depends only on temperature — not directly on pressure or density. The formula is:
At sea level (T = 288.15 K): speed of sound = √(1.4 × 287.058 × 288.15) = 340.29 m/s (1,116 ft/s, 661.5 knots, 1,225 km/h). This is the sea-level speed of sound in standard conditions.
Speed of sound vs altitude — how it changes:
- Troposphere (0–11 km): Speed of sound decreases as altitude increases because temperature decreases. From 340.3 m/s at sea level to 295.1 m/s at 11,000 m.
- Tropopause (11–20 km): Speed of sound is constant at 295.1 m/s — isothermal layer, constant temperature, constant speed of sound.
- Stratosphere (20–47 km): Speed of sound increases because temperature increases. Reaches 329.8 m/s at the stratopause (47 km).
- Mesosphere: Speed of sound decreases again with falling temperature, reaching approximately 282.5 m/s at 80 km.
The Mach number is defined as M = V/c, where V is the object's speed and c is the local speed of sound at altitude. Because the speed of sound decreases with altitude in the troposphere, an aircraft flying at the same true airspeed reaches a higher Mach number at altitude than at sea level — this is why aircraft have both indicated airspeed and Mach number limits.
The speed of sound is an essential output of this standard atmosphere calculator — available for any altitude in all four tools. At sea level the speed of sound is 340.29 m/s; at the tropopause the speed of sound falls to its minimum of 295.1 m/s; and the speed of sound returns to 329.8 m/s at the stratopause where the atmosphere is warmest above the troposphere.
Types of Altitude in Aviation and Engineering
There are six distinct altitude types used in aviation and aerospace engineering, each measuring a different aspect of an aircraft's position:
- Indicated altitude: The altitude shown directly on a barometric altimeter. Accurate only when the altimeter is set to local QNH (sea-level pressure) and conditions match ISA standard. This is indicated altitude.
- Pressure altitude: The altitude where ISA pressure equals your station pressure (altimeter set to 1013.25 hPa / 29.92 inHg). Used above the transition altitude and for aircraft performance calculations. Pressure altitude is independent of temperature.
- Density altitude: The ISA altitude where density equals actual density. Combines the effects of both pressure and temperature. The most performance-relevant altitude type for engines, rotors, and aerodynamics. This density altitude calculator computes it precisely.
- True altitude: Actual height above mean sea level (MSL), corrected for non-standard temperature and pressure. Used for terrain clearance and obstacle avoidance.
- Absolute altitude: Height above ground level (AGL) — the actual distance between the aircraft and the terrain directly below it.
- Geometric vs geopotential altitude: Geometric altitude is the true physical height above the ellipsoid. Geopotential altitude accounts for the variation in gravitational acceleration with height — the ISA uses geopotential altitude. The difference between the two is negligible below 20 km but significant at very high altitudes.
Standard Atmosphere Reference Table — ISA Properties by Altitude
The table in Tab 4 above shows complete ISA atmospheric properties from −1,000 m to 80,000 m. Each row is colour-coded by layer — blue for the troposphere, indigo for the tropopause, amber for the stratosphere, red for the stratopause, and purple for the mesosphere. The tropopause boundary at 11,000 m is clearly marked — note the temperature stops decreasing here, the speed of sound reaches its minimum at 295.1 m/s, and the lapse rate becomes zero (isothermal). The table shows how density drops by nearly four orders of magnitude from sea level (1.225 kg/m³) to 80 km (1.85×10⁻⁵ kg/m³).
How to Calculate Density Altitude — Step-by-Step
Example 1: Hot summer day at sea-level airport (Mode A)
- Given: PA = 0 m, OAT = 35°C = 308.15 K
- ISA temperature at PA = 0 m: T_ISA = 288.15 K (15°C)
- ISA pressure at PA = 0 m: P = 101,325 Pa
- Actual density: ρ = P/(R×T) = 101,325/(287.058×308.15) = 1.1459 kg/m³
- ISA sea-level density: ρ₀ = 1.225 kg/m³ → actual density is lower → DA > 0 m
- Find h where ρ_ISA(h) = 1.1459 kg/m³ via bisection
- Result: Density Altitude ≈ 1,200 m (3,940 ft)
- Simplified check: DA ≈ 0 + 120×(35−15) = 120×20 = 2,400 ft ≈ 732 m (approximate only)
- Interpretation: at this density altitude, air behaves as if you are at 1,200 m in standard conditions — not at sea level
Example 2: Denver, Colorado — Mode B (station conditions)
- Given: P_station = 83,400 Pa, T = 20°C = 293.15 K
- Find pressure altitude: solve isaPressure(h) = 83,400 Pa via bisection → PA ≈ 1,600 m (5,249 ft)
- Compute actual density: ρ = 83,400/(287.058×293.15) = 0.9912 kg/m³
- ISA temperature at 1,600 m: 288.15 − 0.0065×1600 = 277.75 K = 4.6°C
- OAT (20°C) > ISA temp (4.6°C) → DA > PA
- Find h where ρ_ISA(h) = 0.9912 kg/m³ → DA ≈ 2,100 m (6,890 ft)
- ISA deviation: ΔT = 20 − 4.6 = +15.4°C above ISA → high density altitude
Example 3: Cold winter at altitude (Mode A)
- Given: PA = 2,000 m, OAT = −20°C = 253.15 K
- ISA temperature at 2,000 m: 288.15 − 0.0065×2000 = 275.15 K = 2.0°C
- OAT (−20°C) much less than ISA (2°C) → cold dense air → DA < PA
- ISA pressure at 2,000 m: 79,501 Pa
- Actual density: ρ = 79,501/(287.058×253.15) = 1.0944 kg/m³
- ISA density at 2,000 m: 79,501/(287.058×275.15) = 1.0066 kg/m³
- Actual density (1.0944) > ISA at 2,000 m (1.0066) → find lower altitude where ρ_ISA = 1.0944 → DA ≈ 1,050 m (3,445 ft)
- Interpretation: the cold air makes the air denser — density altitude is about 950 m below the actual pressure altitude
Common Questions About Density Altitude
As air temperature increases, density altitude will increase
As air temperature increases, density altitude will increase because warmer air is less dense (from the ideal gas law: ρ = P/RT, as T increases, ρ decreases at constant pressure). Lower density corresponds to a higher altitude in the standard atmosphere. This is why density altitude is always highest on hot days and at high-elevation airports on summer afternoons — the combination of elevation, heat, and sometimes humidity can push density altitude far above the actual field elevation.
High density altitude meaning
High density altitude means the air is less dense than standard — it is the air equivalent of being at a higher altitude in standard conditions. All aerodynamic and thermodynamic performance that depends on air mass is degraded. The ISA model and this density altitude calculator quantify exactly how much.
Low density altitude meaning
Low density altitude means denser-than-standard air — the air behaves as if you are at a lower ISA altitude. Cold temperatures are the most common cause. Performance is better than your actual elevation would suggest on a standard day.
Pressure altitude vs density altitude — when they are equal
Pressure altitude equals density altitude when OAT equals the ISA standard temperature at that pressure altitude — approximately 15 − 0.00198×PA_ft (°C). Any temperature deviation above ISA standard increases density altitude above pressure altitude; any temperature below ISA standard decreases density altitude below pressure altitude. This pressure altitude vs density altitude relationship is the foundation of density altitude calculation.
Worked Examples — Six Full Step-by-Step Problems
Problem 1: ISA properties at 8,000 m
- Layer: Troposphere (0–11,000 m), lapse rate L = −0.0065 K/m
- T = 288.15 + (−0.0065)×8000 = 288.15 − 52.0 = 236.15 K = −37.0°C
- P = 101325 × (236.15/288.15)^(9.80665/(0.0065×287.058)) = 101325 × (0.8195)^5.2561 = 35,600 Pa = 356.0 hPa
- ρ = 35,600/(287.058×236.15) = 0.5260 kg/m³
- c = √(1.4×287.058×236.15) = √(94,894) = 308.1 m/s
- Density ratio σ = 0.5260/1.225 = 0.4294; Pressure ratio δ = 35,600/101,325 = 0.3514; Temperature ratio θ = 236.15/288.15 = 0.8196
Problem 2: Speed of sound at 35,000 ft (10,668 m) — commercial cruise
- Convert: 35,000 ft × 0.3048 = 10,668 m — still in troposphere
- T = 288.15 − 0.0065×10,668 = 288.15 − 69.34 = 218.81 K = −54.34°C
- Speed of sound c = √(1.4 × 287.058 × 218.81) = √(87,977) = 296.6 m/s (578 knots)
- At sea level: 340.3 m/s. Reduction: 340.3 − 296.6 = 43.7 m/s (12.8% slower speed of sound at cruise altitude)
Problem 3: Pressure altitude from QNH = 1005 hPa (below standard)
- P = 1005 hPa = 100,500 Pa (below standard 101,325 Pa → PA positive)
- Find h: isaPressure(h) = 100,500 Pa via bisection
- At h=70m: P ≈ 101,325×(288.15−0.0065×70/288.15)^5.256 ≈ 100,535 Pa ✓
- Pressure altitude ≈ 70 m (230 ft)
- Interpretation: 1,005 hPa is slightly below standard SL pressure → pressure altitude is slightly above sea level (lower pressure = higher PA)
Problem 4: Density altitude at tropopause conditions (11,000 m, ISA day)
- PA = 11,000 m, OAT = −56.5°C = 216.65 K (exactly ISA standard at tropopause base)
- OAT = ISA temp at PA → density altitude = pressure altitude
- DA = 11,000 m (36,089 ft) — they are equal when OAT equals ISA standard
- This demonstrates: when OAT = T_ISA at PA, DA = PA always
Problem 5: Kinematic viscosity at 5,000 m
- T = 288.15 − 0.0065×5000 = 255.65 K = −17.5°C
- Dynamic viscosity (Sutherland's): μ = 1.716×10⁻⁵ × (255.65/273.15)^1.5 × (383.55/366.05) = 1.628×10⁻⁵ Pa·s
- Density at 5,000 m: ρ = 0.736 kg/m³
- Kinematic viscosity: ν = μ/ρ = 1.628×10⁻⁵/0.736 = 2.21×10⁻⁵ m²/s
- Compare to sea level: ν_SL = 1.461×10⁻⁵ m²/s → 51% higher at 5,000 m (lower density has greater effect than reduced viscosity)
Problem 6: Density altitude — negative result (below sea level equivalent)
- Location: below sea level (Death Valley), elevation −86 m. P = 102,700 Pa, T = 45°C = 318.15 K
- Actual density: ρ = 102,700/(287.058×318.15) = 1.1236 kg/m³
- ISA sea-level density: 1.225 kg/m³ → actual is lower than SL → DA > 0 m despite being below sea level
- Find h where ρ_ISA = 1.1236 → DA ≈ +950 m (+3,117 ft)
- Even at 86 m below sea level, a 45°C day produces density altitude nearly 1 km above sea level
Common Questions About Density Altitude and the Standard Atmosphere
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