Barometric Atmospheric Pressure by Altitude
Estimates atmospheric pressure in hPa at an arbitrary altitude in meters using the simplified standard atmosphere formula.
—
Atmospheric pressure vs. altitude
The International Standard Atmosphere (ISA) describes how pressure drops with altitude through P = P₀·(1 − 0.0065·h/T₀)^5.255, where P₀ = 101.325 kPa (sea-level pressure), T₀ = 288.15 K (15 °C), and the lapse rate runs at 6.5 °C per kilometer in the troposphere. Near the surface pressure drops by roughly 12% per 1000 m, and by about 5500 m it has fallen to half. Some reference points: sea level 101.3 kPa, São Paulo (760 m) ≈ 92.7 kPa, Serra paulistana ≈ 950 hPa, and La Paz (3640 m) ≈ 65 kPa, which is low enough to bring on altitude sickness in visitors who haven't acclimatized. This is the formula that altimeters, weather models and climbing tables all rely on.
Applications
You'll find it behind aircraft barometric altimeters (QNH reference), smartphone barometric GPS (where pairing pressure with GPS pulls vertical accuracy down to ±1 m), mountaineering (estimating boiling point and how much supplemental oxygen you'll need), weather forecasting (synoptic maps reduce pressure to sea level), and engineering (HVAC and combustion derate at altitude as air density falls).
FAQ
Why does the formula stop working above ~11 km? That's where the troposphere ends. Above the tropopause the lapse rate shifts (the lower stratosphere is roughly isothermal), so the ISA switches to a different equation for each layer.
Does temperature matter? It does. A warmer air column is less dense, so the real pressure at a given altitude can run 1-3% above the ISA value. That's the reason altimeters get a QNH calibration before each flight.
Why does water boil faster in the mountains? Lower pressure drags the boiling point down. Water boils at 100 °C at sea level but at around 88 °C in La Paz, which is exactly why food up there takes longer to cook through.
Related Tools
Aero Pressure Density Altitude Calculator
Computes pressure altitude from local QNH and density altitude from pressure altitude and ISA temperature deviation in feet for aviators.
Fluid Pressure by Depth
Calculates hydrostatic pressure P=ρ·g·h in pascals from fluid density and depth.
Blood Pressure Classifier (SBC)
Classifies blood pressure (optimal, normal, pre-hypertension, stages 1/2/3) per Brazilian SBC guidelines.
Silo Horizontal Pressure (Janssen)
Calculate the horizontal pressure the stored product exerts on a silo wall by the Janssen equation, p_h = (γ·D)/(4·μ)·(1 − e^(−4·μ·K·z/D)), from the unit weight γ, diameter D, product-wall friction coefficient μ, lateral pressure ratio K and depth z. Horizontal pressure is the outward thrust grains apply against the silo walls — the load that sizes the wall for hoop tension (in cylindrical silos, the wall acts as a ring under internal pressure). It relates to vertical pressure by the lateral pressure ratio K (p_h = K·p_v), typically 0.3-0.6 for granular products and depending on the product's internal friction angle. Like vertical pressure, horizontal pressure tends to an asymptotic value with depth, by the same wall-friction effect of Janssen theory. Horizontal pressure is decisive for the thickness and reinforcement of concrete silo walls and the plating of steel silos, and rises significantly during DISCHARGE (dynamic overpressure), which codes handle with amplification factors. Enter the unit weight, diameter, friction coefficient, lateral pressure ratio and depth.
Aircraft Climb Time
Compute an aircraft's climb time, t = Δaltitude/rate of climb (ROC), dividing the altitude gain by the rate of climb (in ft/min or m/min). It estimates how long the aircraft takes to reach cruise altitude — used in flight planning, climb fuel burn and traffic separation. The rate of climb decreases with altitude, so the result is an average estimate. Enter the altitude gain and the rate of climb.
Vessel Head Axial Force
Calculate the total axial force the internal pressure exerts on a pressure vessel's cover (or head), F = P · (π·D²/4), from the internal pressure P (MPa) and the internal diameter D (mm); the result is in N. A vessel's internal pressure acts on the ENTIRE internal surface, and on the cover (or closure flange) it generates an axial force tending to PUSH the cover outward — equal to pressure times the cross-sectional area. This force can be ENORMOUS: a modest 1 MPa (10 bar) pressure in a 1-metre-diameter vessel generates a force of nearly 800 kN (80 tonnes!) trying to blow off the cover. This force is what the closure-flange BOLTS (or the head weld) must resist — so flanged pressure vessels have many robust bolts, and computing this force is the starting point of sizing the flange, bolts and gasket. The force also explains why one must NEVER open a still-pressurized vessel: the cover can be hurled with lethal force (serious accidents happen this way, especially with autoclaves and filters). Knowing the cover force is essential for safe closure design and operating procedures. Enter the internal pressure and the diameter.
The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.