Altitude from pressure calculator

This calculator takes the pressure you measured and the sea-level pressure you are reducing against — a METAR QNH, an altimeter setting, or a 1013.25 hPa standard-day field — and evaluates h = (T0 / L) × [1 − (P / Psl)^(R L / g)] with the ICAO constants T0 = 288.15 K, L = 0.0065 K/m, specific gas constant 287.05287 J K−1 kg−1 and g = 9.80665 m s−2. Zero or negative values on either pressure are rejected as invalid_input because the power is not defined there.

What the hypsometric equation of the standard atmosphere actually computes

Both pressures must be strictly positive: a zero or negative reading would take a non-positive base of a fractional power, which is not a physical static pressure and is rejected as invalid_input. This single-layer troposphere inversion is the formula used by consumer barometric altimeters and by most altitude-from-pressure classroom problems; above about eleven kilometres the real ICAO atmosphere changes lapse rate and a multi-layer inversion is required.

Input contract, units, response shape, and error behaviour

Both values share that unit; the hypsometric ratio is dimensionless, so mixing hectopascals with inches of mercury in the same request is a client error, not something the solver silently repairs. If either pressure is zero or negative the task fails with a message that the hypsometric equation is not defined for zero or negative pressure — those failures are not billed. POST a JSON body with two required finite numbers: pressure, the measured station or sensor reading (aliases measured_pressure, station_pressure, p, p_station, and observed_pressure); and sea_level_pressure, the reference you are reducing against (aliases slp, p0, p_sea, qnh, and sea_level). An optional pressure_unit field accepts the closed set hpa, pa, kpa, mbar, inhg, mmhg, atm, or psi and defaults to hpa, the unit METAR QNH and most MEMS barometers already use. Each numeric field may arrive as a JSON number or as a strict numeric string; missing fields, empty strings, non-finite values, and magnitudes above 1e15 fail with invalid_input naming the field. On success the body echoes pressure, sea_level_pressure, and the resolved pressure_unit; it then publishes pressure_pa and sea_level_pressure_pa, the dimensionless pressure_ratio, altitude_m, altitude_ft, altitude_km, result as an alias of altitude_m, method set to isa_hypsometric, model set to ICAO_ISA_troposphere, plus formula and equation strings filled with the rounded numbers. Pricing is a flat $0.002 per successful request with unit item; failed validation does not consume prepaid balance.

Field use, the eleven-kilometre ceiling, and searches this page is not answering

Keep both readings inside the published open interval above zero, prefer JSON numbers over pre-formatted strings, and remember that this single-layer model approaches 44330 metres as station pressure tends toward zero — that ceiling is the tropopause-scale height of the ISA troposphere, not a claim that the stratosphere has been inverted. This page targets people searching for an altitude from pressure hypsometric calculator, a barometric height from station pressure and sea-level pressure, or the ISA power-law altimeter formula online. It is not a pressure-unit converter, not a cabin-altitude solver from differential pressure, and not a station-pressure reduction to sea level. Round-trip checks are easy: form the ratio, raise it to 0.190263169, subtract from one, multiply by 44330.76923076923, and confirm altitude_m matches within the same twelve-decimal rounding.