Geopotential to Geometric Height Calculator

This calculator converts a geopotential height in meters into geometric height by accounting for the decrease of gravity with altitude through a fixed mean Earth radius. It also reports the correction between the two heights and the radius used, making the result transparent and easy to reproduce in forecasts, research notebooks, data pipelines, and engineering calculations.

Understand the two definitions of height

Geometric height describes an ordinary distance: it is the vertical separation from a reference surface measured along a radial direction. Geopotential height describes something slightly different. It scales gravitational potential energy by a conventional reference gravity, producing a height-like coordinate that is especially useful when comparing pressure surfaces and atmospheric observations. Near sea level, the two values are almost indistinguishable because gravity has changed very little. As altitude increases, gravity weakens with distance from Earth's center, so a given geopotential height corresponds to a somewhat larger geometric height. That distinction matters in upper-air sounding data, numerical weather products, satellite-related calculations, and any workflow that combines sources using different vertical coordinates. This calculator makes the convention explicit: enter geopotential height in meters, and it returns geometric height in meters, the size of the applied correction, and the Earth radius used. Keeping all four values together prevents a corrected altitude from being mistaken for an unchanged source measurement later in a pipeline or report.

Apply the spherical-Earth conversion correctly

The calculation uses the spherical relation z = R H / (R - H), where H is geopotential height, z is geometric height, and R is Earth's mean radius. This capability fixes R at 6,371,000 meters so every run is deterministic and independently reproducible. The denominator is the important part: it represents how gravitational acceleration changes as distance from Earth's center increases. At low altitude, H is tiny relative to R and the correction is small. At higher altitude, the correction grows and should not be discarded casually. The model deliberately does not ask for latitude, local ellipsoid parameters, or a gravity-field model. Those inputs belong to a more specialized geodetic conversion and would imply precision this spherical approximation does not provide. The input must be a finite JSON number and must remain below the stated radius, because reaching that value makes the formula singular. The returned correction is geometric height minus geopotential height, allowing you to inspect the practical effect without repeating the subtraction yourself.

Interpret and use the returned result

Use the geometric result when another calculation expects physical distance above the reference surface rather than a gravity-normalized coordinate. For example, an atmospheric profile may label levels using geopotential meters, while a visualization, line-of-sight estimate, or geometric model expects meters of spatial altitude. Convert the values before combining those datasets, and preserve the original geopotential height alongside the converted value. The correction field provides a useful quality check: close to the surface it should be modest, while it becomes progressively larger for upper-atmosphere levels. The fixed radius field documents the assumption for reviewers and downstream systems. This result should not be presented as a survey-grade elevation or an ellipsoidal height from GNSS. Earth is not a perfect sphere, local gravity varies with latitude and geology, and meteorological geopotential may be tied to conventions beyond this compact model. For routine spherical conversion, however, the formula is transparent, fast, stable, and well suited to repeated automated processing through the API at $0.002 per request.