Free Air Gravity Correction Calculator
Compute air gravity correction using validated scientific equations. See step-by-step derivations, unit analysis, and reference values.
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Where h = elevation in meters, G = gravitational constant (6.674e-11 m3/kg/s2), rho = rock density in kg/m3. The free-air gradient of 0.3086 mGal/m represents the rate of gravity decrease with elevation above the reference ellipsoid.
Last reviewed: December 2025
Worked Examples
Example 1: Mountain Gravity Station Correction
Example 2: Bouguer Anomaly at Coastal Station
Background & Theory
The Free Air Gravity Correction Calculator applies the following established principles and formulas. Earth science calculators draw on a wide range of measurement scales and physical principles that quantify natural phenomena across geological, atmospheric, and hydrological systems. Earthquake magnitude is most precisely described by the Moment Magnitude Scale (Mw), which replaced the original Richter scale for larger events. Mw is calculated as Mw = (2/3) log10(M0) − 10.7, where M0 is the seismic moment in dyne-centimeters. The Richter scale, while still referenced colloquially, is a local magnitude (ML) measurement derived from peak seismograph amplitude at a standard 100 km distance. Wind intensity is classified using the Beaufort Scale, a 13-point empirical scale (0–12) relating wind speed in knots to observable sea and land effects, with Beaufort 12 corresponding to hurricane-force winds above 64 knots. Tropical cyclone intensity is further categorized by the Saffir-Simpson Hurricane Wind Scale, which assigns Categories 1 through 5 based on sustained wind speed, correlating with expected structural damage. Mineral hardness is quantified on the Mohs scale (1–10), comparing scratch resistance relative to reference minerals from talc (1) to diamond (10). Soil composition analysis measures the proportions of sand, silt, and clay by particle size, alongside organic matter content, bulk density, and porosity, which together determine engineering and agricultural suitability. Seismic wave velocity in rock varies by material: P-waves travel at approximately 5–7 km/s in granite and 1.5 km/s in water, while S-waves travel at roughly 60% of P-wave speeds. Atmospheric pressure decreases with altitude according to the barometric formula: P = P0 × exp(−Mgh / RT), where M is molar mass of air, g is gravitational acceleration, h is altitude, R is the universal gas constant, and T is temperature in Kelvin. Standard sea-level pressure is 101,325 Pa. Tidal calculations use harmonic analysis of gravitational forcing by the Moon and Sun, with the principal lunar semidiurnal tidal constituent (M2) having a period of approximately 12.42 hours.
History
The history behind the Free Air Gravity Correction Calculator traces back through the following developments. The systematic study of Earth's structure and processes spans millennia, but the scientific foundations were laid in the seventeenth century. In 1669, Danish naturalist Nicolas Steno published his principles of stratigraphy, establishing the laws of superposition, original horizontality, and lateral continuity — foundational rules for reading rock layers that remain in use today. Scottish geologist James Hutton introduced the concept of uniformitarianism in 1788, proposing that geological processes observable in the present have operated throughout Earth's history at broadly consistent rates. This idea of deep time challenged prevailing biblical chronologies and set the stage for modern geology. Charles Lyell systematized these ideas in his landmark three-volume work Principles of Geology, published beginning in 1830, which directly influenced Charles Darwin's thinking on biological evolution during the voyage of the Beagle. The nineteenth century saw growing curiosity about continental shapes, but a coherent theory awaited Alfred Wegener, a German meteorologist who proposed continental drift in 1912, arguing that the continents had once formed a supercontinent he called Pangaea. His evidence included matching fossil records and geological formations across the Atlantic, but his mechanism was disputed for decades. The theory gained acceptance in the 1960s when seafloor spreading was confirmed through paleomagnetic studies, and plate tectonics emerged as the unifying framework of modern geoscience. The United States Geological Survey was established by Congress in 1879 to classify public lands and examine the geological structure, mineral resources, and products of the national domain. The twentieth century brought instrumental advances, including the global seismograph network deployed after World War II, initially to monitor nuclear tests, which dramatically improved earthquake detection and characterization. Satellite Earth observation began in earnest with the Landsat program launched in 1972, enabling continuous global monitoring of land use, glacier retreat, and vegetation patterns. Today, GPS networks, LIDAR scanning, and ocean-floor mapping provide centimeter-scale precision for tracking tectonic motion, sea level rise, and volcanic deformation in near real time.
Frequently Asked Questions
Formula
Free-Air Correction = 0.3086 x h (mGal) | Bouguer Correction = 2piGrho*h
Where h = elevation in meters, G = gravitational constant (6.674e-11 m3/kg/s2), rho = rock density in kg/m3. The free-air gradient of 0.3086 mGal/m represents the rate of gravity decrease with elevation above the reference ellipsoid.
Worked Examples
Example 1: Mountain Gravity Station Correction
Problem: A gravity measurement of 979,500 mGal is recorded at elevation 1200 m, latitude 40 degrees. Calculate the free-air correction and free-air anomaly.
Solution: Free-air correction = 0.3086 x 1200 = 370.32 mGal\nNormal gravity at 40 deg = 978032.7 x (1 + 0.0053024 x sin2(40) - 0.0000058 x sin2(80))\n= 978032.7 x (1 + 0.002189 - 0.0000056) = 980175.0 mGal\nFree-air anomaly = 979500 - 980175.0 + 370.32 = -304.68 mGal
Result: Free-Air Correction: +370.32 mGal | Free-Air Anomaly: -304.68 mGal
Example 2: Bouguer Anomaly at Coastal Station
Problem: At a coastal station (elevation 50 m, latitude 30 deg), observed gravity is 979,400 mGal with rock density 2500 kg/m3. Compute corrections.
Solution: Free-air correction = 0.3086 x 50 = 15.43 mGal\nBouguer correction = 2 x pi x 6.674e-11 x 2500 x 50 x 1e5 = 5.24 mGal\nNormal gravity at 30 deg = 978032.7 x (1 + 0.001326 - 0.0000044) = 979329.7 mGal\nFree-air anomaly = 979400 - 979329.7 + 15.43 = 85.73 mGal\nBouguer anomaly = 85.73 - 5.24 = 80.49 mGal
Result: Free-Air: +15.43 mGal | Bouguer: -5.24 mGal | Bouguer Anomaly: +80.49 mGal
Frequently Asked Questions
What is the free-air gravity correction?
The free-air gravity correction (also called the free-air reduction) accounts for the decrease in gravitational acceleration with increasing elevation above a reference surface, typically the geoid or sea level. Gravity decreases with height because the measurement point is farther from Earth's center of mass. The standard free-air gradient is approximately 0.3086 mGal per meter of elevation. This means for every meter you rise above the reference level, gravity decreases by about 0.3086 milligals. The correction is added to the observed gravity to compute what gravity would be at the reference level, removing the effect of elevation alone without considering the mass of rock between the station and the reference surface.
How is the free-air anomaly different from the Bouguer anomaly?
The free-air anomaly corrects only for the elevation difference between the observation point and the reference surface. It does not account for the gravitational attraction of the rock mass between the two surfaces. The Bouguer anomaly goes one step further by subtracting the gravitational effect of an infinite slab of rock with average crustal density (typically 2670 kg/m3) between the station and sea level. The formula for the Bouguer correction is 2 x pi x G x rho x h, where G is the gravitational constant and rho is rock density. The Bouguer anomaly is more useful for geological interpretation because it reveals subsurface density variations, while the free-air anomaly still contains the signal from topographic mass.
What is normal gravity and how is it calculated?
Normal gravity is the theoretical gravitational acceleration at any point on the reference ellipsoid, which approximates Earth's shape. It varies with latitude because the Earth is an oblate spheroid (flattened at the poles) and rotates. At the equator, normal gravity is about 978,032 mGal, and at the poles it is approximately 983,218 mGal, a difference of about 5,186 mGal. The International Gravity Formula (GRS80) calculates normal gravity using: g = 978032.7 x (1 + 0.0053024 sin2(phi) - 0.0000058 sin2(2phi)) mGal, where phi is geodetic latitude. This formula accounts for both the centrifugal effect of Earth's rotation and the equatorial bulge. Gravity anomalies are computed relative to this normal gravity field.
Why is rock density important in gravity corrections?
Rock density is a critical parameter in the Bouguer correction because it determines the gravitational attraction of the rock slab between the observation point and the reference level. The standard assumed density is 2670 kg/m3, representing average upper continental crust composed primarily of granite and granodiorite. Using incorrect density leads to systematic errors in the Bouguer anomaly. In areas with volcanic rock (density ~2900 kg/m3) or sedimentary basins (density ~2200-2400 kg/m3), the standard density may be inappropriate. The Nettleton method determines optimal density by selecting the value that minimizes correlation between the Bouguer anomaly and topography. Density errors become more significant at higher elevations, where the Bouguer correction magnitude is larger.
What are practical applications of free-air gravity corrections?
Free-air gravity corrections are essential in geophysics and geodesy for numerous practical applications. In mineral exploration, gravity surveys corrected for free-air and Bouguer effects reveal subsurface density anomalies that may indicate ore deposits, cavities, or geological structures. In petroleum exploration, gravity data helps map sedimentary basin depth and locate salt domes. Geodetic applications include determining the geoid shape for precise GPS height conversions. In volcanology, temporal gravity changes corrected for elevation indicate magma movement beneath volcanoes. Civil engineering uses gravity surveys to detect underground voids, abandoned mines, and karst features. Archaeologists employ microgravity surveys to find buried structures. The free-air anomaly itself is important for studying isostatic compensation and tectonic processes.
Does Free Air Gravity Correction Calculator work offline?
Once the page is loaded, the calculation logic runs entirely in your browser. If you have already opened the page, most calculators will continue to work even if your internet connection is lost, since no server requests are needed for computation.
References
Reviewed by Daniel Agrici, Founder & Lead Developer · Editorial policy