Gravity Anomaly Calculator
Free Gravity anomaly Calculator for geology & geophysics. Enter variables to compute results with formulas and detailed steps.
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Where g_obs = observed gravity (mGal), g_theo = theoretical gravity from International Gravity Formula, h = elevation (m), rho = density (kg/m^3), TC = terrain correction (mGal). The 0.3086 is the free-air gradient and 0.04193 is the Bouguer slab constant (2*pi*G in mGal units).
Last reviewed: December 2025
Worked Examples
Example 1: Mountain Station Gravity Survey
Example 2: Coastal Plain Gravity Measurement
Background & Theory
The Gravity Anomaly 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 Gravity Anomaly 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
Bouguer Anomaly = g_obs - g_theo + 0.3086*h - 0.04193*rho*h + TC
Where g_obs = observed gravity (mGal), g_theo = theoretical gravity from International Gravity Formula, h = elevation (m), rho = density (kg/m^3), TC = terrain correction (mGal). The 0.3086 is the free-air gradient and 0.04193 is the Bouguer slab constant (2*pi*G in mGal units).
Worked Examples
Example 1: Mountain Station Gravity Survey
Problem: Observed gravity is 979,600 mGal at latitude 45 degrees, elevation 1500 m, using standard density 2670 kg/m^3. Calculate the gravity anomalies.
Solution: Theoretical gravity at 45 deg = 978031.85 * (1 + 0.005278895 * sin^2(45) + 0.000023462 * sin^4(45))\n= 978031.85 * (1 + 0.002639 + 0.000006) = 980,621.25 mGal\nFree-air correction = 0.3086 * 1500 = 462.90 mGal\nBouguer correction = 0.04193 * 2670 * 1500 = 167,932.35 * 0.001 = 167.93 mGal\nFree-air anomaly = 979600 - 980621.25 + 462.90 = -558.35 mGal\nSimple Bouguer anomaly = -558.35 - 167.93 = -726.28 mGal
Result: Free-air anomaly: -558.35 mGal | Simple Bouguer anomaly: -726.28 mGal
Example 2: Coastal Plain Gravity Measurement
Problem: Observed gravity 979,100 mGal at latitude 30 degrees, elevation 50 m, density 2400 kg/m^3, terrain correction 2 mGal.
Solution: Theoretical gravity at 30 deg = 978031.85 * (1 + 0.005278895 * sin^2(30) + 0.000023462 * sin^4(30))\n= 978031.85 * (1 + 0.001320 + 0.000001) = 979,323.14 mGal\nFree-air correction = 0.3086 * 50 = 15.43 mGal\nBouguer correction = 0.04193 * 2400 * 50 = 5,031.60 * 0.001 = 5.03 mGal\nFree-air anomaly = 979100 - 979323.14 + 15.43 = -207.71 mGal\nSimple Bouguer = -207.71 - 5.03 = -212.74 mGal\nComplete Bouguer = -212.74 + 2 = -210.74 mGal
Result: Free-air: -207.71 mGal | Simple Bouguer: -212.74 mGal | Complete Bouguer: -210.74 mGal
Frequently Asked Questions
What is a gravity anomaly and why is it important?
A gravity anomaly is the difference between the observed gravitational acceleration at a point on Earth and the theoretical value expected at that location based on a simplified Earth model. Gravity anomalies reveal subsurface density variations that indicate geological structures such as ore bodies, salt domes, sedimentary basins, and fault zones. Positive anomalies indicate denser-than-expected material below the surface, while negative anomalies suggest less dense material. Gravity surveys are fundamental tools in exploration geophysics, used extensively in oil and gas exploration, mineral prospecting, groundwater studies, and tectonic research. The measurements are typically expressed in milliGals (mGal), where 1 Gal equals 1 cm/s squared.
How is the theoretical gravity at a location calculated?
Theoretical gravity is calculated using the International Gravity Formula, which models Earth as a rotating ellipsoid. The 1967 formula gives gravity as g = 978031.85 * (1 + 0.005278895 * sin^2(lat) + 0.000023462 * sin^4(lat)) in mGal. This accounts for Earth being an oblate spheroid with greater radius at the equator, causing gravity to increase from approximately 978,000 mGal at the equator to about 983,200 mGal at the poles. The variation is due to two competing effects: the centrifugal force from Earth rotation (reducing gravity at equator) and the equatorial bulge (increasing distance from center). More recent formulations like the WGS84 gravity formula provide improved accuracy with updated geodetic constants.
How are gravity anomaly maps used in exploration?
Gravity anomaly maps are interpreted to identify subsurface geological structures of economic or scientific interest. In petroleum exploration, negative Bouguer anomalies can indicate sedimentary basins with significant hydrocarbon potential, while localized positive anomalies might reveal basement highs that create structural traps. In mineral exploration, dense ore bodies like iron, chromite, and massive sulfides produce positive gravity anomalies. Salt domes, which trap oil, appear as negative anomalies because salt is less dense than surrounding sediments. Regional gravity maps help delineate tectonic boundaries, crustal thickness variations, and ancient rift zones. Modern gravity gradiometry and satellite gravity data complement ground surveys for large-scale geological mapping applications.
Can I use Gravity Anomaly Calculator on a mobile device?
Yes. All calculators on NovaCalculator are fully responsive and work on smartphones, tablets, and desktops. The layout adapts automatically to your screen size.
How do I interpret the result?
Results are displayed with a label and unit to help you understand the output. Many calculators include a short explanation or classification below the result (for example, a BMI category or risk level). Refer to the worked examples section on this page for real-world context.
Why might my result differ from another tool or reference?
Differences typically arise from rounding conventions, the specific version of a formula (for example, simple vs compound interest), or unit inconsistencies between inputs. Check that both tools are using the same formula variant and the same units. The References section links to the authoritative source behind the formula used here.
References
Reviewed by Daniel Agrici, Founder & Lead Developer · Editorial policy