Bouguer Correction Calculator
Our geology & geophysics calculator computes bouguer correction accurately. Enter measurements for results with formulas and error analysis.
Calculator
Adjust values & calculateStandard crustal density: 2,670 kg/m³
Formula
The Bouguer plate correction equals 2πGρh, which simplifies to approximately 0.04193 × ρ × h in milligals, where ρ is rock density in kg/m³ and h is elevation in meters. The free-air correction is 0.3086 × h mGal. The Bouguer anomaly combines these corrections with observed and theoretical gravity.
Last reviewed: December 2025
Worked Examples
Example 1: Mountain Station Survey
Example 2: Sedimentary Basin Survey
Background & Theory
The Bouguer 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 Bouguer 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
Bouguer Correction = 0.04193 × ρ × h (mGal)
The Bouguer plate correction equals 2πGρh, which simplifies to approximately 0.04193 × ρ × h in milligals, where ρ is rock density in kg/m³ and h is elevation in meters. The free-air correction is 0.3086 × h mGal. The Bouguer anomaly combines these corrections with observed and theoretical gravity.
Worked Examples
Example 1: Mountain Station Survey
Problem: A gravity station at 1,500 m elevation with observed gravity 979,450 mGal and rock density 2,670 kg/m³.
Solution: Free-air correction = 0.3086 × 1,500 = 462.90 mGal\nBouguer correction = 0.04193 × 2,670 × 1,500 = 167.93 mGal\nCorrected gravity = 979,450 + 462.90 - 167.93 = 979,744.97 mGal
Result: Free-air: +462.90 mGal | Bouguer: -167.93 mGal
Example 2: Sedimentary Basin Survey
Problem: A station at 200 m elevation in a sedimentary area (density 2,400 kg/m³). Calculate the corrections.
Solution: Free-air correction = 0.3086 × 200 = 61.72 mGal\nBouguer correction = 0.04193 × 2,400 × 200 = 20.13 mGal\nNet correction = 61.72 - 20.13 = 41.59 mGal
Result: Free-air: +61.72 mGal | Bouguer: -20.13 mGal | Net: +41.59 mGal
Frequently Asked Questions
What is the Bouguer correction in gravity surveying?
The Bouguer correction (also called the Bouguer plate correction) accounts for the gravitational attraction of the rock mass between the observation point and the reference datum (usually sea level). Named after French mathematician Pierre Bouguer (1698-1758), this correction approximates the rock layer as an infinite horizontal slab (Bouguer plate) of uniform thickness and density. The formula is deltaG_B = 2 pi G rho h, where G is the gravitational constant, rho is the rock density, and h is the elevation above the datum. In milligals, this simplifies to approximately 0.04193 times rho times h. The Bouguer correction is subtracted from the observed gravity because the rock between the station and datum adds extra gravitational pull that must be removed to isolate subsurface density anomalies.
What is the free-air correction and how does it differ from Bouguer?
The free-air correction accounts for the decrease in gravitational acceleration with increasing distance from Earth's center, without considering any intervening mass. It assumes there is only air (free space) between the observation point and the datum. The free-air correction rate is approximately 0.3086 mGal per meter of elevation. For a station 100 meters above sea level, the free-air correction is +30.86 mGal (added to observed gravity because gravity decreases with altitude). The key difference is that the free-air correction only addresses the change in distance from Earth's center, while the Bouguer correction additionally accounts for the gravitational pull of the rock mass between the station and the datum. Together, they form the Bouguer anomaly: observed gravity plus free-air correction minus Bouguer correction minus theoretical gravity.
What rock density should I use for the Bouguer correction?
The standard density used for the Bouguer correction is 2,670 kg/m³ (2.67 g/cm³), which represents the average density of continental crustal rocks, approximately equivalent to granite. However, the appropriate density depends on the local geology. Sedimentary basins may require lower densities (2,200-2,500 kg/m³), while areas dominated by basalt or gabbro may need higher values (2,800-3,000 kg/m³). For precise surveys, the optimal density can be determined using the Nettleton method, which involves computing Bouguer anomalies across a topographic feature using different densities and selecting the one that minimizes correlation between the anomaly and topography. Alternatively, density can be estimated from borehole gravity measurements, laboratory measurements of rock samples, or published density data for the local geological formations.
What is a Bouguer anomaly and what does it tell us?
A Bouguer anomaly is the difference between the observed gravity at a station (after applying free-air and Bouguer corrections) and the theoretical gravity at that location. It reveals lateral variations in subsurface density. A positive Bouguer anomaly indicates denser material than expected below the surface, which could signify dense igneous intrusions, mineral ore bodies, or oceanic crust. A negative Bouguer anomaly indicates less dense material, suggesting features like sedimentary basins, salt domes, granitic batholiths, or mountain roots (isostatic compensation). Bouguer anomaly maps are essential tools in petroleum exploration for identifying sedimentary basins, in mining for locating dense ore bodies, in geotechnical engineering for mapping bedrock depth, and in academic research for studying crustal structure and isostasy.
How accurate are the results from Bouguer Correction Calculator?
All calculations use established mathematical formulas and are performed with high-precision arithmetic. Results are accurate to the precision shown. For critical decisions in finance, medicine, or engineering, always verify results with a qualified professional.
How do I get the most accurate result?
Enter values as precisely as possible using the correct units for each field. Check that you have selected the right unit (e.g. kilograms vs pounds, meters vs feet) before calculating. Rounding inputs early can reduce output precision.
References
Reviewed by Daniel Agrici, Founder & Lead Developer · Editorial policy