Free-Air Gravity Correction Calculator
Find the free-air gravity anomaly from an observed gravity reading, station latitude, and elevation, with no rock-density correction applied.
🛰️ What is Free-Air Gravity Correction?
The free-air gravity correction adjusts an observed gravity reading for the station's height above sea level, correcting purely for the geometric effect of distance from Earth's center of mass. Applying it to observed gravity, after also subtracting theoretical normal gravity for that latitude, produces the free-air anomaly, a gravity anomaly with no rock-density term applied at all.
Geophysicists use the free-air anomaly constantly, as the standard correction for marine gravity surveys conducted from ships, where there is no solid rock between the gravimeter and sea level to correct for. Airborne gravity surveys use the same approach. Free-air anomalies also serve as an intermediate step feeding into the Bouguer anomaly on land, and as a first-pass indicator of large-scale mass anomalies such as ocean trenches or seamounts before any density modeling is done.
A common point of confusion is mistaking the free-air anomaly for the Bouguer anomaly. The free-air anomaly corrects only for elevation and stops there, it never subtracts the gravitational pull of rock mass beneath the station. The Gravity Anomaly (Bouguer) Calculator on this site adds that additional rock-density slab correction, which is why the two anomalies can differ substantially at the same location, especially over mountains where the free-air anomaly is often strongly positive while the Bouguer anomaly turns negative.
This calculator applies the 1967 International Gravity Formula for normal gravity plus the standard free-air correction to compute the free-air anomaly directly from a station's observed gravity, latitude, and elevation, and charts how normal gravity itself varies with latitude.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — Mid-Latitude Station at Moderate Elevation
gobs = 980489.74 mGal, φ = 45°, h = 500 m
Example 2 — High Mountain Station
gobs = 977962.18 mGal, φ = 28°, h = 4500 m
Example 3 — Near-Equator Marine Station
gobs = 978055.45 mGal, φ = 5°, h = 2 m
❓ Frequently Asked Questions
🔗 Related Calculators
How do you calculate the free-air gravity anomaly?
Free-air anomaly equals observed gravity minus theoretical normal gravity at that latitude, plus the free-air correction: Delta g_FA = g_obs - g_phi + 0.3086h, where h is station elevation in meters above sea level. Unlike the Bouguer anomaly, no rock-density term is subtracted.
What is the free-air correction formula?
The free-air correction is FAC = 0.3086 x h, in milligals, where h is the station's elevation in meters above sea level. It corrects only for the geometric effect of being farther from Earth's center of mass, regardless of what material fills that space.
What is the difference between free-air anomaly and Bouguer anomaly?
The free-air anomaly corrects observed gravity for elevation only, treating the space beneath the station as empty. The Bouguer anomaly goes one step further and also subtracts the gravitational pull of the actual rock mass filling that space, using a rock-density value. Free-air anomaly is used standalone in marine and airborne surveys where no rock sits beneath the sensor.
Why is free-air anomaly typically large and positive over mountains?
Because no density correction has been applied, the visible mass excess of the mountain itself pulls the free-air anomaly strongly positive. Once the Bouguer correction subtracts that rock mass, the anomaly usually turns negative due to the low-density crustal root beneath the range.
What is a typical range for free-air anomaly values?
Over most stable terrain, free-air anomalies fall roughly between -50 and +50 mGal. Near steep mountain ranges or ocean trenches, values can swing much larger in either direction, from over +200 mGal on high mountains to strongly negative over deep subduction trenches.
Why does normal gravity depend on latitude?
Earth bulges at the equator and flattens at the poles due to rotation, and centrifugal force from that rotation is strongest at the equator. Both effects combine so theoretical (normal) gravity is lower at the equator and higher at the poles, the sin-squared latitude dependence in the 1967 International Gravity Formula.
Is free-air anomaly used for marine gravity surveys?
Yes, free-air anomaly is the standard correction for marine and airborne gravity surveys. Since there is no solid rock between the gravimeter and sea level in those settings, a Bouguer-style density correction does not apply, and the free-air anomaly is reported directly.
Do I need a rock density value for this calculator?
No. This calculator stops at the free-air correction and does not require or apply a rock-density term. If you need the additional Bouguer slab correction for a land station, use the separate Gravity Anomaly (Bouguer) Calculator.
What units does this calculator use?
Observed gravity and all correction results are in milligals (mGal), the standard gravimetry unit (1 mGal = 0.00001 m/s2). Latitude is in decimal degrees and elevation is in meters above sea level.
Can the free-air anomaly be negative?
Yes. A negative free-air anomaly indicates observed gravity is lower than the elevation-corrected theoretical value, which can occur over ocean trenches, sedimentary basins, or other regions of local mass deficit even before any density correction is applied.
Why does this calculator use the 1967 International Gravity Formula instead of WGS84?
The 1967 formula is a well-established reference standard widely used in classical gravimetry and matches the same normal-gravity model used by this site's Bouguer Anomaly Calculator, so results are directly comparable. The newer WGS84 ellipsoidal normal gravity formula gives very similar results in practice.