Acceleration Due to Gravity
Find gravitational acceleration g at any altitude and latitude using the international formula. Free gravity calculator for physics students and geophysics.
About This Calculator
The Acceleration Due to Gravity Calculator helps physics students, geophysicists, engineers, and science enthusiasts compute the precise value of gravitational acceleration g at any altitude above Earth's surface. By entering the altitude in meters and latitude in degrees, the calculator applies the internationally recognized Geodetic Reference System 1980 (GRS80) formula with free-air altitude correction to deliver accurate results.
The calculation uses the international gravity formula: g(φ) = 9.780327 × (1 + 0.0053024 × sin²(φ) − 0.0000058 × sin²(2φ)) to compute the theoretical gravity at sea level for any latitude. This accounts for Earth's rotation (centrifugal effect) and its oblate spheroid shape. The free-air correction Δg = −0.000003086 × h is then applied to adjust for altitude, where h is the height above sea level in meters. If a mass is provided, the calculator also computes the object's weight (W = mg) at both sea level and altitude.
Gravity varies measurably across Earth's surface. At the equator (0° latitude), g is approximately 9.780 m/s² due to stronger centrifugal force and greater distance from Earth's center. At the poles (90° latitude), g reaches approximately 9.832 m/s². Altitude effects are smaller but still significant in geophysics — the free-air correction is used in gravity surveys for mineral and oil exploration, where precise gravity measurements reveal subsurface density variations. This calculator is ideal for physics homework, geophysics field work, and understanding how everyday weight changes with altitude.
Frequently Asked Questions
What is acceleration due to gravity?
Acceleration due to gravity (g) is the acceleration experienced by an object when it falls freely under the influence of Earth's gravity alone. Its standard value at sea level and 45° latitude is approximately 9.80665 m/s². It varies with latitude (due to Earth's rotation and shape) and altitude (decreasing with height above sea level).
How does altitude affect gravitational acceleration?
Gravitational acceleration decreases with increasing altitude due to the greater distance from Earth's center. The free-air correction is approximately -0.003086 m/s² per meter of altitude gain. At 10 km (typical commercial aircraft cruising altitude), gravity is about 9.78 m/s² compared to 9.81 m/s² at sea level.
Why does latitude affect gravity?
Gravity varies with latitude due to two factors: Earth's rotation creates centrifugal force that counteracts gravity (strongest at the equator, zero at the poles), and Earth is an oblate spheroid — the equatorial radius is about 21 km larger than the polar radius, placing the equator farther from Earth's center. These effects make gravity about 0.052 m/s² stronger at the poles than at the equator.
What is the international gravity formula?
The international gravity formula (Geodetic Reference System 1980) calculates theoretical gravity at sea level as a function of latitude: g(φ) = 9.780327 × (1 + 0.0053024 × sin²(φ) - 0.0000058 × sin²(2φ)) m/s², where φ is the latitude in degrees. The free-air correction subtracts 0.000003086 × h m/s² for altitude h in meters.
How much does gravity change from sea level to Mount Everest's summit?
At the summit of Mount Everest (8,848 m), gravitational acceleration is approximately 9.78 m/s² compared to 9.81 m/s² at sea level — a reduction of about 0.25%. This is why objects weigh slightly less at high altitudes, though the difference is imperceptible for everyday activities.
What is the difference between g and G?
Lowercase g (9.80665 m/s²) represents the acceleration due to gravity at Earth's surface — a measure of how fast objects accelerate when falling. Uppercase G (6.67430 × 10⁻¹¹ N·m²/kg²) is the universal gravitational constant that appears in Newton's law of universal gravitation. G is a fundamental constant of nature, while g is a derived quantity that depends on the mass and radius of the celestial body.
How is gravitational acceleration calculated on other planets?
On any celestial body, surface gravity is calculated using the formula g = G × M / R², where G is the universal gravitational constant, M is the body's mass in kg, and R is its radius in meters. For example, the Moon's surface gravity is about 1.62 m/s² (1/6 of Earth's), and Mars' surface gravity is about 3.71 m/s².