What is Acceleration Due to Gravity at Altitude?

Acceleration due to gravity is not a fixed constant across the entire universe, or even across the vertical profile of Earth. While we commonly use 9.80665 m/s² as the standard value for physics calculations at sea level, this force weakens as you move further away from the Earth's center of mass. This phenomenon is governed by Newton's Law of Universal Gravitation.

The Acceleration Due to Gravity at Altitude Calculator allows you to determine exactly how much gravitational pull an object experiences at a specific height above the mean sea level. Whether you are studying atmospheric science, aerospace engineering, or basic physics, understanding this decrease is vital for calculating orbital mechanics and weight changes at high altitudes.

How the Calculation Works

The gravitational force follows an inverse-square law. The formula used for this calculation is:

g_h = g₀ * (R / (R + h))²

Where:

• g_h is the acceleration at altitude h.
• g₀ is the standard gravity at sea level (9.80665 m/s²).
• R is the mean radius of the Earth (approximately 6,371 kilometers).
• h is the height or altitude above the Earth's surface.

Why Gravity Changes with Height

As you increase your altitude, the distance between you and the Earth's center of mass increases. Since gravity is inversely proportional to the square of the distance, even small increases in altitude result in a measurable reduction in gravitational acceleration. For example, at the top of Mount Everest, gravity is roughly 0.28% less than at sea level. In the International Space Station (ISS), which orbits at about 400 km, gravity is still about 90% of what it is on the surface—the "weightlessness" astronauts feel is actually due to being in constant freefall (orbit), not a lack of gravity.

Frequently Asked Questions

What is the Earth's average radius?

For most scientific calculations, the mean radius of Earth is considered to be 6,371 kilometers (3,958.8 miles). However, since Earth is an oblate spheroid, the radius is slightly larger at the equator than at the poles.

Does gravity change at different locations on Earth?

Yes. Factors such as the Earth's rotation (centrifugal force), local geology (density of rocks), and the equatorial bulge cause gravity to vary slightly even at sea level, ranging from about 9.78 m/s² at the equator to 9.83 m/s² at the poles.

Can this be used for other planets?

Absolutely. By replacing the Earth's surface gravity (g₀) and the Earth's radius (R) with the values for another celestial body (like Mars or the Moon), you can calculate the gravitational acceleration at various altitudes above those surfaces as well.