Acceleration Due To Gravity Interactive Calculator

If you’re designing for altitude—whether it’s for a balloon payload, rocket flight, or just calibrating an IMU—you need to know the local value of gravity at your working height. The Acceleration Due to Gravity Calculator here lets you determine gravitational acceleration g(h) and gravitational force using both altitude and mass. Altitude makes a noticeable difference in aerospace projects, satellite work, instrumentation, or any sort of high-elevation lifting or actuation. The page covers the relevant formulas, shows a solving example, explains the theory behind the numbers, and answers common practical questions.

What is acceleration due to gravity at altitude?

Acceleration due to gravity at altitude is simply how hard Earth pulls on something when it’s above sea level. As you move up, gravity weakens—but not as rapidly as many anticipate.

Simple Explanation

Gravity works like a light bulb’s brightness: farther away means weaker effect. If you double your distance from Earth’s center, gravity drops to one quarter. Even up where the International Space Station orbits, you’re still seeing about 89% of the surface gravity. The drop isn’t as extreme as most think.

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Gravity vs Altitude Diagram

How to Use This Calculator

1. Input your altitude and select the unit—kilometres, metres, feet, or miles.
2. Enter the object’s mass and pick the unit—kilograms, pounds, or grams. Set this to 1 kg if you just want the value of g(h).
3. Double-check that the altitude and mass match what you actually need.
4. Click Calculate. Results will show up below.

Acceleration Due to Gravity Calculator

Equations

Here’s how to figure out the strength of gravity at any given altitude using the altitude and Earth’s radius:

To get the gravitational force on a mass at altitude, use this formula:

Simple Example

Altitude: 400 km (ISS orbit). Mass: 80 kg.

g(400) = 9.80665 × (6371 / (6371 + 400))² = 9.80665 × (6371 / 6771)² ≈ 8.686 m/s²

Gravitational force: F = 80 × 8.686 ≈ 694.9 N — compared to 784.5 N at sea level.

Reduction from sea level: ≈ 11.4%.

Theory & Applications

Why Gravity Changes With Altitude

The force of gravity comes down to Newton’s law: gravity strength is proportional to mass, and inversely proportional to the square of the distance to Earth’s center. Earth’s surface is about 6,371 km from the center, so every bit of altitude adds to that distance and causes a decrease in gravitational pull. But even a few hundred kilometers up, the reduction is gradual—at the ISS’s 408 km orbit, you still have roughly 89% of surface gravity.

The Weightlessness Misconception

On the ISS, astronauts look weightless, but gravity hasn’t vanished. At 408 km, g is still 8.69 m/s². Astronauts feel weightless because they (and the station) are in the same free fall around Earth. They’re falling as fast as their orbit curves away, so there’s no normal force between astronaut and floor. The physics is the same as a person in a freely falling elevator: you’re still under gravity, but you don’t press on the floor during the fall.

Engineering Applications

If you’re building anything for aircraft, satellites, rockets, or high-altitude research, you can’t get away with just using 9.81 m/s² for g. Rocket paths and reentry trajectories need continuously updated g as the vehicle’s altitude shifts. IMUs and accelerometers for airborne or space use have to be corrected for local gravity. In satellite design, accurate values of g(h) matter for computing stable orbital speeds and required forces. For actuators used above sea level—on planes, balloons, or high remote outposts—the lower gravity will slightly reduce the force needed for lifting jobs, but usually by a small margin for most real-world projects.

Earth's Radius and Model Assumptions

This calculator uses an average Earth radius (6,371 km). Earth is slightly squashed (oblate), so if you really need to, note that there’s about a 0.5% difference in gravity from pole to equator at sea level (roughly 9.832 m/s² at the poles, 9.780 m/s² at the equator). Most engineering calculations treat this as a second-order effect, but for navigation systems and exacting geodetic work, both latitude and altitude might need accounting for.

Frequently Asked Questions

📹 Video Walkthrough — How to Use This Calculator

📹 Video Walkthrough — How to Use This Calculator