Acceleration Due To Gravity Interactive Calculator

Designing for altitude — whether you're building a high-altitude balloon payload, planning a rocket trajectory, or calibrating an IMU — requires knowing exactly how much gravity you're working with at a given height above Earth's surface. Use this Acceleration Due to Gravity Calculator to calculate gravitational acceleration g(h) and gravitational force using altitude and mass as inputs. It matters across aerospace engineering, satellite design, precision instrumentation, and any lifting or actuation system deployed above sea level. This page includes the inverse-square law formula, a worked example, full theory, and an FAQ.

What is acceleration due to gravity at altitude?

Acceleration due to gravity at altitude is how strongly Earth pulls an object toward its centre at a given height above sea level. The higher you go, the weaker the pull — but it decreases more slowly than most people expect.

Simple Explanation

Think of gravity like the brightness of a light bulb — the further away you stand, the dimmer it gets. Earth's gravity works the same way: double your distance from Earth's centre and gravity drops to a quarter of its original strength. Even at the height of the International Space Station, gravity is still about 89% as strong as it is on the ground.

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Gravity vs Altitude Diagram

How to Use This Calculator

1. Enter your altitude value and select the unit — kilometres, metres, feet, or miles.
2. Enter the mass of your object and select the unit — kilograms, pounds, or grams. Leave it at 1 kg if you only need g(h).
3. Review the inputs to confirm altitude and mass are correct for your scenario.
4. Click Calculate to see your result.

Acceleration Due to Gravity Calculator

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Equations

Use the formula below to calculate gravitational acceleration at any altitude above Earth's surface.

Use the formula below to calculate the gravitational force acting on a mass at altitude.

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

Newton's Law of Universal Gravitation states that the gravitational force between two masses is proportional to the product of their masses and inversely proportional to the square of the distance between them. At Earth's surface, the distance from the centre is approximately 6,371 km. As altitude increases, the total distance from Earth's centre increases, and because of the inverse-square relationship, gravity weakens — but far more slowly than most people expect. Even at the altitude of the International Space Station (408 km), gravity is still about 89% of its sea-level value.

The Weightlessness Misconception

Astronauts aboard the ISS appear weightless, but this is not because gravity is absent — at 408 km altitude, g is still approximately 8.69 m/s². The sensation of weightlessness occurs because both the astronaut and the space station are in continuous free fall around Earth. They are falling at the same rate as their orbital path curves away beneath them, so there is no contact force between the astronaut and the station floor. This is the same physics as being in a falling elevator — during the fall, you feel weightless, but gravity is acting on you the entire time.

Engineering Applications

Accurate knowledge of gravitational acceleration at altitude is critical in several engineering fields. In aerospace engineering, trajectory calculations for rockets and re-entry vehicles must account for continuously changing g values throughout ascent and descent. In precision instrumentation, accelerometers and inertial measurement units (IMUs) are calibrated to local gravity — instruments used at high altitude or on aircraft require correction factors.

In satellite design, orbital mechanics calculations use g(h) to determine the velocity required for stable orbit at a given altitude: orbital velocity v = √(g(h) × r) where r is the distance from Earth's centre. For linear actuator and automation systems deployed on high-altitude research platforms or aircraft, the reduced gravitational load at altitude affects force requirements for lifting and positioning mechanisms.

Earth's Radius and Model Assumptions

This calculator uses Earth's mean radius of 6,371 km, which is an average of the equatorial radius (6,378 km) and polar radius (6,357 km). Earth is an oblate spheroid — slightly flattened at the poles — so actual gravitational acceleration varies by latitude as well as altitude. At sea level, g ranges from approximately 9.832 m/s² at the poles to 9.780 m/s² at the equator, a difference of about 0.5%. For most engineering applications this latitude variation is secondary to altitude effects, but high-precision geodetic and navigation systems account for both.

Frequently Asked Questions