Free Acceleration due to Gravity Calculator

When curious about how objects fall on different planets, a Gravitational Acceleration Calculator (also known as a G Value Calculator or Gravity on Planets Calculator) provides instant answers. This free online tool helps you determine the acceleration due to gravity on any celestial body based on its mass and radius, making it an essential resource for students, educators, and space enthusiasts alike.

Defining Gravitational Acceleration

Gravitational acceleration, denoted by $g$, is the rate at which a body accelerates when falling freely under the sole influence of gravity. Its standard unit is $\text{m/s}^2$. As a vector quantity, $g$ always points toward the center of the attracting celestial body. Importantly, the value of $g$ is independent of the falling object’s mass—a feather and a hammer experience the same acceleration in a vacuum.

The Core Formula

The magnitude of gravitational acceleration at the surface of any spherical body is derived from Newton’s law of universal gravitation:

$$g = \frac{G \cdot M}{R^2}$$

where:

• $M$ = mass of the celestial body (kg)
• $R$ = radius of the celestial body (m)
• $G = 6.674 \times 10^{-11}\ \text{m}^3\ \text{kg}^{-1}\ \text{s}^{-2}$ (universal gravitational constant)

This equation clearly shows that $g$ depends only on the planet’s mass and radius, not on any property of the falling object.

Calculating $g$ on Earth

To find the gravitational acceleration on Earth, you can substitute the planet’s known parameters directly into the formula:

• Mass of Earth, $M = 5.972 \times 10^{24}\ \text{kg}$
• Mean radius of Earth, $R = 6.371 \times 10^{6}\ \text{m}$

Performing the calculation:

$$g_{\text{Earth}} = \frac{(6.674 \times 10^{-11}) \cdot (5.972 \times 10^{24})}{(6.371 \times 10^{6})^2} \approx 9.8\ \text{m/s}^2$$

This familiar value ($9.8\ \text{m/s}^2$) is what we experience as Earth’s surface gravity. The same method applies to any other world. For example:

• Mars: $M = 6.4185 \times 10^{23}\ \text{kg}$, $R = 3.390 \times 10^{6}\ \text{m}$ → $g \approx 3.7\ \text{m/s}^2$
• Moon: $M = 7.346 \times 10^{22}\ \text{kg}$, $R = 1.737 \times 10^{6}\ \text{m}$ → $g \approx 1.6\ \text{m/s}^2$

Using the Free Fall Acceleration Calculator

Operating this Gravitational Acceleration Calculator is remarkably simple:

1. Enter the mass of the celestial body in kilograms (e.g., $5.972 \times 10^{24}$ for Earth).
2. Enter its radius in meters (e.g., $6.371 \times 10^{6}$); many versions of the G Value Calculator also accept kilometers and convert automatically.
3. Click the calculate button—the tool instantly outputs the gravitational acceleration in $\text{m/s}^2$.

By eliminating manual arithmetic, this Gravity on Planets Calculator lets you explore gravity across moons, planets, asteroids, or even hypothetical objects. Whether you are studying free‑fall motion or planning interplanetary missions, the Free Fall Acceleration Calculator gives you fast, accurate results with minimal effort.