Acceleration Due to Gravity Calculator

Calculate the acceleration due to gravity at a given altitude using the equation:
$$g(h)=g_0{\left(\frac{R}{R+h}\right)}^2$$ where $g_0=9.81$ m/s² and $R=6.371\times {10}^6$ m.

* Enter the altitude (in meters).

Step 1: Enter Altitude

Altitude, $h$ (m):

Example: 1000 m

Calculate Gravity

Calculated Gravity

Recalculate

Acceleration Due to Gravity Calculator

Gravity is a fundamental force that governs how objects attract each other, most noticeably how Earth pulls us and other objects toward its surface. The Acceleration Due to Gravity on Earth’s surface is approximately $9.8{\text{m/s}}^2$, but this value changes slightly with altitude (and other factors like latitude and local geology). An Acceleration Due to Gravity Calculator lets you estimate how $g$ varies if you move above (or even below) Earth’s surface.

What is Acceleration Due to Gravity?

On or near Earth’s surface, the acceleration due to gravity $g$ is often treated as a constant ($9.8{\text{m/s}}^2$). However, as you move away from the surface (e.g., climbing a mountain or sending a satellite into orbit), Earth’s gravitational pull decreases slightly because the distance from Earth’s center increases.

Why Does $g$ Change with Altitude?

If you consider $r=R_{\oplus }+h$ where $R_{\oplus }$ is Earth’s mean radius ($\approx \mathrm{6,371}\text{km}$) and $h$ is your altitude above sea level, then as $h$ increases, $r$ gets bigger, making $g$ smaller. This is because gravitational attraction falls off with the square of distance.

How the Calculator Works

The Acceleration Due to Gravity Calculator typically asks for:

• Altitude (h): The height above sea level (in meters, kilometers, or feet).
• Earth’s Mean Radius (optional): Often preloaded as $\approx \mathrm{6,371}\text{km}$ but can be adjusted for more precision.
• Mass of Earth (optional): Usually a fixed constant in the calculator, $\approx 5.972\times {10}^{24}\text{kg}$.
• Gravitational Constant (G): Also a known constant ($\approx 6.674\times {10}^{-11}\text{N}\cdot {\text{m}}^2/{\text{kg}}^2$).

Then it computes the distance from Earth’s center, $r=R_{\oplus }+h$, and applies $g=\frac{GM}{r^2}$ to output the local acceleration due to gravity at that altitude.

Practical Examples of Using the Calculator

Why Use an Acceleration Due to Gravity Calculator?

• Quick Estimations: Instantly see how $g$ changes with altitude.
• Educational Insight: Understand how orbital mechanics and satellite altitudes relate to Earth’s gravitational pull.
• Geophysical Research: Fine-tune local gravity estimates for surveying or Earth science calculations.
• Astronomy & Space Exploration: Useful for planning rocket stages or analyzing gravitational fields near Earth.

Important Considerations

Conclusion

The Acceleration Due to Gravity Calculator provides a straightforward way to see how Earth’s gravitational pull decreases slightly with altitude. Whether you’re studying basic physics, planning a high-altitude balloon experiment, or just curious about how gravity changes with altitude, this tool offers quick, insightful calculations. Try inputting different altitudes and see how $g$ shifts, reinforcing your understanding of our planet’s gravitational field.