Gravity Calculator
Gravity Change Graph
The graph shows how gravity changes with altitude above Earth.
Example Data Table
| Case | Mass | Radius or Distance | Altitude | Approx Gravity |
|---|---|---|---|---|
| Earth surface | 5.97219 × 10²⁴ kg | 6,371,000 m | 0 m | 9.8203 m/s² |
| Earth at 10 km | 5.97219 × 10²⁴ kg | 6,371,000 m | 10,000 m | 9.7895 m/s² |
| Moon surface | 7.342 × 10²² kg | 1,737,400 m | 0 m | 1.624 m/s² |
| Mars surface | 6.4171 × 10²³ kg | 3,389,500 m | 0 m | 3.727 m/s² |
Formula Used
Newton Gravity
g = GM / r²
Here, G is the universal gravitational constant. M is mass. r is the distance from the center of the body.
Altitude Method
r = R + h
R is body radius. h is altitude. Gravity decreases as the total radius increases.
Rotation Correction
g apparent = GM / r² − ω²r cos²φ
This adjusts gravity for the outward effect caused by planetary rotation.
Pendulum Method
g = 4π²L / T²
This estimates gravity from pendulum length and measured period.
How to Use This Calculator
- Select the gravity method that matches your problem.
- Enter mass, radius, altitude, latitude, distance, or pendulum values.
- Use SI units for the most reliable result.
- Press the calculate button.
- Read the result above the form.
- Check the step by step explanation.
- Download the result as CSV or PDF when needed.
Acceleration of Gravity Guide
What Gravity Acceleration Means
Acceleration of gravity tells how quickly an object speeds up when gravity acts alone. Near Earth, this value is close to 9.81 m/s². It is not exactly the same everywhere. Height, latitude, mass, radius, and rotation can change it. This calculator helps you study those changes with several physics methods.
Why the Value Changes
Gravity follows an inverse square relation. When distance from a planet center grows, gravity becomes weaker. A mountain top has slightly lower gravity than sea level. The Moon has lower gravity because its mass is much smaller than Earth. Large planets can create stronger gravity when their mass is high.
Latitude and Rotation Effects
Earth is not a perfect sphere. It is wider near the equator. Rotation also creates a small outward effect. This effect is strongest at the equator. It is nearly zero at the poles. Therefore, measured gravity is usually lower near the equator. It is often higher near the poles.
Pendulum Measurement
A pendulum can estimate local gravity. The length and period are measured. The formula assumes small swing angles. Large angles introduce error. Air resistance and timing error also affect the result. Still, the pendulum method is useful in classrooms. It links motion, time, and gravity in a direct way.
Best Use Cases
Use Newton mode for planets, moons, and altitude problems. Use latitude mode for Earth location studies. Use rotation mode for apparent gravity on a spinning body. Use pendulum mode for lab measurements. Use orbital mode for satellites and spacecraft. Always keep units consistent. Small unit mistakes can create very large answer errors.
FAQs
1. What is acceleration of gravity?
It is the acceleration produced by gravitational force. Near Earth, it is about 9.81 m/s². The value changes with altitude, latitude, mass, and distance from the center of the attracting body.
2. Why is gravity lower at higher altitude?
Gravity weakens as distance from the planet center increases. The inverse square law controls this change. A higher altitude means a larger radius, so the calculated gravity becomes smaller.
3. Which units should I enter?
Use kilograms for mass, meters for radius, meters for altitude, degrees for latitude, meters for pendulum length, and seconds for period. SI units keep the formulas consistent.
4. Can I calculate gravity on other planets?
Yes. Choose the Newton method. Enter the planet mass and radius. The calculator will estimate surface gravity or gravity at altitude using the same universal formula.
5. What is the pendulum method?
The pendulum method uses length and period to estimate gravity. It works best when the swing angle is small and the period is measured carefully over many oscillations.
6. Why does latitude affect gravity?
Latitude matters because Earth rotates and is slightly flattened. Rotation reduces apparent gravity near the equator. The polar radius is also smaller, which can increase gravity near the poles.
7. What is standard gravity?
Standard gravity is defined as 9.80665 m/s². It is a reference value used in physics, engineering, aviation, and measurement systems. Local gravity can be slightly different.
8. Why are my results different from textbook values?
Textbook values may use rounded constants, simplified planet data, or sea level assumptions. Your input values, altitude correction, latitude correction, and chosen method can all change the final answer.