Acceleration due to Gravity Calculator
Calculate gravitational acceleration on any celestial body using mass and radius
Calculate Gravitational Acceleration
Select a celestial body to use preset values or choose custom to enter your own
Mass of the celestial body
Radius of the celestial body
Gravitational Acceleration Results
Formula used: g = GM/R²
Input values: Mass: 0.000e+0 kg, Radius: 0.000e+0 m
G (Universal gravitational constant): 6.674 × 10⁻¹¹ m³ kg⁻¹ s⁻²
Gravity Analysis
Example Calculation
Earth's Gravitational Acceleration
Mass of Earth: M = 5.972 × 10²⁴ kg
Radius of Earth: R = 6.371 × 10⁶ m
Universal gravitational constant: G = 6.674 × 10⁻¹¹ m³ kg⁻¹ s⁻²
Calculation
g = GM/R²
g = (6.674 × 10⁻¹¹) × (5.972 × 10²⁴) / (6.371 × 10⁶)²
g = 3.986 × 10¹⁴ / 4.058 × 10¹³
g = 9.82 m/s²
Gravity Comparison
Physics Facts
Gravity is independent of object mass - all objects fall at the same rate
Gravity decreases with distance squared (inverse square law)
Earth's gravity varies slightly by location due to altitude and density
At Earth's center, gravitational acceleration would be zero
Understanding Acceleration due to Gravity
What is Gravitational Acceleration?
Acceleration due to gravity (g) is the acceleration experienced by any object when falling freely under the influence of gravity alone. It depends only on the mass and radius of the celestial body, not on the mass of the falling object.
Key Characteristics
- •Directed toward the center of the celestial body
- •Independent of the falling object's mass
- •Decreases with altitude (distance from center)
- •Measured in meters per second squared (m/s²)
The Formula
g = GM/R²
- g: Acceleration due to gravity (m/s²)
- G: Universal gravitational constant (6.674 × 10⁻¹¹ m³ kg⁻¹ s⁻²)
- M: Mass of the celestial body (kg)
- R: Radius of the celestial body (m)
Note: This formula gives the surface gravity. At different altitudes, replace R with (R + h) where h is the height above the surface.
Applications
Space Exploration
Calculate landing conditions and fuel requirements for different planets
Engineering
Design structures and vehicles for different gravitational environments
Astronomy
Study celestial bodies and their properties using gravity measurements