Gravitational Force Calculator
Calculate gravitational force between two masses using Newton's law F = G·m₁·m₂/r². Enter masses in kg and distance in meters for instant force in newtons with charts and breakdown.
About This Calculator
The Gravitational Force Calculator computes the attractive force between any two objects with mass using Newton's law of universal gravitation. This tool is essential for students studying physics, engineers working with orbital mechanics, and anyone curious about the forces that govern planetary motion, tides, and falling objects.
Newton's law states that every particle of matter in the universe attracts every other particle with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. The formula is F = G × m₁ × m₂ / r², where G = 6.67430 × 10⁻¹¹ N·m²/kg² is the universal gravitational constant. This inverse-square law means that doubling the distance reduces the force to one-quarter, making gravity a short-range but powerful force at planetary scales.
For example, the gravitational force between Earth (5.972 × 10²⁴ kg) and a 70 kg person standing on the surface (6,371 km from Earth's center) is approximately 687 N, which equals the person's weight. The force between Earth and the Sun (1.989 × 10³⁰ kg at 149.6 million km) is about 3.54 × 10²² N, which keeps Earth in its orbit.
How to use this calculator
Enter Mass 1 and Mass 2 in kilograms. You can use scientific notation (e.g., 5.972e24 for Earth's mass, 1.989e30 for the Sun's mass). Enter the center-to-center distance in meters. Click Calculate to see the gravitational force in newtons, along with a detailed breakdown and interactive charts.
Applications
Gravitational force calculations are used in astronomy (planetary orbits, satellite trajectories), geophysics (gravitational anomalies), engineering (tidal forces, spacecraft design), and education (understanding fundamental physics concepts).
Frequently Asked Questions
What is gravitational force?
Gravitational force is an attractive force between any two objects with mass. It is one of the four fundamental forces of nature and follows Newton's law of universal gravitation: every mass attracts every other mass with a force proportional to the product of their masses and inversely proportional to the square of the distance between them.
What is the formula for gravitational force?
The gravitational force formula is F = G × m₁ × m₂ / r², where G = 6.67430 × 10⁻¹¹ N·m²/kg² is the gravitational constant, m₁ and m₂ are the masses in kilograms, and r is the distance between their centers in meters.
What units does this calculator use?
This calculator uses SI units: masses in kilograms (kg), distance in meters (m), and force output in newtons (N). You can enter values in scientific notation like 5.972e24 for Earth's mass.
Can I calculate the force between Earth and another object?
Yes, enter Earth's mass (5.972 × 10²⁴ kg) for Mass 1, the object's mass in kg for Mass 2, and the distance from Earth's center in meters (Earth's radius is 6,371,000 m) to get the gravitational force.
What is the gravitational constant G?
The gravitational constant G = 6.67430 × 10⁻¹¹ N·m²/kg² is a fundamental physical constant that appears in Newton's law of universal gravitation. It was first measured by Henry Cavendish in 1798 using a torsion balance experiment.
Why does distance affect gravitational force so strongly?
Gravitational force follows an inverse-square law, meaning it decreases with the square of the distance. If you double the distance, the force becomes only one-quarter as strong. This is why gravity on Earth's surface feels strong but quickly weakens as you move away.
Is gravitational force always attractive?
Yes, gravitational force is always attractive — it never repels. Unlike electric forces which can attract or repel, gravity only pulls masses together. This is why planets orbit stars and why objects fall toward Earth.
What is the difference between mass and weight?
Mass is the amount of matter in an object, measured in kilograms. Weight is the gravitational force exerted on that mass, measured in newtons. Your weight = your mass × local gravitational acceleration. On Earth, a 70 kg person weighs about 687 N.