force gravity calculator

What This Force Gravity Calculator Does

The force gravity calculator helps you find the force of attraction between masses. Depending on your scenario, you can use one of two common physics models:

• Universal gravitational force: Best for two objects separated by a known distance (such as planets, moons, satellites, or any two masses).
• Weight force: Best near the surface of a planet where gravity is approximately constant.

Both models output force in newtons (N), the SI unit of force.

Formulas Used

1) Universal Gravitation

F = G × m₁ × m₂ / r²

• F = gravitational force (N)
• G = gravitational constant (approximately 6.67430 × 10⁻¹¹ N·m²/kg²)
• m₁, m₂ = masses (kg)
• r = center-to-center distance between the masses (m)

2) Weight Force Near a Planet

F = m × g

• F = weight force (N)
• m = mass of object (kg)
• g = local gravitational acceleration (m/s²)

On Earth, a typical average value is g = 9.80665 m/s² (often rounded to 9.81).

Worked Examples

Example A: Person on Earth (Universal Formula)

If a person has mass 80 kg, Earth has mass 5.972 × 10²⁴ kg, and Earth radius is 6.371 × 10⁶ m, the universal formula gives a force close to 785 N. That agrees with the simpler weight formula (80 × 9.81 ≈ 785 N).

Example B: Weight Formula

An object with mass 15 kg on Earth has weight:

F = 15 × 9.80665 = 147.09975 N

So the force is about 147.10 N.

When to Use Each Method

• Use universal gravitation when distance between two objects is a major variable.
• Use F = mg when you are close to a planet's surface and just need practical weight force.

Common Input Mistakes

• Using radius instead of distance between centers: In universal gravitation, r is always center-to-center.
• Entering distance in km instead of m: Convert first (1 km = 1000 m).
• Negative or zero distance: Not physically valid for this formula.
• Confusing mass with weight: Mass is in kg; weight is force in N.

Quick Planet g Reference (Approx.)

• Earth: 9.81 m/s²
• Moon: 1.62 m/s²
• Mars: 3.71 m/s²
• Jupiter: 24.79 m/s²

Try these values in weight mode to compare how your weight changes across celestial bodies.

FAQ

Is gravity force always attractive?

With normal mass in classical physics, yes. Gravity pulls masses together.

Why does force change with distance so strongly?

Because force is proportional to 1 / r². Doubling distance reduces force to one-fourth.

Can I use this for satellites and orbital estimates?

Yes, for force estimates. For full orbital analysis, you also need velocity, energy, and orbital mechanics equations.