Gravitational Force
Newton's law of universal gravitation
About this calculator
The Gravitational Force Calculator applies Newton's law of universal gravitation F = G·m₁·m₂/r² with G = 6.67430×10⁻¹¹ N·m²/kg² (CODATA 2018) to two point masses. Besides the attractive force it reports each body's acceleration toward the other (a₁ = G·m₂/r², a₂ = G·m₁/r²) and the pair's gravitational potential energy U = −G·m₁·m₂/r. Masses and the centre-to-centre distance must be positive.
How to use the Gravitational Force calculator
- Enter the quantities you know, using the units shown on each field.
- Read the computed results — they update instantly as you type.
- Use the visual explanation to see how the quantities relate.
- Copy the page URL to share the exact calculation.
Common examples
- Earth (5.972×10²⁴ kg) and Moon (7.348×10²² kg) at 3.844×10⁸ m → F ≈ 1.98×10²⁰ N
- Earth–Moon: the Moon accelerates at ≈ 0.0027 m/s² toward Earth, Earth at only ≈ 3.3×10⁻⁵ m/s²
- Two 70 kg people 1 m apart → F ≈ 3.27×10⁻⁷ N — gravity is astonishingly weak at human scale
- m₁ = 1000 kg, m₂ = 2000 kg, r = 10 m → F ≈ 1.335×10⁻⁶ N, U ≈ −1.335×10⁻⁵ J
Frequently asked questions
How does the Gravitational Force calculator work?
Enter the known quantities and the calculator applies the governing physical law or scientific formula to find the unknowns, stating the equation it used and the units of every result. Computations run at high precision.
When would I use the Gravitational Force calculator?
It suits physics and chemistry homework, lab work, engineering estimates, and any time you want to explore how changing one quantity affects the others in a well-defined scientific relationship.
How accurate are the results?
The formula itself is evaluated at 30 significant digits of precision. Keep in mind that idealized models — such as neglecting friction, air resistance or measurement error — bound the real-world accuracy more than the arithmetic does.
Can I share a specific calculation with someone else?
Yes. Every value you enter updates the URL, so copying the address bar and sharing the link reopens the exact same calculation for whoever clicks it.