Example 1
Earth and a 70 kg person, r = 6371000 m.
Gravitational Force Calculator
Enter two masses and the center-to-center distance. You get the force that pulls them together. Earth and a 70 kg person at r = 6371 km is 687 N, the same order as weight at g ≈ 9.82 m/s².
Field g: g = GM/r². Near the surface: Ep = m·g·h. In orbit this F is centripetal force. Motion at constant g: free fall.
Result
Constant G (N·m²/kg², optional), Mass m₁ (kg), Mass m₂ (kg) and Distance r (m). The result shows up here.
How it works
Any two masses pull on each other. Newton’s formula is F = G·m₁·m₂/r². The force runs along the line of centers and is the same on both bodies. Only the acceleration a = F/m differs. In SI, G is 6.67430×10⁻¹¹ N·m²/kg². You can leave G empty: the calculator uses that value.
Take Earth M = 5.972×10²⁴ kg, a 70 kg person, and r = 6.371×10⁶ m, Earth’s radius. F = 6.67430×10⁻¹¹ × 5.972×10²⁴ × 70 / (6.371×10⁶)² = 687 N. That is the same order as 70 × 9.82. One kilogram at the same surface is 9.82 N.
Force falls with the square of distance. Twice the r means a quarter of the F. At 400 km altitude (r ≈ 6.771×10⁶ m) the same person feels about 608 N, not zero. “Weightlessness” on a station is falling together along the orbit, not gravity switching off.
Two 1500 kg cars 3 m apart attract with F ≈ 1.67×10⁻⁵ N. You do not feel that with a hand. Two 1 kg masses 10 cm apart give 6.67×10⁻⁹ N. In a lab you only see it on a sensitive balance.
r is center to center, not surface to surface. Masses and r must be positive. The result is in newtons, or pounds-force with the US switch. If you type your own G, it stays in SI scientific form.
From this F you can get g = F/m₂, or open the g = GM/r² page. On a circular orbit the same F plays the role of centripetal force m v²/r. That is where first cosmic velocity comes from.
How to use
- Leave G empty unless the problem asks for another constant. Empty means 6.67430×10⁻¹¹.
- Type m₁ and m₂ in kilograms. For Earth and a person: 5.972e24 and 70.
- Type r between centers in meters, for example 6371000, not “from the surface”.
- Click Calculate. 5.972×10²⁴ kg, 70 kg and 6371 km give 687 N.
- For the field alone, open g = GM/r². Here you stay with the force between two masses.
Formula
F = G · m1 · m2 / r2
Default G = 6.67430×10−11 N·m2/kg2. The force is mutual along r.
Letters in F = G m₁ m₂ / r²
Newton: F = G·m₁·m₂/r². Earth and a 70 kg person at r = 6371 km give 687 N, the same order as weight at g ≈ 9.82 m/s².
- F
- Mutual force in newtons. 6.67430×10⁻¹¹ × 5.972×10²⁴ × 70 / (6.371×10⁶)² ≈ 687 N.
- G
- Constant 6.67430×10⁻¹¹ N·m²/kg². A blank field takes that value; you do not type g = 9.82.
- m₁
- First mass in kilograms. In the example Earth is 5.972×10²⁴ kg, not 70.
- m₂
- Second mass. The 70 kg person; swapping m₁ and m₂ leaves F unchanged and only a = F/m flips.
- r
- Center-to-center distance in meters. 6.371×10⁶ m is Earth radius; r in kilometers understates F by 10⁶×10⁶.
Real-life examples
Example 2
m₂ = 0.20 kg, r = Earth radius.
Example 3
m₂ ≈ 7.35e+22 kg, r ≈ 384400000 m.
Example 4
1500 kg and 1500 kg at 3 m.
Example 5
m₂ = 500 kg, r ≈ 6771000 m.
Example 6
80 kg at r ≈ 6771000 m.
Example 7
m₁ = m₂ = 1 kg, r = 0.10 m.
Example 8
M_☉ ≈ 1.989e+30 kg, r ≈ 149600000000 m.
Example 9
Two 10 kg masses at 0.5 m.
Example 10
G = 6.67e-11, m₁ = Earth, m₂ = 1 kg.
Ways to use this calculator
- You check that 70 kg at Earth’s surface really is about 687 N.
- You compare surface weight with the force on LEO at r = 6771 km.
Frequently asked questions
How much F for Earth, 70 kg and r = 6371 km?
F = 687 N. At 1 kg on the same r you get 9.82 N, which is surface g.
What do I type in the G field?
You can type nothing. This formula uses 6.67430×10⁻¹¹. Your own G, for example 6.67e-11, is used as typed.
Is F the same on both masses?
Yes, equal and opposite. The person and Earth pull with 687 N. Earth barely accelerates because its mass is huge.
Why is r squared?
The inverse-square law. Twice as far is four times weaker. Three times as far is nine times weaker.
Is r the gap between surfaces?
No. In the formula r is the distance between centers. For Earth and a person you take Earth’s radius plus height, but height is lost in 6371 km.
How much for two 1500 kg masses at 3 m?
F ≈ 1.67×10⁻⁵ N. Two 1 kg masses at 0.10 m give 6.67×10⁻⁹ N.
How do I get g from F?
g = F/m₂, or go straight to g = GM/r² on the next page. At 70 kg and 687 N you get 9.82 m/s².
Does a comma in 5,972e24 work?
Yes. 5,972e24 and 5.972e24 are the same Earth mass.
How does this connect to an orbit?
On a circular orbit gravitational F equals m v²/r. That gives v₁ = √(GM/r) on the first cosmic velocity page.
How much F does Earth pull the Moon with at 384,400 km?
About 1.98×10²⁰ N. Moon mass ≈ 7.35×10²² kg, r ≈ 3.844×10⁸ m.
Knowledge sources
The formula is the school one. Units follow SI; NIST SP 330 and BIPM define the measures, not your result.
Page updated in 2026.