Gravitational Force Calculator – F = G·m₁m₂/r² (Free)
Estimate gravitational force between two masses.
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Quick answer
A gravitational force calculator applies Newton’s law of universal gravitation: F = G · m₁ · m₂ / r², where G ≈ 6.674 × 10⁻¹¹ N·m²/kg² is the universal gravitational constant.
Enter both masses in kilograms and the centre-to-centre distance in metres to get the attractive force in newtons—valid for point masses or spherically symmetric bodies outside their surfaces.
It is a classical (non-relativistic) result; very small distances, very large masses near light speed, or strong gravity regimes need general relativity rather than this formula.
A gravitational force calculator applies Newton’s law of universal gravitation: F = G · m₁ · m₂ ÷ r², where G ≈ 6.674 × 10⁻¹¹ N·m²/kg² is the universal gravitational constant. Enter both masses in kilograms and the centre-to-centre distance in metres to get the attractive force in newtons—free, instant, and tuned for physics homework, exam prep, and quick orbital estimates.
Result
Enter values and click calculate.
Formula
F = G x (m1 x m2) / r^2
Explanation
Gravitational Force Calculator applies Newton’s law of universal gravitation, F = G · m₁ · m₂ / r², with G ≈ 6.674 × 10⁻¹¹ N·m²/kg². Enter both masses in kilograms and the centre-to-centre distance in metres; the calculator returns the attractive force in newtons. The formula treats each body as a point mass or, equivalently, a spherically symmetric body viewed from outside its surface.
Distance dominates the result because of the inverse-square term: doubling r divides the force by four, while doubling either mass only doubles the force. That single fact explains why orbital mechanics is so sensitive to radius and why surface gravity changes appreciably with altitude even though planetary masses are huge.
Use this tool for homework, exam prep, and quick astrophysics estimates—Earth–Moon attraction, Earth–Sun attraction, satellites at orbital radius, and similar two-body setups. It is a classical (non-relativistic) result; very strong gravity regimes near compact objects or relativistic speeds require general relativity rather than Newtonian gravitation.
How to Use
- Enter or choose Mass 1, Mass 2, and Distance as indicated.
- Use the units shown under each field (for example kg, m, cm, years).
- Click Calculate to run the F = G x (m1 x m2) / r^2 formula.
- Read the result and compare with alternate values if you want scenario-based planning.
Example
Sample inputs: Mass 1 = 5.972e+24, Mass 2 = 7.342e+22, Distance = 384400000
Calculated result: Unable to generate sample output for this formula.
You can replace these values with your own numbers to calculate a real-world result instantly.
What is gravitational force?
Gravitational force is the mutual attraction every pair of masses exerts on each other. Newton’s law of universal gravitation states that the magnitude of this force is proportional to the product of the two masses and inversely proportional to the square of the distance between their centres of mass. The force always points along the line joining the two bodies and is attractive in classical mechanics.
Newton’s law of universal gravitation (formula)
The formula is F = G · m₁ · m₂ / r², with the universal gravitational constant G = 6.674 × 10⁻¹¹ N·m²/kg². Treat each body as a point mass (or use the centre of mass for spherically symmetric bodies viewed from outside). Use SI units throughout and the result naturally comes out in newtons.
How to calculate gravitational force
- Convert both masses to kilograms.
- Convert the separation to metres—use centre-to-centre distance for spherical bodies.
- Compute F = (G · m₁ · m₂) ÷ r² with G ≈ 6.674 × 10⁻¹¹.
- Read the result in newtons; convert to other units only outside the formula.
Worked examples
| Scenario | m₁ (kg) | m₂ (kg) | r (m) | F (N) ≈ |
|---|---|---|---|---|
| Two 1 kg balls, 1 m apart | 1 | 1 | 1 | 6.674 × 10⁻¹¹ |
| Earth ↔ Moon | 5.972 × 10²⁴ | 7.342 × 10²² | 3.844 × 10⁸ | 1.98 × 10²⁰ |
| Earth ↔ Sun | 5.972 × 10²⁴ | 1.989 × 10³⁰ | 1.496 × 10¹¹ | 3.54 × 10²² |
Reproduce any row by entering the same masses and distance into the calculator above. Differences in the last decimal are normal due to rounded astronomical constants.
Why distance matters more than mass
Because of the inverse-square term r², doubling the distance between the bodies makes the force one quarter, while doubling either mass only doubles the force. This is why orbits depend strongly on radius and why gravity drops off so quickly with altitude even though Earth’s mass is enormous.
Common mistakes
- Forgetting r²: dividing by r instead of r² is the single most common source of wrong answers.
- Wrong units: entering masses in grams or distance in kilometres without converting; G is defined in SI, so use kg and m.
- Surface vs centre distance: for planets, r is the centre-to-centre distance, not the surface separation.
- Treating the formula as relativistic: Newton’s law is an excellent approximation for everyday and most astronomical scales, but extreme regimes (very close to black holes, near light speed) need general relativity.
Related physics tools on this site
For Newton’s second law (F = m·a), use the force calculator. When the question is about contact pressure rather than gravitational pull, see the pressure calculator. For motion that follows once you know the force, jump to the acceleration calculator or velocity calculator, and for energy reasoning use the kinetic energy calculator.
FAQ
What is the gravitational force formula this calculator uses?
It uses Newton’s law of universal gravitation: F = G · m₁ · m₂ / r², where G ≈ 6.674 × 10⁻¹¹ N·m²/kg². Both masses go in kilograms and r in metres, so the result comes out in newtons.
What is the value of G in this calculator?
The universal gravitational constant G is approximately 6.674 × 10⁻¹¹ N·m²/kg² (CODATA recommended). Some textbooks round it to 6.67 × 10⁻¹¹; expect tiny differences in the last decimal places.
What units should I use for the masses and distance?
Use kilograms for the masses and metres for the distance between centres of mass. If your data is in grams, kilometres, or astronomical units, convert first so the SI definition of G stays valid.
Is this calculator only for planets and stars?
No. It works for any pair of masses—two atoms, two cricket balls, or two stars—although for everyday objects the resulting force is incredibly small. That is exactly why we mostly notice gravity from very large bodies like Earth.
Why does distance affect the force more strongly than mass?
Because the formula is inverse-square in r. Doubling either mass doubles the force, but doubling the distance reduces the force by a factor of four. Halving the distance multiplies the force by four.
Does this calculator account for general relativity?
No. It implements the classical Newtonian formula, which is highly accurate for normal masses and distances. For very strong gravity (near black holes or neutron stars) or very high speeds, general relativity is required.
How is gravitational force different from weight?
Weight is the gravitational force a planet exerts on a specific object at its surface, often written W = m·g. This calculator computes the more general two-body attraction. On Earth’s surface, weight is just a special case of F = G·m_Earth·m / R_Earth².
Is this gravitational force calculator free to use?
Yes. It runs in your browser with no signup, install, or paywall, like the other physics calculators on CalcSuite Pro.
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