Gravitational Force Calculator — Newton's Law of Gravitation
Compute the gravitational force between any two masses separated by a known distance using Newton's universal law of gravitation. The calculator also shows the resulting acceleration on each body. The Earth–Moon system is pre-loaded as a worked example.
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How does this calculator work?
F = G·m₁·m₂/r² with G = 6.674 × 10⁻¹¹ N·m²/kg². For Earth–Moon (masses 5.97 × 10²⁴ kg and 7.34 × 10²² kg, distance 3.84 × 10⁸ m) the attractive force is ≈ 1.98 × 10²⁰ N. Force grows with each mass and falls with the square of the distance.
Formula
How this is calculated
Newton's law of universal gravitation states that every pair of masses attracts each other with a force proportional to the product of their masses and inversely proportional to the square of their centre-to-centre separation. The constant of proportionality G = 6.674 × 10⁻¹¹ N·m²/kg² is extremely small, which is why gravity is the weakest of the four fundamental forces — yet its infinite range and universal attraction make it dominant on astronomical scales.
The inverse-square dependence on r means that doubling the separation reduces the force to one quarter; halving it quadruples it. By Newton's third law both bodies experience an equal and opposite force along their connecting line. The acceleration experienced by each body is F/m, so the lighter body accelerates far more than the heavier one — the Moon accelerates toward Earth at about 0.0027 m/s² while Earth accelerates toward the Moon at only ~3 × 10⁻⁵ m/s².
This formula assumes point masses or uniform spherical bodies (the result then equals that of a point mass at each body's centre of mass). General relativistic corrections are negligible except near extremely compact objects such as neutron stars or black holes.
Frequently asked questions
G = 6.674 × 10⁻¹¹ N·m²/kg² is the proportionality constant in Newton's law of universal gravitation. First measured by Henry Cavendish in 1798 with a torsion balance, it is one of the most difficult fundamental constants to pin down — it carries a relative uncertainty of about 2.2 × 10⁻⁵ in the CODATA 2018 recommended values.
Doubling the distance quarters the force; tripling it reduces it to one ninth; halving it quadruples it. This rapid fall-off explains why gravitational influence from even very massive bodies becomes tiny at large separations, even though it never drops to exactly zero.
Surface gravity g = G·M_Earth/R_Earth² ≈ 9.81 m/s². Set m₁ = 5.972 × 10²⁴ kg (Earth), m₂ = 1 kg, r = 6,371,000 m (Earth's mean radius) and the force in newtons numerically equals g for any 1 kg test mass, since F/m₂ = g.
Also known as
TG we-Calculate Editorial Team. (2026). Gravitational Force Calculator — Newton's Law of Gravitation [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/gravitational-force-calculator
TG we-Calculate Editorial Team. "Gravitational Force Calculator — Newton's Law of Gravitation." TG we-Calculate. 2026. https://we-calculate.com/calculator/gravitational-force-calculator.
TG we-Calculate Editorial Team, "Gravitational Force Calculator — Newton's Law of Gravitation," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/gravitational-force-calculator
@misc{wecalculate_gravitational_force_calculator, title = {Gravitational Force Calculator — Newton's Law of Gravitation}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/gravitational-force-calculator}}, year = {2026}, note = {TG we-Calculate} }
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