Gravitational Force Calculator

Before Newton, gravity was thought to be a property of certain "heavy" objects falling toward their natural place — an Aristotelian view that held for nearly 2000 years. Galileo's 1604 inclined-plane experiments showed all objects accelerate equally under gravity — the seed of the equivalence principle Einstein would later use.

Isaac Newton made the universal leap in his 1687 Principia: the same force that drops an apple also holds the Moon in orbit, with magnitude F = G m₁ m₂ / r². He could not, however, measure G directly. That came 111 years later in 1798 when Henry Cavendish used a torsion-balance pendulum to weigh two lead balls' mutual attraction to within 1% of today's value, 6.674 × 10⁻¹¹ N·m²/kg².

In 1843 James Prescott Joule established the mechanical equivalent of heat, threading thermodynamics into the same energy framework gravity would soon join. Hermann von Helmholtz's 1847 conservation-of-energy paper unified mechanical, gravitational, electrical and thermal energy. Meanwhile Robert Hooke's 1660 spring law — F = -kx — quietly hinted that all linear restoring forces share a common form, which we exploit in the spring-constant calculator linked from this suite.

In 1851 George Stokes derived the viscous-drag law that lets us compute terminal velocity for raindrops and skydivers — a friction analogue to gravity that always shows up the moment objects fall through fluids. The 19th-century synthesis culminated in James Clerk Maxwell's 1873 unification of electricity and magnetism into a field theory — a model that would inspire Einstein to recast gravity itself as a field-theoretic phenomenon.

Einstein's general relativity (1915) replaced Newton's instantaneous force with curved spacetime. For Earth-scale physics the two agree to 1 part in 10⁹, which is why our calculator uses Newton's formula. For Mercury's perihelion precession (43 arcsec/century), GPS clock corrections (38 µs/day), and gravitational lensing of background quasars, only GR fits the data.

In 2015 LIGO directly detected gravitational waves from a binary black-hole merger 1.3 billion light-years away — a wobble of 10⁻¹⁸ m, smaller than a proton's diameter, exactly as Einstein predicted in 1916. As of 2026 the LIGO-Virgo-KAGRA network catalogues several hundred such events a year, including neutron-star inspirals that produce both gravitational and electromagnetic signals.

Why this calculator exists: in 2026 a CubeSat propulsion engineer in Bangalore sizing the delta-v budget for a Lagrange-point insertion needs F = GM_earth m_sat / r² at a dozen orbital altitudes in under a minute. A printed astrodynamics table can't scroll; this page can. That's the reason it's here.