Gravitational Force Calculator

Newton's law of universal gravitation states that every pair of masses attracts each other. The force magnitude equals the gravitational constant multiplied by both masses and divided by the square of the distance between their centers. This calculator uses G equal to 6.6743 × 10^-11 newton square meters per kilogram squared, with masses entered in kilograms and distance in meters. The resulting force is expressed in newtons. Force grows directly with either mass. Doubling one mass doubles the attraction, and doubling both masses makes it four times larger. Distance has an inverse-square effect. Doubling the center-to-center separation reduces force to one quarter, while tripling it reduces force to one ninth. This rapid decrease explains why ordinary objects exert gravitational forces too small to notice even though gravity acts between all masses. For spherical bodies with symmetric density, the external gravitational effect can be modeled as though each body's mass were concentrated at its center. For compact objects whose dimensions are small compared with their separation, the point-mass approximation is also useful. It becomes less accurate for nearby irregular or extended bodies because different portions of each object have different separations. Detailed models then integrate force over the mass distribution. The Newtonian equation works extremely well for classroom problems, laboratory-scale estimates, spacecraft calculations in many ordinary regimes, and planetary comparisons. General relativity is required for the highest precision, very strong gravitational fields, or relativistic conditions. Other forces may dominate at small scales, and an object's apparent weight near a planet also depends on rotation, altitude, latitude, and local geology. Use center-to-center distance rather than the gap between object surfaces. Keep all entries in SI units unless you convert them first; grams must be divided by 1000 to obtain kilograms, and kilometers multiplied by 1000 to obtain meters. The displayed scientific notation preserves very small and very large results clearly. This educational result does not include other bodies, motion, tidal effects, or relativistic corrections, but it provides a direct and reproducible application of Newton's foundational model.