Newton's Gravitational Force Calculator

All three are related but have different units. Gravitational force (F, newtons) is the pull between TWO masses: F = G·M·m/r² — this is what the calculator computes (e.g. Earth–Moon: 1.98049e+20 N). Weight (W, newtons) is a special case: a planet's gravitational force on a body near its surface, W = m·g. The gravitational field (g, m/s²) is the force PER UNIT MASS at a point: g = G·M/r² — a property of the location, not of the body. Example: Earth's gravitational field at the Moon's position is only 2.697e-3 m/s² (0.0275% of standard gravity), while the weight of 1 kg on Earth's surface is 9.80665 N.

F = G·M·m/r². M and m are the masses of the two bodies (kg), r is the distance between their centers of mass (m), and G = 6.67430×10⁻¹¹ m³/(kg·s²) is the universal gravitational constant (CODATA 2018). Force is directly proportional to both masses and inversely proportional to the square of the distance. A complete step-by-step worked example is in the “Earth–Moon worked example” section above.

G = 6.67430×10⁻¹¹ m³/(kg·s²) per CODATA 2018. This is a UNIVERSAL constant — the same value everywhere in the universe, from falling apples to galaxies. G is also the least precisely known physical constant (relative uncertainty around 2.2×10⁻⁵), because gravity is so weak it's hard to measure in a lab. Don't confuse it with lowercase g: g is the LOCAL gravitational field, which varies with the celestial body and distance.

Because 9.80665 m/s² is STANDARD gravity — a defined value used as the international reference, not a measurement at one spot. The calculator computes purely from the formula: F = G·M·m/r² = 6.67430×10⁻¹¹ × 5.97237×10²⁴ × 1 / (6,371,000)² = 9.821 N. The 0.14% difference comes from rounding of the preset constants and from the fact that Earth's surface gravity genuinely varies (about 9.78 at the equator to 9.83 at the poles). For all “weight on Earth” comparisons, the calculator uses 9.80665, exact by definition.

Three reasons. First, that huge force acts on a giant mass (the Moon, 7.342×10²² kg), so the acceleration it produces is only a = F/m = 2.697e-3 m/s² — almost exactly the centripetal acceleration needed to orbit. Second, we move along with Earth, so the pull cancels out in our frame; what remains is only its differential effect — ocean tides. Third, this force equals the weight of a 2.01954e+19 kg mass on Earth — huge, but “spread out” over a Moon-sized mass.

Yes. Newton's third law applies fully to gravity: attraction always comes in pairs, equal in magnitude, opposite in direction. Earth pulls the Moon with 1.98049e+20 N, and the Moon pulls Earth with exactly 1.98049e+20 N as well. What differs is the acceleration (a = F/m): Earth barely budges because its mass is about 81 times the Moon's, while the Moon is accelerated enough to stay in orbit.

The force becomes ONE QUARTER — because it's inversely proportional to the square of the distance (1/r²). Triple the distance → 1/9 the force; 10× the distance → 1/100 the force. A real example: although the Sun's mass is about 333,000 times Earth's, at 1 AU its force on Earth is 3.54177e+22 N — only 178.8 times the Moon's force on Earth (1.98049e+20 N), because 1 AU is about 389 times the Earth–Moon distance and force weakens with the square of distance.

The main result is always newtons (N), plus automatic conversion to kilonewtons (kN), meganewtons (MN), and pound-force (lbf). 1 N = 0.224809 lbf, since 1 lbf = 4.4482216152605 N. Input mass can be in kg, grams, tons, Earth masses, or Sun masses; distance can be in m, cm, km, astronomical units/AU (1 AU = 149,597,870,700 m), or Earth radii. The calculator can also invert the formula: find M, m, or r when the force and two other quantities are known.

Tiny: two 1 kg balls 1 m apart pull each other with only 6.67430e-11 N — eleven orders of magnitude below 1 newton. That's why G is hard to measure (the Cavendish experiment, 1797–1798) and why gravity is “unfelt” between everyday objects. Gravity only dominates at planetary mass scales, because — unlike electric force — it never cancels out: always attractive and cumulative.

They compute different quantities. This calculator computes the attractive FORCE (newtons) between two masses — e.g. 1.98049e+20 N between Earth and Moon. The escape velocity calculator computes the minimum SPEED (km/s) for a body to escape a celestial body's gravity — e.g. 11.186 km/s from Earth's surface. Both use the same constant G, but answer different physics questions: “how strong is the pull?” vs “how fast must it go to escape?”. See the escape velocity calculator for the second quantity.

Compare it with the other forces acting on the same system. Rule of thumb: if gravity is below 1% of the dominant force (engine thrust, friction, electromagnetic forces), its contribution usually drowns in measurement uncertainty. For bodies under 1 ton at distances over 1 m, the force is below 10⁻⁴ N — negligible in almost all engineering calculations, except precision instruments like gravimeters or space missions.