Gravitational Force Calculator
Calculate the gravitational attraction between any two masses using Newton's Law of Universal Gravitation, then take it further: find surface gravity and weight on other worlds, work out orbital speed and period, or compute escape velocity — each with its own visual and a plain-English explanation of what the number actually means.
Background
Every pair of masses in the universe attracts every other pair, with a force given by F = G·m₁·m₂/r², where G is the gravitational constant (6.6743 × 10⁻¹¹ N·m²/kg²). The same law, applied a bit differently, also explains why things weigh less on the Moon, how fast a satellite must move to stay in orbit, and how fast something must launch to escape a planet's pull entirely.
How to use this calculator
- Choose Force Between Masses to apply Newton's law directly to any two objects, with a log-log curve showing how fast the force falls off with distance.
- Choose Surface Gravity & Weight to find g on another world and see what your (or any object's) weight would be there, compared against every planet in the solar system.
- Choose Orbital Speed & Period to find the speed and time needed to stay in a stable circular orbit at a given radius.
- Choose Escape Velocity to find the speed needed to break free of a body's gravity entirely, compared on a scale against the Moon, Earth, the Sun, and even the speed of light.
- Click Calculate to see the visual plus a full step-by-step explanation and a callout on what the result actually means.
How gravity works
Gravitational force depends on both masses and falls off with the square of the distance between them — doubling the distance cuts the force to a quarter, not half.
Surface gravity (g) depends only on the central body's mass and radius, not on the object being pulled — that's why a feather and a bowling ball fall at the same rate in a vacuum.
An orbit is really just falling with enough sideways speed to keep missing the ground. Orbital velocity is the exact sideways speed needed for gravity to supply the centripetal force for a circular path.
Escape velocity is always exactly √2 (≈1.414×) the local orbital velocity at the same distance — a neat, memorable relationship that comes straight out of energy conservation.
Surface gravity, orbital velocity, and escape velocity all ignore the mass of the smaller object — a pebble and a spacecraft need the identical speed to escape the same planet from the same altitude.
Formula & Equations Used
Newton's Law of Universal Gravitation: F = G·m₁·m₂ / r²
Surface gravity: g = G·M / R² · Weight: W = m·g
Orbital velocity (circular orbit): v = √(G·M / r)
Orbital period: T = 2π·√(r³ / (G·M))
Escape velocity: v_esc = √(2·G·M / r) = √2 · v_orbit
Gravitational constant: G = 6.6743 × 10⁻¹¹ N·m²/kg²
Example Problems & Step-by-Step Solutions
Example 1 — Earth and Moon
m₁ = 5.972×10²⁴ kg (Earth), m₂ = 7.342×10²² kg (Moon), r = 3.844×10⁸ m.
Step: F = (6.6743×10⁻¹¹)(5.972×10²⁴)(7.342×10²²) / (3.844×10⁸)² ≈ 1.981×10²⁰ N.
Result: a force of about 198 billion trillion newtons keeps the Moon in orbit.
Example 2 — Two 1 kg balls, 1 m apart
m₁ = m₂ = 1 kg, r = 1 m.
Step: F = G × 1 × 1 / 1² = G ≈ 6.674×10⁻¹¹ N.
Result: utterly imperceptible — this is why we never notice gravity between everyday objects.
Example 3 — Weight on Mars
M = 6.417×10²³ kg, R = 3.3895×10⁶ m, object mass = 70 kg.
Step: g = GM/R² ≈ 3.728 m/s². Weight = 70 × 3.728 ≈ 261 N.
Result: that 70 kg person would weigh the equivalent of about 26.6 kg on Earth — well under half their usual weight.
Example 4 — ISS orbital period
M = 5.972×10²⁴ kg (Earth), r ≈ 6.771×10⁶ m (400 km altitude).
Step: v = √(GM/r) ≈ 7.67 km/s. T = 2π√(r³/GM) ≈ 92.4 minutes.
Result: the ISS circles Earth roughly every hour and a half — about 15.6 orbits per day.
Example 5 — Escaping Earth
M = 5.972×10²⁴ kg, r = 6.371×10⁶ m (Earth's surface).
Step: v_esc = √(2GM/r) ≈ 11.19 km/s.
Result: this is the famous "11.2 km/s" figure rockets must reach to leave Earth's gravity entirely, never to fall back.
Frequently Asked Questions
What is G, and why is it such a tiny number?
G (6.6743×10⁻¹¹ N·m²/kg²) is the universal gravitational constant — it sets how strong gravity is per unit of mass. It's tiny because gravity is by far the weakest of the four fundamental forces; it only becomes obvious at planetary scales because planets have so much mass.
What's the difference between g and G?
G is the universal constant that never changes. g is local surface gravity (like Earth's familiar 9.81 m/s²) — it depends on the mass and radius of whichever body you're standing on, and is different on every planet and moon.
Why does gravity fall off so fast with distance?
Because force is proportional to 1/r² — an inverse-square law. Tripling the distance doesn't cut the force to a third; it cuts it to a ninth. This is also why the force curve in this calculator looks like a straight line on a log-log plot — that's the signature of any inverse-square relationship.
Does the mass of my spacecraft (or satellite) affect its orbital or escape speed?
No — surprisingly, it cancels out completely. Orbital velocity and escape velocity only depend on the mass of the body you're orbiting or escaping, and the distance from its center, not on your own mass.
Is this calculator accurate for something as extreme as a black hole or neutron star?
Only as a rough illustration. Newtonian gravity (the formulas used here) breaks down once escape or orbital velocity becomes a significant fraction of the speed of light — that's exactly the regime where Einstein's general relativity takes over, and a true black hole (escape velocity = c) can't be handled by this formula at all. The calculator will flag results that fall in this territory.
Why is escape velocity always √2 times orbital velocity?
Orbital velocity comes from balancing kinetic energy against the centripetal requirement; escape velocity comes from setting total kinetic + potential energy to exactly zero. Working through both formulas algebraically, the r and GM terms leave behind a constant factor of exactly √2 — no coincidence, just energy conservation.
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