One law of gravity, four questions.
Pick a mode below — everything recalculates live as you type, units convert themselves, and every result explains itself.
Any object — a person, a planet, a star. 1 M⊕ = 5.972×10²⁴ kg, 1 M☉ = 1.989×10³⁰ kg.
The other object. Swap m₁ and m₂ — the force on each is identical (Newton's third law).
Center-to-center, not surface-to-surface. 1 R⊕ = 6,371 km, 1 AU = 149.6 million km.
The world you're standing on — a planet, moon or star. Presets below fill in real bodies.
Center to surface. Earth: 6,371 km; Moon: 1,737 km; Sun: 695,700 km.
Enter your mass to see what you'd weigh there. Leave it empty to skip the weight line.
The body being orbited — Earth for satellites, the Sun for planets.
Measured from the center of the central body, not from its surface — the ISS orbits at R⊕ + 400 km ≈ 6,771 km.
The world you're leaving — its gravity is what you must beat.
You launch from the surface, so use the body's radius, center to surface.
Two masses to a full answer, in four steps.
No manual unit conversion, no sign-up — the panel handles grams to solar masses and centimeters to astronomical units for you.
Pick your question
Four tabs cover the four classic questions: how hard do two objects pull on each other, how strong is gravity on a surface, how fast must something orbit, and how fast to escape forever.
Enter masses & distance
Type any values and choose a unit per field — kg, tonnes, Earth or solar masses; centimeters up to astronomical units. Or tap a preset chip for real bodies like Earth, the Moon or Mars.
Read the live answer
Results update as you type: a headline number, plain-language context, the quantities in SI units, and the formula with your numbers substituted in, step by step.
Copy or keep exploring
One click copies the whole result — values, units and formula — for your notes or homework. Switch tabs anytime; each mode keeps its own inputs.
Six formulas, one constant.
Everything this calculator does comes from Newton's law of universal gravitation and a single universal constant, G = 6.6743×10⁻¹¹ N·m²/kg².
Universal gravitation
The pull between two masses, measured center to center. Double either mass and F doubles; double the distance and F falls to a quarter.
Surface gravity
The acceleration every object experiences at a body's surface — 9.81 m/s² on Earth, set by Earth's mass and radius alone.
Weight
Your weight is your mass times the local g. Your mass is the same everywhere; your weight changes from world to world.
Orbital velocity
The exact speed for a circular orbit at radius r — fast enough that "falling around" the body replaces falling into it.
Orbital period
Time for one full orbit. Notice the r³ inside the root — orbit further out and the period grows fast (Kepler's third law).
Escape velocity
The minimum speed to leave a body's gravity forever — always √2 times the speed of a surface-skimming orbit, and independent of the object's own mass.
Gravity, answered.
The questions students ask most about gravitation — short, straight answers, all consistent with what the calculator above computes.
What is Newton's law of universal gravitation?+
Every mass in the universe pulls on every other mass with a force that acts along the line joining their centers: F = G·m₁·m₂ / r². The force grows in proportion to each mass and shrinks with the square of the distance between the centers — double the distance and the pull drops to a quarter. The same law describes an apple falling, the Moon orbiting Earth and galaxies holding together.
What is the gravitational constant G, and how is it different from g?+
G = 6.6743×10⁻¹¹ N·m²/kg² is a universal constant — the same everywhere in the universe, first measured in Henry Cavendish's lab experiment. Lowercase g is different: it is the acceleration a body's surface produces (g = GM/R²) and changes from world to world — 9.81 m/s² on Earth, 1.62 on the Moon.
How do I calculate the gravitational force between two objects?+
Put the masses in kilograms and the center-to-center distance in meters, then apply F = G·m₁·m₂ / r². Two people standing a meter apart pull on each other with about 3×10⁻⁷ N — imperceptible. Earth and the Moon pull with about 1.98×10²⁰ N. The calculator converts units for you, from grams to solar masses and from centimeters to astronomical units.
How do I find gravity and my weight on other planets?+
Use g = GM/R² with the planet's mass and radius. The Surface gravity tab has one-click presets: the Moon gives 1.62 m/s², Mars 3.73 m/s², Jupiter about 25.9 m/s². Your weight there is simply your mass multiplied by that g — your mass never changes, but the scale reading does.
How quickly does gravity weaken with distance?+
By the inverse-square law: at twice the distance the force is four times weaker; at ten times the distance, one hundred times weaker. Gravity never reaches exactly zero, though — even at the ISS's 400 km altitude it is still about 89% as strong as on the ground.
What is orbital velocity, and why do astronauts float?+
Orbital speed for a circular orbit is v = √(GM/r), measured from the body's center — about 7.7 km/s for the ISS. One full lap takes T = 2π·√(r³/GM), roughly 92 minutes. Astronauts float not because gravity is gone but because the station is in continuous free fall around Earth.
What is escape velocity, and why is it the same for every object?+
Escape velocity is the minimum launch speed needed to leave a body's gravity forever: vₑ = √(2GM/R) — 11.19 km/s from Earth. It doesn't involve the object's own mass at all, because it is an energy-per-kilogram requirement, so a pebble and a spacecraft need exactly the same speed.
Is this calculator free, and is my data sent anywhere?+
Completely free, with no sign-up and no limits. Everything runs in your browser — nothing you type is uploaded, logged or sent to a server, and results update live as you type.