Gravity Calculator: Surface Gravity, Weight on Planets, and F = ma

Formulas Used

• Surface or altitude gravity: r = R + h, then g = G·M / r².
• Weight from mass: W = m·g.
• Newton’s second law: F = m·a, rearranged as m = F/a or a = F/m.
• Universal gravitation: F = G·M·m / r², where r is center-to-center distance.

Worked Examples

Use these to prefill the calculator and inspect the calculation steps.

Reference Surface Gravity

Approximate values from the same preset data used in the calculator. On narrow screens, scroll the table sideways.

Data, Constants, and Assumptions

• Gravitational constant: G = 6.67430×10⁻¹¹ m³·kg⁻¹·s⁻², the CODATA value published by NIST.
• Standard Earth gravity: g₀ = 9.80665 m/s², used for Earth-g multiples and kgf conversion.
• Preset masses and radii: planet values are aligned with NASA planetary fact sheet style mean masses and mean radii; small-body and compact-object entries are approximate educational presets.
• Model assumptions: bodies are treated as spherical, using mean radius, with no rotation, oblateness, latitude, atmosphere, or tidal correction. Gas giant values are approximate reference-level gravities rather than solid-surface values.
• Sources: NIST CODATA gravitational constant, NIST standard acceleration of gravity, and NASA planetary fact sheets.

How to Use This Calculator

1. Choose Gravity & Weight, F = m·a Solver, or Gravitational Force.
2. Enter your known values and choose units beside each input.
3. Open Show calculation steps to see the substituted formula.
4. For custom worlds, open Advanced custom body and enter mass and radius with scientific notation if needed.

FAQ

Understanding Gravity: From Falling Apples to Orbiting Worlds

Gravity is the attractive interaction between objects that have mass or energy. It governs everything from a ball dropping to the ground to the choreography of planets, moons, and galaxies. In everyday terms, gravity is why you feel weight and why things fall when you let go. In physics terms, your weight is the force of gravity acting on your mass: W = m·g, where m is mass (in kilograms) and g is the local gravitational acceleration (in m/s²).

Surface Gravity vs. Altitude

On (roughly) spherical worlds, gravity near the surface is well-approximated by g = G·M / (R + h)², where G is the gravitational constant, M is the body’s mass, R its mean radius, and h your altitude above the surface. Two immediate takeaways:

• Bigger mass → stronger gravity. Jupiter’s huge mass produces a much larger g than Earth’s.
• Greater distance → weaker gravity. As you climb to higher altitudes, g decreases with the square of distance from the center.

This is why astronauts in low Earth orbit feel weightless: they are in continuous free-fall around Earth. Gravity is still strong there; they’re just perpetually falling sideways fast enough to miss the ground—an orbit.

Mass, Weight, and “g” Units

It’s common to mix up mass and weight. Mass is the amount of matter in an object and does not change when you travel. Weight is the gravitational force on that mass and does change with g. On Earth’s surface, standard gravity is about 9.80665 m/s². If a world’s surface gravity is 0.17 g (like the Moon), a 70 kg person would still have 70 kg of mass but would weigh only about 12%–17% of their Earth weight. Our calculator reports g in m/s² and in “Earth g” for quick comparisons.

Newton’s Second Law and Motion

Gravity provides a real-world context for Newton’s Second Law, F = m·a. When gravity is the only force acting, the acceleration you experience is simply a = g. Add other forces—like a rocket’s thrust, air resistance, or a spring—and the total acceleration comes from the vector sum of all forces divided by mass. This is why the same push (force) produces a smaller acceleration on a heavy object than on a light one.

Why Worlds Differ

Surface gravity depends on both mass and radius. A dense, compact body can have strong gravity even if it isn’t very massive, while a large, puffy world (like Saturn) can have moderate surface gravity despite enormous mass because its radius is so large. Our presets capture these differences so you can explore how weight and g vary from the Moon to Neptune—and beyond with custom mass and radius.

Try adjusting altitude in the tool to see how g changes with height, or switch bodies to compare your weight across the Solar System.