What is the formula for calculating gravity?

Newton's law of universal gravitation gives the gravitational force between two masses: F = G × (m₁ × m₂) / r², where G = 6.674×10⁻¹¹ N·m²/kg². To find the surface gravity (acceleration) of a planet instead of a force, use g = G × M / r², where M is the planet's mass and r is its radius.

What is the value of the gravitational constant G?

G = 6.674×10⁻¹¹ N·m²/kg² (also written as m³·kg⁻¹·s⁻²). It was first measured experimentally by Henry Cavendish in 1798 using a torsion balance, and its currently accepted CODATA value is 6.67430×10⁻¹¹ N·m²/kg².

Why is Earth's gravity 9.8 m/s² and not exactly 9.81 or 10?

Earth's surface gravity varies slightly by location (roughly 9.76 to 9.83 m/s²) due to altitude, latitude, and local geology — Earth is not a perfect sphere and its mass isn't perfectly uniform. The internationally agreed standard value, used for engineering and unit definitions, is g = 9.80665 m/s² exactly.

How much weaker is gravity if you double the distance?

Gravity follows an inverse-square law, so doubling the distance between two objects reduces the gravitational force to 1/4 of its original value (since 2² = 4). Tripling the distance reduces it to 1/9. This is why gravity drops off quickly as objects move apart.

How do I calculate how much I would weigh on another planet?

First find that planet's surface gravity using g = GM/r² with its mass and radius. Then multiply your mass (in kg) by that g value to get your weight in newtons on that planet, or divide your Earth weight by 9.8 and multiply by the planet's g to compare directly.

Is gravitational force the same as weight?

Yes — weight is simply the gravitational force acting on an object's mass at a given location, calculated as W = m × g. On Earth, g ≈ 9.8 m/s²; on the Moon, g ≈ 1.62 m/s², so the same object weighs about six times less on the Moon than on Earth, even though its mass never changes.

Gravity Calculator

Science

Calculate gravitational force

Mass 1 (kg)

Mass 2 (kg)

Distance (m)

Every object with mass pulls on every other object with mass — that pull is gravity, and Isaac Newton was the first to describe it with a precise mathematical law. Newton's law of universal gravitation says the force between two objects depends on their masses and the square of the distance separating them. It explains why you stay on the ground, why the Moon orbits Earth, and why you would weigh less on Mars than on Earth.

The formula involves multiplying two masses, dividing by distance squared, and scaling everything by the gravitational constant G — a number so small (6.674×10⁻¹¹) that doing the arithmetic by hand is error-prone and tedious. Our gravity calculator does it instantly. Enter two masses and a separation distance to find the gravitational force between them, or enter a planet's mass and radius to find its surface gravity — the acceleration you would feel standing on it.

Whether you're checking physics homework, comparing planetary gravity for a science project, or just curious how strong gravity really is between everyday objects, this calculator gives exact, formula-based answers.

Why Gravity Calculator Matters

Gravity is one of the four fundamental forces of nature and the first one humans described mathematically, making it a cornerstone topic in every introductory physics course. Students encounter Newton's law of universal gravitation when studying mechanics, orbital motion, and later general relativity as a conceptual stepping stone. Being able to compute gravitational force and surface gravity accurately is essential for homework problems, lab reports, and standardized tests like AP Physics and the SAT Subject Tests.

Beyond the classroom, gravity calculations matter in real engineering and science: aerospace engineers use them to compute orbital velocities and escape velocities for satellites, astronomers use them to estimate the mass of exoplanets from their gravitational effects on nearby stars, and even everyday questions like "how much would I weigh on Mars" rely on the same surface gravity formula. Understanding that gravitational force falls off with the square of distance (the inverse-square law) also explains why astronauts in low Earth orbit still experience about 90% of Earth's surface gravity — they are weightless because they are in freefall, not because gravity has vanished.

The Gravity Calculator Formula, Explained

F = G × (m₁ × m₂) / r² and g = G × M / r²

Where: F = gravitational force in newtons (N), G = the gravitational constant, 6.674×10⁻¹¹ N·m²/kg², m₁ and m₂ = the masses of the two objects in kilograms, and r = the distance between the centers of the two masses in meters.

The second formula is a special case used to find surface gravity: g = G × M / r², where M is the mass of a planet or body and r is its radius. This gives the acceleration due to gravity at the surface — the number that determines how much you weigh there. Earth's standard surface gravity is g ≈ 9.80665 m/s², the internationally accepted reference value used to define the kilogram-force and to convert between mass and weight.

Notice that r is squared in the denominator: doubling the distance between two objects reduces the gravitational force to one-quarter of its original value. This inverse-square relationship is why gravity feels overwhelmingly strong right at a planet's surface but becomes negligible across interstellar distances.

How to Use the Gravity Calculator: Step by Step

Choose force or surface gravity mode
Decide whether you want the gravitational force between two objects (use F = Gm₁m₂/r²) or the surface gravity of a planet or moon (use g = GM/r²).
Enter the mass values
For force mode, input both masses in kilograms. For surface gravity mode, input the single mass of the planet or body in kilograms.
Enter the distance or radius
Input the distance between the two objects' centers (force mode) or the radius of the planet (surface gravity mode), in meters.
Read the result
The calculator returns the gravitational force in newtons, or the surface gravity in m/s², along with an equivalent weight if you also entered an object's mass.

Gravity Calculator Examples: Real-World Scenarios

Gravitational Force Between Two People

Two people, each with a mass of 70 kg, stand 1 meter apart. What is the gravitational force pulling them together?

Mass 1 (m₁):70 kg

Mass 2 (m₂):70 kg

Distance (r):1 m

Calculation

F = 6.674×10⁻¹¹ × (70 × 70) / 1² = 6.674×10⁻¹¹ × 4900

Result

F ≈ 3.27×10⁻⁷ N — about 0.0000003 newtons, roughly the weight of a single grain of dust. This shows why gravity between everyday objects is completely unnoticeable; it only becomes significant with planet-sized masses.

Earth's Surface Gravity and Your Weight

Earth has a mass of 5.972×10²⁴ kg and a radius of 6.371×10⁶ m. What is its surface gravity, and how much would an 80 kg person weigh?

Mass of Earth (M):5.972×10²⁴ kg

Radius of Earth (r):6.371×10⁶ m

Person's mass:80 kg

Calculation

g = 6.674×10⁻¹¹ × 5.972×10²⁴ / (6.371×10⁶)² = 9.82 m/s²; Weight = 80 × 9.82

Result

g ≈ 9.82 m/s² (close to the standard 9.80665 m/s² reference value). The 80 kg person weighs about 785.6 N, equivalent to roughly 176.6 pounds-force.

Weight on Mars vs. Earth

Mars has a mass of 6.4171×10²³ kg and a radius of 3.3895×10⁶ m. How much would the same 80 kg person weigh there?

Mass of Mars (M):6.4171×10²³ kg

Radius of Mars (r):3.3895×10⁶ m

Person's mass:80 kg

Calculation

g_mars = 6.674×10⁻¹¹ × 6.4171×10²³ / (3.3895×10⁶)² = 3.73 m/s²; Weight = 80 × 3.73

Result

g_mars ≈ 3.73 m/s², about 38% of Earth's gravity. The person weighs only about 298.2 N (67.0 lbf) on Mars — they'd feel roughly two-thirds lighter than on Earth despite having the exact same mass.

Common Mistakes to Avoid

Confusing mass and weight — mass (kg) is constant everywhere, but weight (N or lbf) depends on local gravity and changes from planet to planet. The calculator's F and g outputs are forces/accelerations, not mass.
Forgetting to convert units — the formula requires mass in kilograms and distance in meters. Plugging in grams, pounds, or kilometers without converting gives answers off by many orders of magnitude.
Mixing up G (gravitational constant, 6.674×10⁻¹¹) with g (acceleration due to gravity, ~9.8 m/s² on Earth) — they are related but not interchangeable, and using the wrong one invalidates the whole calculation.

Tips & Tricks

For quick Earth-based physics problems, you can usually just use g = 9.8 m/s² (or 9.80665 m/s² for precision) rather than recomputing it from G, M, and r every time.
When comparing surface gravity across planets, it's often more intuitive to express the result as a ratio to Earth's gravity (e.g., Mars is about 0.38g) rather than in raw m/s².

Newton's law of universal gravitation turns an invisible force into precise, predictable numbers — whether you're finding the pull between two masses or the surface gravity of an entire planet. Use this calculator for physics homework, science fair projects, or satisfying your curiosity about gravity elsewhere in the solar system. Pair it with our force calculator and acceleration calculator to explore Newton's second law, F = ma, in more depth.

Gravity Calculator — Frequently Asked Questions

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Authoritative References

NIST — CODATA Value of the Gravitational Constant

nist.gov — Authoritative reference value for G

Khan Academy — Newton's Law of Gravitation

khanacademy.org — Free lesson explaining the derivation and use of the gravity formula

External links open in a new tab. OmniCalc.us is not affiliated with these organisations.

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