Gravitational Force Calculator
Input Parameters
Celestial Body Examples
Click on an example to calculate the gravitational force:
Calculate the gravitational force between Earth and the Moon.
Calculate the gravitational force between Earth and the Sun.
Calculate the gravitational force between Jupiter and the Sun.
Calculate the gravitational force between two 70 kg people standing 1 meter apart.
About Newton's Law of Universal Gravitation
Newton's Law of Universal Gravitation states that every particle attracts every other particle with a force proportional to the product of their masses and inversely proportional to the square of the distance between them.
The gravitational constant G = 6.674e-11 N·m²/kg² is a fundamental constant of nature that determines the strength of gravity.
This calculator supports multiple unit systems and provides scientific notation for handling very large or very small values commonly found in astronomical calculations.
About This Tool
Understanding Gravitational Force
Gravitational force is one of the four fundamental forces of nature, governing the attraction between all objects with mass in the universe. Newton's Law of Universal Gravitation provides the mathematical framework for calculating this force using the formula F = G × (m₁ × m₂) / r², where F is the gravitational force, G is the gravitational constant, m₁ and m₂ are the masses of two objects, and r is the distance between their centers. Our gravitational force calculator helps physicists, astronomers, students, and engineers compute gravitational attractions with precision, supporting multiple unit systems and providing scientific notation for handling astronomical values. Whether you're calculating orbital mechanics, studying celestial bodies, or exploring fundamental physics, this tool delivers accurate results with detailed step-by-step solutions.
Newton's Law of Universal Gravitation
Sir Isaac Newton formulated the Law of Universal Gravitation in 1687, establishing that every particle in the universe attracts every other particle with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. The formula quantifies this relationship, where G is the gravitational constant (6.674 × 10⁻¹¹ N·m²/kg²).
F = G × (m₁ × m₂) / r²This inverse square law means that if you double the distance between two objects, the gravitational force becomes one-quarter as strong. Similarly, if you triple the distance, the force becomes one-ninth as strong, demonstrating how rapidly gravity weakens with distance.
The Gravitational Constant (G)
The gravitational constant G is a fundamental physical constant that determines the strength of gravitational attraction in the universe. Its value is approximately 6.674 × 10⁻¹¹ N·m²/kg², making it one of the weakest forces in nature.
💡 Interesting Fact
Despite its small magnitude, gravity becomes dominant at astronomical scales because it acts over infinite distances and always attracts (never repels). The measurement of G is challenging due to its weak nature—it wasn't accurately measured until Henry Cavendish's famous torsion balance experiment in 1798, over a century after Newton's theory.
How Distance Affects Gravitational Force
The inverse square law relationship (1/r²) in Newton's gravitational formula has profound implications for how gravity operates across the universe. As objects move apart, the gravitational force decreases rapidly—not linearly, but quadratically.
Distance vs Force Relationship
2× distance →
1/4 force3× distance →
1/9 force10× distance →
1/100 forceThis relationship explains why astronauts experience weightlessness in orbit despite being only a few hundred kilometers above Earth's surface—the reduction in gravitational force combined with their orbital velocity creates the sensation of free fall.
Gravitational Force Between Everyday Objects
While gravity governs the motion of planets, stars, and galaxies, the gravitational attraction between everyday objects is extraordinarily weak and imperceptible to human senses.
⚠️ Real-World Example
Two 70 kg people standing 1 meter apart experience a gravitational attraction of only about 3.3 × 10⁻⁷ Newtons—far too small to feel or measure without sophisticated equipment.
This minuscule force is why we only notice gravity's effects when at least one object has enormous mass, like Earth (5.97 × 10²⁴ kg).
Calculating Earth-Moon Gravitational Force
One of the most iconic applications of Newton's law is calculating the gravitational force between Earth and the Moon. Using the following values:
Earth's mass:
5.97 × 10²⁴ kgMoon's mass:
7.35 × 10²² kgAverage distance:
3.84 × 10⁸ mGravitational force:
1.98 × 10²⁰ NThis immense force keeps the Moon in its elliptical orbit around Earth, completing one revolution approximately every 27.3 days. This same gravitational interaction causes ocean tides on Earth through tidal forces—the differential gravitational pull across Earth's diameter creates two tidal bulges that produce high and low tides as Earth rotates.
Applications in Astronomy and Space Exploration
Gravitational force calculations are essential for space mission planning, satellite deployment, and understanding celestial mechanics. Engineers use these calculations to determine orbital trajectories, escape velocities, and gravitational assists (gravity slingshots) that allow spacecraft to gain speed by passing near planets.
🌌 Dark Matter Discovery
The formula helps astronomers calculate the masses of distant planets, stars, and even galaxies by observing the gravitational effects they have on nearby objects. Dark matter was first hypothesized when astronomers noticed that galaxies rotate too fast for their visible mass—the extra gravitational force required must come from unseen matter, leading to one of the greatest mysteries in modern astrophysics.
Unit Conversions and Scientific Notation
Working with gravitational force often requires handling extremely large or small numbers, making unit conversions and scientific notation essential. Masses in astronomy range from kilograms (everyday objects) to solar masses, while distances span from meters to astronomical units (AU) and light-years.
Common Unit Conversions
Mass Units:
• Kilograms (kg) – SI standard
• Solar masses – 1.989 × 10³⁰ kg
• Pounds (lb) – Imperial system
Distance Units:
• Meters (m) – SI standard
• Astronomical units (AU) – 1.496 × 10¹¹ m
• Light-years – 9.461 × 10¹⁵ m
Our calculator supports multiple unit systems including SI units (kg, m, N), imperial units (lb, ft, lbf), and astronomical units, automatically converting between them for accurate calculations.
Beyond Newton: Einstein's General Relativity
While Newton's law of universal gravitation accurately describes gravity in most situations, Albert Einstein's General Theory of Relativity (1915) provides a more complete description. Einstein showed that gravity isn't a force in the traditional sense but rather a curvature of spacetime caused by mass and energy.
⚡ When General Relativity Matters
• Near black holes and neutron stars
• At cosmological distances
• GPS satellite calculations (gravitational time dilation)
• Mercury's orbital precession
• Gravitational lensing observations
Despite this advancement, Newton's law remains the practical choice for the vast majority of gravitational calculations due to its simplicity and sufficient accuracy for everyday applications.
Using the Gravitational Force Calculator
Our calculator simplifies gravitational force computations by handling all unit conversions, scientific notation, and formula substitutions automatically. Simply enter the two masses (with their respective units), the distance between their centers, and click calculate.
✅ Calculator Features
• Multiple unit system support (SI, Imperial, Astronomical)
• Automatic scientific notation for large/small values
• Step-by-step calculation breakdown
• Preset examples for Earth-Moon, Earth-Sun systems
• Force comparison with everyday objects
• Real-time validation and error checking
The tool displays the result in Newtons and converts it to other force units for convenience. It also shows the complete calculation process, making it valuable for educational purposes and helping students understand the physics behind gravitational interactions.
Frequently Asked Questions
Yes, Gravitational Force Calculator is totally free :)
Yes, you can install the webapp as PWA.
Yes, any data related to Gravitational Force Calculator only stored in your browser (if storage required). You can simply clear browser cache to clear all the stored data. We do not store any data on server.
Newton's Law of Universal Gravitation states that every particle attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. The formula is F = G × (m₁ × m₂) / r², where G is the gravitational constant (6.674 × 10⁻¹¹ N·m²/kg²).
The gravitational constant, denoted as G, is a fundamental physical constant that appears in Newton's Law of Universal Gravitation. Its value is approximately 6.674 × 10⁻¹¹ N·m²/kg² (or m³·kg⁻¹·s⁻²). This constant determines the strength of gravitational attraction between objects with mass.
Gravitational force follows an inverse square law with respect to distance. This means if you double the distance between two objects, the gravitational force becomes one-quarter as strong. If you triple the distance, the force becomes one-ninth as strong. This relationship (1/r²) shows that gravity weakens rapidly with increasing distance.
In the SI system, gravitational force is measured in Newtons (N), masses in kilograms (kg), and distance in meters (m). The gravitational constant G has units of N·m²/kg². For very large or small values, scientific notation is commonly used, such as 5.97 × 10²⁴ kg for Earth's mass.
The gravitational force between everyday objects is extremely weak. For example, the gravitational attraction between two 70 kg people standing 1 meter apart is only about 3.3 × 10⁻⁷ Newtons—far too small to feel. Gravity only becomes noticeable with astronomical objects that have enormous masses, like planets, moons, and stars.
Yes! Using Earth's mass (5.97 × 10²⁴ kg), Moon's mass (7.35 × 10²² kg), and the average Earth-Moon distance (3.84 × 10⁸ m), the gravitational force is approximately 1.98 × 10²⁰ Newtons. This immense force keeps the Moon in orbit around Earth and causes ocean tides.