Calculate gravitational force, mass, or distance using F = G × (m₁ × m₂) / r². Free online mechanics calculator for physics and astronomy with Newton's law of universal gravitation.
Calculate gravitational force using F = G × (m₁ × m₂) / r²
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Gravitational force is one of the four fundamental forces in nature and is responsible for keeping planets in orbit, holding galaxies together, and causing objects to fall to Earth. Sir Isaac Newton discovered that every object in the universe attracts every other object with a force proportional to their masses and inversely proportional to the square of the distance between them. Our Gravitational Force Calculator makes it easy to calculate gravitational force, mass, or distance using Newton's law of universal gravitation: F = G × (m₁ × m₂) / r².
This fundamental law describes the attractive force between any two objects with mass. Whether you're studying planetary motion, calculating orbital mechanics, or understanding the force between everyday objects, understanding gravitational force is essential to physics and astronomy. Despite being the weakest of the four fundamental forces, gravity has infinite range and shapes the large-scale structure of the universe.
Our Gravitational Force Calculator is designed for simplicity and accuracy. Follow these steps to get your calculation:
The calculator uses Newton's law of universal gravitation: F = G × (m₁ × m₂) / r²
You can rearrange this formula to solve for any variable:
Newton's law of universal gravitation is one of the most important equations in physics:
F = G × (m₁ × m₂) / r²
Where: F = gravitational force, G = gravitational constant, m₁, m₂ = masses, r = distance
The gravitational constant (G) is a fundamental physical constant:
G = 6.67430 × 10⁻¹¹ N⋅m²/kg²
This small value explains why gravitational forces between everyday objects are imperceptible, while the force between massive objects like planets is significant.
Gravitational force calculations are used in countless real-world scenarios across various fields:
It's crucial to use consistent units in your calculations. Our calculator supports multiple unit systems and automatically converts between them:
Tip: The calculator automatically handles unit conversions, so you can mix different unit systems. However, note that the gravitational constant G is always in SI units (N⋅m²/kg²), so conversions are done internally.
Two objects with masses of 100 kg and 200 kg are 5 meters apart. What is the gravitational force between them?
F = G × (m₁ × m₂) / r² = 6.67430 × 10⁻¹¹ × (100 × 200) / 5² = 5.34 × 10⁻⁸ N
This is an extremely small force, which is why we don't notice gravity between everyday objects
Calculate the gravitational force between Earth (5.97 × 10²⁴ kg) and the Moon (7.35 × 10²² kg) at their average distance (3.84 × 10⁸ m).
F = 6.67430 × 10⁻¹¹ × (5.97 × 10²⁴ × 7.35 × 10²²) / (3.84 × 10⁸)² ≈ 1.98 × 10²⁰ N
This massive force keeps the Moon in orbit around Earth
The gravitational force between two objects is 1.0 × 10⁻⁶ N. One object has a mass of 500 kg, and they are 10 m apart. What is the mass of the second object?
m₂ = (F × r²) / (G × m₁) = (1.0 × 10⁻⁶ × 10²) / (6.67430 × 10⁻¹¹ × 500) ≈ 299.6 kg
Two 1000 kg objects attract each other with a force of 6.67 × 10⁻⁶ N. How far apart are they?
r = √(G × m₁ × m₂ / F) = √(6.67430 × 10⁻¹¹ × 1000 × 1000 / 6.67 × 10⁻⁶) ≈ 1.0 m
Calculate the gravitational force between Earth (5.97 × 10²⁴ kg) and a 70 kg person at Earth's surface (radius = 6.37 × 10⁶ m).
F = 6.67430 × 10⁻¹¹ × (5.97 × 10²⁴ × 70) / (6.37 × 10⁶)² ≈ 686 N
This equals the person's weight: 686 N ≈ 70 kg × 9.8 m/s²
Gravitational force follows an inverse square law with distance:
This relationship means gravitational force decreases rapidly with distance, which is why the force between distant objects is so small, while nearby objects (like you and Earth) experience significant gravitational attraction.
It's important to understand the difference between gravitational force and weight:
When you calculate the gravitational force between a person and Earth using Newton's law, you get the same result as calculating weight using W = mg.
While gravitational forces between everyday objects are too small to notice, understanding them has practical applications:
Gravitational force (F) is directly proportional to the product of the two masses (m₁ × m₂) and inversely proportional to the square of the distance (r²): F = G × (m₁ × m₂) / r². This means larger masses produce stronger forces, and increasing distance dramatically decreases the force (inverse square law).
The gravitational constant (G) is 6.67430 × 10⁻¹¹ N⋅m²/kg². It's a fundamental physical constant that appears in Newton's law of universal gravitation. Despite being very small, it allows us to calculate gravitational forces between any two objects with mass. It was first measured by Henry Cavendish in 1798.
Gravitational force is weak because the gravitational constant G is extremely small (6.67430 × 10⁻¹¹). This means you need very large masses (like planets) or very small distances to produce noticeable forces. For example, the gravitational force between two 1 kg objects 1 meter apart is only about 6.67 × 10⁻¹¹ Newtons - completely imperceptible.
Gravitational force follows an inverse square law with distance. If you double the distance, the force becomes 1/4 as strong. If you triple the distance, the force becomes 1/9 as strong. This is because force is proportional to 1/r². The rapid decrease with distance explains why only nearby or very massive objects produce significant gravitational forces.
Gravitational force (F) is the actual force between two objects. Gravitational field (g) is the force per unit mass that would be experienced by a test mass at a point in space. On Earth's surface, g ≈ 9.8 m/s². The field strength is related to force by: g = F/m, and for a point mass M, g = G × M / r².
Gravitational force is always attractive, so it's always positive in magnitude. However, when working with vectors (forces with direction), gravitational force vectors point toward each other. The magnitude is always positive, but the direction indicates attraction.
Gravitational force provides the centripetal force needed for orbital motion. For a circular orbit, F_gravity = F_centripetal, so G × m₁ × m₂ / r² = m × v² / r. This relationship determines orbital speed and period. Without gravitational force, objects would move in straight lines rather than orbits.
Einstein's general relativity is a more complete theory that reduces to Newton's law for weak gravitational fields and low speeds. Newton's law is still accurate for most practical purposes (planets, satellites, everyday objects). General relativity is needed for extremely strong fields (black holes), high speeds, or when extreme precision is required (like GPS systems).
Understanding gravitational force and Newton's law of universal gravitation is fundamental to mechanics, astronomy, and our understanding of the universe. Our Gravitational Force Calculator simplifies these calculations, making it easy to solve problems involving gravitational attraction, orbital mechanics, and celestial motion.
Whether you're calculating forces between planets, understanding orbital mechanics, or studying fundamental physics, this calculator provides accurate results with support for multiple unit systems. Ready to explore more physics concepts? Check out our other calculators like the Torque Calculator for rotational mechanics, or use our Acceleration Calculator for acceleration calculations that often complement gravitational force analysis in orbital dynamics.
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