Introduction
Every object in the universe pulls on every other object through gravity. This invisible force is what keeps the Moon orbiting Earth, Earth orbiting the Sun, and your feet on the ground. The strength of this pull depends on two things: how much mass the objects have and how far apart they are. Sir Isaac Newton described this relationship with his law of universal gravitation, giving us a simple formula to calculate the exact force between any two masses.
Our Gravitational Force Calculator lets you quickly solve Newton's gravitational equation without doing the math by hand. Enter the masses of two objects and the distance between them, and the tool instantly computes the gravitational force in newtons. You can also work backward — if you already know the force, you can solve for a missing mass or distance instead. The calculator supports a wide range of units, from kilograms and meters to solar masses and light-years, making it useful for both everyday physics problems and astronomy-scale calculations.
Built-in presets for common objects like Earth, the Moon, the Sun, and Jupiter let you explore real-world scenarios with a single click. The tool also shows step-by-step calculations, gravitational field strength, escape velocity, and what happens if you halve or double the distance between the objects. Whether you are a student learning about gravity for the first time or someone working through orbital mechanics problems, this calculator gives you fast, accurate results every time.
How to use our Gravitational Force Calculator
Enter the masses of two objects and the distance between them, and this calculator will find the gravitational force pulling them together using Newton's law of universal gravitation. You can also solve for any unknown variable — mass or distance — if you already know the force.
What do you want to calculate: Choose what you want to solve for — Force, Mass 1, Mass 2, or Distance. The calculator will adjust the input fields based on your choice. By default, it solves for gravitational force.
Mass 1: Enter the mass of the first object. Type a base number and an exponent (power of 10) to handle very large or small values. Pick a unit from the dropdown, such as kilograms, grams, pounds, or even Earth masses and Solar masses. You can also click a preset button like Earth, Moon, Sun, Mars, Jupiter, or Human (70 kg) to fill in the value right away.
Mass 2: Enter the mass of the second object the same way. It also supports scientific notation, multiple units, and preset buttons including Earth, Moon, ISS, Satellite, and Human (70 kg).
Distance: Enter the distance between the centers of the two objects. Use the base number and exponent fields for scientific notation, and choose a unit like meters, kilometers, miles, astronomical units (AU), or light-years. Preset buttons let you quickly set common distances such as Earth-Moon, Earth-Sun, Geostationary orbit, and ISS Orbit. If you need help computing the straight-line separation between two points, our Distance Calculator can assist.
Gravitational Force (input mode): This field appears only when you are solving for Mass 1, Mass 2, or Distance. Enter the known gravitational force value and select a unit such as Newtons, kilonewtons, meganewtons, dynes, or pound-force.
Calculate & Reset: Click "Calculate" to run the computation, or turn on the "Auto-calculate" toggle to get results instantly as you change any input. Click "Reset" to return all fields to the default Earth-Moon example.
Results: The calculator displays the answer in a highlighted box at the top of the results section. Below that, you will see the full formula and each step of the math worked out. An Additional Information table shows the gravitational field strength at the given distance, escape velocity, and more. A Comparison Scenarios section shows how the force would change if you halved or doubled the distance. If you need to express results in scientific notation for other work, try our Scientific Notation Calculator.
Visualization: A visual diagram of the two objects and the force arrows between them is shown by default. You can toggle it on or off with the "Show Visualization" switch.
Understanding Gravitational Force
Gravitational force is the pull that every object with mass has on every other object with mass. It is the force that keeps your feet on the ground, holds the Moon in orbit around Earth, and keeps Earth traveling around the Sun. The bigger the masses and the closer they are, the stronger this pull becomes.
Newton's Law of Universal Gravitation
In 1687, Sir Isaac Newton described this force with a simple formula known as the Law of Universal Gravitation:
F = G × (m₁ × m₂) / r²
Here is what each part means:
- F is the gravitational force between two objects, measured in newtons (N). For a broader look at how force relates to mass and acceleration, see our Force Calculator.
- G is the gravitational constant, which equals 6.6743 × 10⁻¹¹ N·m²/kg². This number is the same everywhere in the universe.
- m₁ is the mass of the first object.
- m₂ is the mass of the second object.
- r is the distance between the centers of the two objects.
How Mass and Distance Affect Gravity
Two rules make gravitational force easy to understand. First, more mass means more force. If you double the mass of one object, the gravitational pull doubles too. Second, more distance means less force — and it drops off fast. Because distance is squared in the formula, doubling the distance makes the force four times weaker. Cutting the distance in half makes the force four times stronger. This is called the inverse square law.
The Gravitational Constant (G)
The gravitational constant G is an extremely small number. This tells us that gravity is actually a very weak force compared to other forces like magnetism or electricity. You only notice gravity when at least one of the objects is very massive, like a planet or a star. Two people standing next to each other have a gravitational pull between them, but it is far too tiny to feel.
Real-World Examples
The gravitational force between Earth (5.972 × 10²⁴ kg) and the Moon (7.342 × 10²² kg) at their average distance of 384,400 km is about 1.98 × 10²⁰ newtons. That enormous force is what keeps the Moon in orbit and causes ocean tides on Earth. Between Earth and the Sun, the force is even larger — roughly 3.54 × 10²² newtons — because the Sun's mass is about 333,000 times greater than Earth's.
On a smaller scale, the gravitational force between a 70 kg person standing on Earth's surface (about 6,371 km from Earth's center) is roughly 686 newtons. We call this the person's weight. Weight is simply the gravitational force between you and the planet you are standing on. To explore how acceleration due to gravity affects objects in motion near a planet's surface, try our Free Fall Calculator.
Related Concepts
Gravitational field strength (often written as g) describes how strong gravity is at a certain point in space. On Earth's surface, g is about 9.8 m/s². This means any object in free fall near Earth speeds up by 9.8 meters per second every second. You can explore the effects of acceleration in more detail with our Acceleration Calculator or examine the forces experienced during rapid changes in velocity using our G Force Calculator.
Escape velocity is the minimum speed an object needs to break free from another object's gravitational pull without any additional thrust. For Earth, this speed is about 11.2 km/s (roughly 25,000 mph). This concept ties directly into kinetic energy — an object must have enough kinetic energy to overcome the gravitational potential energy binding it to the planet.
Why Gravitational Force Matters
Newton's law of gravitation explains a wide range of events, from how planets orbit stars to how galaxies form and hold together. Engineers use it to plan satellite orbits, spacecraft trajectories, and even GPS systems. Understanding gravitational force also connects to many other areas of mechanics: it determines the momentum changes in orbiting bodies, governs projectile motion near planetary surfaces, and plays a central role in calculating the Schwarzschild radius of black holes. For problems involving mass-energy equivalence at relativistic scales, our E = mc² Calculator is a helpful companion. While Einstein's general relativity gives a more complete picture of gravity at extreme scales, Newton's formula remains accurate and practical for nearly all everyday and astronomical calculations.