Updated on April 20th, 2026

Gravitational Force Calculator

Created By Jehan Wadia

M₁
M₂

Gravitational Force

1.982 × 10²⁰ N

Between Earth and Moon

Formula & Calculation
F = G × (m₁ × m₂) / r²

G = 6.6743 × 10⁻¹¹ N·m²/kg²

m₁ = 5.972 × 10²⁴ kg

m₂ = 7.342 × 10²² kg

r = 3.844 × 10⁸ m

F = 6.6743 × 10⁻¹¹ × (5.972 × 10²⁴ × 7.342 × 10²²) / (3.844 × 10⁸)²

F = 1.982 × 10²⁰ N

Additional Information
Gravitational Field (g₁): 0.0027 m/s²
Gravitational Field (g₂): 2.70 × 10⁻³ m/s²
Weight on M₁: --
Escape Velocity (v₁): 11.2 km/s
Comparison Scenarios

If distance was halved:

Force would be 4× stronger: 7.928 × 10²⁰ N

If distance was doubled:

Force would be 4× weaker: 4.955 × 10¹⁹ N


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.


Frequently Asked Questions

What is the gravitational constant G?

The gravitational constant G is a fixed number used in Newton's gravity formula. Its value is 6.6743 × 10⁻¹¹ N·m²/kg². It is the same everywhere in the universe. This tiny number tells us gravity is a very weak force — you only notice it when at least one object is extremely massive, like a planet or star.

Why can't the distance be zero in this calculator?

In Newton's formula, distance (r) is in the bottom of the equation as r². If r equals zero, you would be dividing by zero, which is impossible in math. In real life, two objects can never occupy the exact same point in space. The distance used is always measured between the centers of mass of the two objects, so even when objects touch, the distance is still greater than zero.

What units can I use for mass in this calculator?

The calculator supports many mass units, including:

  • Kilograms (kg), grams (g), milligrams (mg), and micrograms (μg)
  • Metric tons, pounds (lb), and ounces (oz)
  • Astronomical units like Earth mass, Lunar mass, Solar mass, Jupiter mass, and atomic mass units (amu)

Pick any unit from the dropdown, and the calculator converts it to kilograms automatically before calculating.

What units can I use for distance?

You can use meters, kilometers, centimeters, millimeters, nanometers, miles, feet, inches, astronomical units (AU), light-years, parsecs, and Earth radii. The calculator converts your chosen unit to meters behind the scenes to solve the equation.

How do I enter very large or very small numbers?

Use the scientific notation fields. Type the base number in the first box and the power of 10 in the second box. For example, to enter 5.972 × 10²⁴, type 5.972 in the base field and 24 in the exponent field. This makes it easy to work with planet-sized masses or tiny atomic-scale values.

Can I solve for mass or distance instead of force?

Yes. Use the buttons at the top labeled Force, Mass 1, Mass 2, and Distance. Pick the variable you want to find. The calculator will hide that input field and show a field for gravitational force instead. Enter the known force along with the other known values, and it will solve for the missing variable.

What do the preset buttons do?

Preset buttons fill in real-world values with one click. For mass, you can load values for Earth, the Moon, the Sun, Mars, Jupiter, or a 70 kg human. For distance, you can load the Earth-Moon distance, Earth-Sun distance, geostationary orbit altitude, or ISS orbit altitude. This saves time and helps you explore real scenarios quickly.

What is gravitational field strength?

Gravitational field strength tells you how strong gravity is at a specific distance from an object. It is measured in m/s². For example, Earth's gravitational field strength at its surface is about 9.8 m/s². The calculator shows this value for both objects in the Additional Information section.

What does the Comparison Scenarios section show?

It shows how the gravitational force changes if you halve or double the distance between the two objects. Because gravity follows the inverse square law, halving the distance makes the force 4 times stronger, and doubling the distance makes it 4 times weaker. This helps you see how sensitive gravity is to distance changes.

Is this calculator accurate for objects near black holes or moving near the speed of light?

No. This calculator uses Newton's law of universal gravitation, which works great for everyday and most astronomical situations. For extreme conditions — like near black holes, at very high speeds, or in very strong gravitational fields — you need Einstein's general relativity. For nearly all school, engineering, and standard astronomy problems, Newton's formula is accurate enough.

Why is the gravitational force between two people so small?

Because the gravitational constant G is extremely tiny (6.6743 × 10⁻¹¹). Two 70 kg people standing 1 meter apart feel a gravitational pull of only about 3.27 × 10⁻⁷ newtons. That is far too small to notice. You only feel gravity when one of the objects is huge, like a planet.

What is the difference between mass and weight?

Mass is the amount of matter in an object, measured in kilograms. It stays the same no matter where you are. Weight is the gravitational force pulling on that mass, measured in newtons. Your weight changes depending on the planet or moon you are on, but your mass does not.

How does the auto-calculate feature work?

When the Auto-calculate toggle is turned on, the calculator updates the result automatically every time you change any input value. You do not need to click the Calculate button. If you turn it off, you must click Calculate manually to see new results.

Does this calculator measure distance from the surfaces or centers of the objects?

Newton's law uses the distance between the centers of mass of the two objects, not their surfaces. For example, when calculating the force between you and Earth, the distance is from Earth's center to your location — about 6,371 km — not zero just because you are standing on the surface.

What is escape velocity and how is it calculated?

Escape velocity is the minimum speed an object needs to leave another object's gravitational pull without any extra push. The formula is v = √(2GM/r), where M is the mass of the body you are escaping from and r is the distance from its center. The calculator shows this value in the Additional Information section.


Related Calculators

Free Fall Calculator

Visit Free Fall Calculator

Kinetic Energy Calculator

Visit Kinetic Energy Calculator

Potential Energy Calculator

Visit Potential Energy Calculator

Force Calculator

Visit Force Calculator

Spring Force Calculator

Visit Spring Force Calculator

Acceleration Calculator

Visit Acceleration Calculator

G Force Calculator

Visit G Force Calculator

Projectile Motion Calculator

Visit Projectile Motion Calculator

Momentum Calculator

Visit Momentum Calculator

Torque Calculator

Visit Torque Calculator

Moment of Inertia Calculator

Visit Moment of Inertia Calculator

Displacement Calculator

Visit Displacement Calculator

Impulse Calculator

Visit Impulse Calculator

Pulley Calculator

Visit Pulley Calculator

Speed Calculator

Visit Speed Calculator