Gravity Calculator
Calculate acceleration due to gravity at a planet's surface or any altitude using g = GM/r², with clear written solution steps.
Gravity at Altitude Diagram
Step-by-Step Gravity Solution
Step 1: Find the distance from the planet's centre
Gravity depends on distance from the centre of mass. Add altitude to the planet radius.
Step 2: Use Newton's gravitational acceleration formula
The gravitational acceleration at distance r from an object of mass M is given by:
Step 3: Substitute the known values
Step 4: Calculate gravitational acceleration
This is 100% of the gravitational acceleration at the planet's surface.
Gravity Calculator
This Gravity Calculator calculates gravitational acceleration at the surface of a planet, moon, star, or other object, or at a selected altitude above it. Enter the object's mass, its radius, and the altitude of the point you want to measure. The calculator uses Newton's law of gravitation to return gravity in metres per second squared and newtons per kilogram, with written solution steps that show every stage of the calculation.
It is useful for physics students, teachers, astronomy learners, and anyone comparing gravity on different worlds. The default values represent Earth, so an altitude of zero gives close to the familiar value of 9.81 m/s squared. Change the values to explore Mars, the Moon, Jupiter, an artificial planet, or a location far above a planet's surface.
Gravity Formula: g = GM/r Squared
The gravitational acceleration formula is g = GM divided by r squared. Here, g is gravitational acceleration, G is the universal gravitational constant, M is the mass of the central object, and r is the distance from that object's centre of mass. The gravitational constant is approximately 6.67430 x 10 to the power of negative 11 N m squared per kg squared.
At a planet's surface, r is equal to the planet radius R. At altitude h above the surface, use r = R + h. This distinction is important because gravity does not depend only on altitude. It depends on the total distance from the centre. The larger that distance becomes, the weaker the gravitational field becomes.
How to Use the Acceleration Due to Gravity Calculator
Start by entering the mass of the planet or object in kilograms. Then enter its mean radius in metres. Finally, enter the altitude above its surface in metres. If you want surface gravity, leave altitude at zero. The calculator adds the radius and altitude to determine the correct centre-to-centre distance before applying the formula.
The result is shown in m/s squared and N/kg. These units have the same numerical value: a field strength of 9.81 N/kg gives a one-kilogram mass a gravitational acceleration of 9.81 m/s squared. The live solution below the calculator labels Step 1 through Step 4 so you can see the distance calculation, formula, substitution, and final answer.
Earth Gravity at the Surface and Altitude
Earth has a mass of approximately 5.972 x 10 to the power of 24 kg and a mean radius of about 6,371,000 m. At sea level, Newton's formula gives roughly 9.82 m/s squared, close to the standard gravity value of 9.81 m/s squared. The small difference depends on the exact reference radius and the simplifying assumptions used in the calculation.
As altitude rises, the distance from Earth's centre increases and gravity decreases. At the altitude of the International Space Station, gravity is still strong: it is roughly 90 percent of its surface value. Astronauts float because they and their spacecraft are in continuous orbit, not because gravity is absent. This is a common and useful application of the gravity-at-altitude formula.
Why Gravity Decreases with Distance
Gravity follows an inverse-square law. Because r is squared in the denominator, doubling the distance from a body's centre reduces gravitational acceleration to one quarter. Tripling the distance reduces it to one ninth. This relationship explains why gravity becomes much weaker far from a planet, even though it never completely reaches zero.
The inverse-square law also means unit conversion is critical. If a radius is entered in kilometres instead of metres, the final answer is wrong by a factor of one million because the distance is squared. Always convert kilometres to metres before using this calculator. For example, 6,371 km must be entered as 6,371,000 m.
Mass, Weight, and Gravitational Acceleration
Mass and weight are related but different. Mass is the amount of matter in an object and is measured in kilograms. It remains the same wherever you travel. Weight is the force caused by gravity on that mass and is measured in newtons. The formula for weight is W = mg, where m is the object's mass and g is local gravitational acceleration.
A person with a mass of 60 kg has the same mass on Earth, Mars, and the Moon. Their weight changes because each body has a different value of g. On Earth their weight is about 589 N, while on the Moon it is much smaller. This calculator finds g; multiply its result by an object's mass to calculate the object's weight at that location.
Gravity on Other Planets and Moons
Different celestial bodies have different surface gravities because their masses and radii differ. A greater mass tends to produce stronger gravity, while a larger radius spreads that mass farther from the surface and can reduce the surface value. Jupiter has much stronger surface gravity than Earth, while the Moon and Mars have lower gravity.
Use consistent values when comparing worlds. Enter the body's total mass in kilograms and mean radius in metres. The simple Newtonian calculation is excellent for learning, though a rapidly rotating or highly irregular body can have local variations. A planet's rotation also slightly reduces apparent weight at its equator, an effect not included in this basic model.
Gravity, Orbits, and Escape Velocity
Gravity is the force that keeps moons and satellites in orbit. At a given distance from a central body, the gravitational acceleration calculated here provides the inward acceleration needed for a circular orbit. Orbital velocity is found from v = square root of GM divided by r. A lower orbit has stronger gravity and requires a higher orbital speed.
Escape velocity is also connected to the same mass and distance. It is vesc = square root of 2GM divided by r, which is square root of 2 times circular orbital velocity at the same radius. Use the related Escape Velocity Calculator and Orbital Velocity Calculator to explore these results after calculating local gravity.
Common Gravity Calculation Mistakes
A frequent error is using altitude alone for r. The formula requires distance from the centre, so add altitude to the body's radius. Another error is confusing the gravitational constant G with local gravitational acceleration g. G is a universal constant; g changes with the mass and distance of the body being studied.
Other mistakes include entering kilometres instead of metres, using weight instead of mass, and forgetting that r is squared. Keep intermediate figures accurate and round the final answer to an appropriate number of significant figures. The written calculation steps on this page are designed to make each of these checks visible.
Applications of the Gravity Formula
The gravity formula is used in school science, astronomy, aerospace engineering, satellite analysis, planetary studies, and mission planning. It helps estimate how quickly an object accelerates when falling, the weight of equipment on another world, and the gravitational environment around a planet or moon. It also supplies the foundation for orbital and escape-speed calculations.
For everyday engineering near Earth's surface, a fixed value such as 9.81 m/s squared is often sufficient. For high altitude, another planet, or an astronomy problem, calculating g from mass and distance is more accurate. Advanced real-world models can include rotation, irregular shapes, atmospheric drag, and the gravity of multiple bodies. This calculator uses the standard Newtonian two-body approximation.
Checking a Gravity Calculation
A quick reasonableness check can prevent many errors. If you use Earth values at the surface, expect a result close to 9.8 m/s squared. At a small altitude compared with Earth's radius, the result should be only slightly lower. At a much larger distance, it should fall rapidly according to the inverse-square law. If the answer increases as altitude increases, recheck the denominator and confirm that the total distance was squared.
You can also compare the output with familiar physical behaviour. A falling object accelerates downward at the calculated value when air resistance is negligible. A one-kilogram object experiences a gravitational force numerically equal to the field strength in newtons. For a different planet, a high mass does not automatically guarantee high surface gravity: radius matters too. These checks make the calculator a useful learning tool as well as a fast source of results.
Gravity Calculator FAQ
What is the value of gravity on Earth? Standard gravity is 9.80665 m/s squared, while local values vary slightly with location and altitude. Does gravity exist in space? Yes. Astronauts in orbit experience gravity and appear weightless because they are falling around Earth. Does gravity become zero at a certain altitude? No, it gets weaker with distance but theoretically extends indefinitely.
For accurate results, use kilograms and metres, measure distance from the centre of the object, and enter a non-negative altitude. The Gravity Calculator provides the numerical answer and the explanation needed to understand how it was obtained, making it useful for both quick calculations and learning Newtonian gravitation.
Frequently Asked Questions
What formula calculates gravitational acceleration?
Use g = GM/r squared, where r is the distance from the centre of the object.
Is gravity measured in m/s squared or N/kg?
Both units are valid and have the same numerical value for gravitational field strength.
How does altitude affect gravity?
Gravity decreases with the square of the distance from the planet's centre as altitude increases.
Why is the gravity on Earth close to 9.81 m/s squared?
Earth's mass and radius produce this value through the formula g = GM/r squared.
Do I use radius or altitude in the formula?
Use total distance from the centre: planet radius plus altitude.