Calculate Planetary Gravitational Force
Enter a planet, object, and altitude. The calculator converts units before applying Newton's law.
Example Data Table
| World or position | Planet mass | Radius or distance | Object mass | Force | Field strength |
|---|---|---|---|---|---|
| Earth surface | 5.9722 × 1024 kg | 6,371 km | 70 kg | 687.42 N | 9.82 N/kg |
| Moon surface | 7.342 × 1022 kg | 1,737.4 km | 70 kg | 113.64 N | 1.62 N/kg |
| Mars surface | 6.4171 × 1023 kg | 3,389.5 km | 70 kg | 260.96 N | 3.73 N/kg |
| Earth, 400 km high | 5.9722 × 1024 kg | 6,771 km | 70 kg | 608.60 N | 8.69 N/kg |
Values are rounded. They use the same gravitational constant as this calculator.
Formula Used
- F
- Gravitational force in newtons.
- G
- Universal gravitational constant.
- M
- Mass of the planet in kilograms.
- m
- Mass of the object in kilograms.
- r
- Distance from the planet center, equal to radius plus altitude.
How to Use This Calculator
- Enter the planet mass. Use scientific notation for large values.
- Enter its mean radius and select the matching unit.
- Enter the mass of the object experiencing gravity.
- Enter altitude above the surface. Use zero at ground level.
- Select Calculate Force. Review force, field strength, and distance.
- Use Download CSV or Download PDF after a successful result.
Understanding Planetary Gravity
Gravity and Mass
Gravity is the attraction between masses. A planet pulls an object toward its center. The pull changes with distance. It also changes with planet mass. Large dense worlds create stronger gravity. A smaller object feels the same field strength. Its force changes because force depends on object mass. This calculator keeps those quantities separate. That makes results easier to interpret.
Why Distance Matters
The main equation is Newton's universal gravitation law. It multiplies planet mass by object mass. It then divides by the square of center-to-center separation. At ground level, separation is planet radius. Above the surface, altitude must be added. Squaring distance matters. Doubling distance reduces force to one quarter. This inverse-square pattern explains why gravity weakens during flights and distant orbits.
Mass Is Not Weight
Mass and weight differ. Mass describes matter in an object. It remains nearly constant between planets. Weight is gravitational force acting on that mass. A 70 kilogram traveler keeps mass on Earth, Mars, and Jupiter. Their weight changes with worlds. Reporting force directly in newtons avoids confusion. This calculator shows kilogram-force and pounds-force. Those scales describe force, not new mass.
Planet Size Changes Surface Pull
A planet's radius influences gravity as much as mass. Worlds may have equal mass but different sizes. A smaller world places you closer to its center. Its pull becomes stronger. A low-density planet can have weaker pull despite substantial mass. Use measured mean radius when possible. For oblate planets, radius differs between equator and poles. This page gives an estimate.
Altitude Changes the Result
Altitude is measured from the reference surface. Enter zero for a surface calculation. Enter a value for a mountain, balloon, aircraft, or spacecraft. Low altitudes produce small changes. Orbital distances produce major changes. Keep radius and altitude conversions consistent. The form handles units before applying the equation. Review the displayed center distance. It catches kilometer-to-meter errors before using final force.
Field Strength and Comparisons
Field result expresses force per kilogram. It is written in newtons per kilogram or meters per second squared. Multiply that value by mass to estimate weight. Relative gravity compares the field with Earth gravity. Values near one feel familiar. Values below one reduce weight. Values above one increase loads on structures, vehicles, and people. These comparisons turn force into meaning.
Reliable Inputs
Use scientific notation for planetary values. Planet masses are enormous. Astronomical radii may be large. The calculator accepts entries such as 5.972e24. It converts units automatically. Inputs must remain positive because zero mass or zero center distance has no valid result. The model assumes a spherical planet and point-like object. Terrain, rotation, and density differences can change local gravity.
Limits of the Model
For work, compare results with measured surface gravity. Differences may reveal rounded inputs or reference values. Rotating planets create outward effect that reduces apparent weight near the equator. This calculator reports gravitational attraction only. It does not subtract rotational acceleration. Engineers can add that correction when needed. For classroom work, travel comparisons, and estimates, Newton's equation gives a starting point.
Frequently Asked Questions
What does this calculator find?
It finds gravitational force between a planet and an object at a selected altitude. The main answer is newtons. It also provides equivalent force units and field-strength comparisons.
Which equation does it use?
It uses Newton's universal gravitation law: F = G × M × m / r². The separation r is the planet radius plus the entered altitude.
Does planet radius matter?
Yes. A smaller radius places the object closer to the planet center. Because distance is squared in the denominator, radius can strongly affect surface gravity.
Why is altitude included?
Altitude increases the center-to-center distance. Gravity becomes weaker as that distance rises. The change is small near a surface but important for high flights and orbits.
Can I use Earth masses or Earth radii?
Yes. The unit selectors accept Earth-based reference units. They are converted to kilograms and meters before the formula is evaluated.
What is field strength?
Field strength is force per kilogram at a location. It is shown in N/kg, which has the same dimensions as m/s².
Is this the same as apparent weight?
Not always. This page calculates gravitational attraction. Apparent weight can also reflect rotation, acceleration, contact forces, and local terrain effects.
Can I calculate force for a satellite?
Yes. Enter the satellite mass and its altitude above the planet surface. The output is the force at that orbital position.
Why do results use scientific notation?
Planetary values can be extremely large or small. Scientific notation keeps those numbers readable while preserving useful precision.
Does the calculator include planetary rotation?
No. It calculates gravitational force only. Rotation can slightly reduce apparent weight, especially near an equator, but that correction is not subtracted here.
How can I get dependable results?
Use a consistent mean radius, verified mass, and correct altitude reference. Correct units keep every gravity estimate reliable and useful.