Newtonian gravitational field strength
The magnitude of the Newtonian gravitational field outside a spherically symmetric body is GM/r². It is also the ideal gravitational acceleration experienced by a small test mass at that location.
Distance r is measured from the source center, not from its surface. The scalar result reports magnitude; the gravitational field vector points toward the attracting mass.
How to use the gravitational field calculator
- Choose the unknown: Select field strength, source mass, or distance.
- Use center distance: For a planet, add altitude to the applicable reference radius.
- Enter SI values: Use kilograms, meters, and newtons per kilogram.
- Check the model: Confirm the point-mass or external spherical-body approximation is appropriate.
Formula and variables
The calculator uses the 2022 CODATA value G = 6.67430 × 10⁻¹¹ m³ kg⁻¹ s⁻².
g = GM/r²- g — Field strength
- Magnitude of gravitational force per unit test mass (N/kg)
- G — Gravitational constant
- Newtonian constant of gravitation (m³ kg⁻¹ s⁻²)
- M — Source mass
- Attracting point or spherical mass (kg)
- r — Center distance
- Distance from the source center (m)
Ideal field near Earth radius
Use M = 5.972 × 10²⁴ kg and r = 6.371 × 10⁶ m.
- Source mass
- 5.972 × 10²⁴ kg
- Center distance
- 6.371 × 10⁶ m
- g = 6.67430 × 10⁻¹¹ × 5.972 × 10²⁴ / (6.371 × 10⁶)²
Result: Ideal field magnitude is approximately 9.820 N/kg.
This spherical Newtonian estimate omits rotation, latitude, altitude reference, and mass-distribution details.
Understanding your results
Field strength is a magnitude
N/kg is dimensionally equivalent to m/s², but the direction must be supplied separately.
- Doubling source mass doubles the field at fixed distance.
- Doubling distance reduces the field to one quarter.
- Inside an extended body, total mass divided by r² is generally not the correct model.
Assumptions
- Newtonian gravity is sufficient.
- The source is a point mass or the evaluation point is outside a spherically symmetric mass.
- The test mass is small enough not to alter the source system.
Limitations
- Does not model nonspherical mass distributions, multiple bodies, rotation, relativistic gravity, or interior density profiles.
- Uses center distance and SI units only.
- The numerical uncertainty of G and input quantities is not propagated.
Common mistakes
- Entering altitude instead of distance from the center.
- Using kilometers without converting to meters.
- Treating the positive magnitude as a vector direction.
- Applying the external-body equation inside a planet or star.
Practical use cases
Planetary estimates
Estimate ideal external gravitational acceleration from mass and radius.
Inverse-square study
Explore how field magnitude changes with source mass and distance.
Frequently asked questions
Is N/kg the same as m/s²?
Yes dimensionally. One newton per kilogram equals one meter per second squared.
Should I enter altitude or radius?
Enter distance from the source center. For an ideal spherical planet, this is planet radius plus altitude.
Why is the field shown as positive?
The calculator reports magnitude. The vector direction is radially toward the attracting source.
Sources and review
- 2022 CODATA Recommended Values of the Fundamental Physical Constants — National Institute of Standards and Technology. Accessed 2026-07-13.
- Gravitation Near Earth's Surface — OpenStax University Physics Volume 1. Accessed 2026-07-13.
Reviewed 2026-07-13.