Tidal force calculator inputs
Example data table
| Scenario | Source mass | Distance | Target radius | Test mass | Full tidal acceleration | Tidal force |
|---|---|---|---|---|---|---|
| Moon acting on Earth | 1 Moon mass | 384,400 km | 6,371 km | 1,000 kg | 2.199765e-6 m/s² | 2.199765e-3 N |
| Sun acting on Earth | 1 Solar mass | 1 AU | 6,371 km | 1,000 kg | 1.010220e-6 m/s² | 1.010220e-3 N |
| Jupiter acting on Io | 1 Jupiter mass | 421,700 km | 1,821.6 km | 1,000 kg | 1.230977e-2 m/s² | 12.309774 N |
Formula used
Tidal force comes from the gravity difference across an extended body. This calculator evaluates the exact near side and far side gravity first, then converts that differential acceleration into force on the chosen test mass.
Here, G is the gravitational constant, M is the source mass, r is the center distance, R is target radius or offset, and m is the test mass.
How to use this calculator
- Enter a scenario label so exported files stay easy to identify.
- Provide the source mass and choose its unit.
- Enter the center-to-center distance between the two bodies.
- Enter the target radius, or the offset from the target center.
- Enter the test mass that will experience the differential pull.
- Press Calculate tidal force to show the result above the form.
- Use the CSV button for spreadsheets and the PDF button for reports.
Frequently asked questions
1. What does this calculator measure?
It measures the gravity difference across an object. That difference creates tidal acceleration and a corresponding tidal force on the selected test mass.
2. Why does the result depend strongly on distance?
Tidal effects scale with distance cubed in the common approximation. Small reductions in separation can therefore create much larger differential gravity.
3. What is the difference between exact and approximate values?
The exact value uses near and far side gravity directly. The approximation uses a compact formula that works best when the target radius is small compared with distance.
4. What should I enter as target radius?
Use the body radius for full object stretching. Use a smaller offset if you only want the gravity difference across a limited internal span or structure.
5. Can I use astronomical units and planet masses?
Yes. The calculator supports kilograms, common astronomical mass units, meters, kilometers, Earth radii, lunar distance, and astronomical units.
6. Does this calculator model fluid tides directly?
No. It computes the driving differential gravity. Real fluid tides also depend on rotation, resonance, bathymetry, elasticity, and dissipation.
7. Why can the tidal force be tiny but still important?
Because tides act over large masses and long times. Even modest differential acceleration can shape oceans, heat moons, and stress orbiting bodies.
8. When is the approximation unreliable?
It becomes weaker when radius is not small relative to distance. In close encounters, the exact near and far gravity values are the safer choice.