Enter attraction parameters
Use positive magnitudes. The calculator applies the negative sign for an attractive potential energy.
Example data
| Mode | Object values | Separation | Medium | Expected relationship |
|---|---|---|---|---|
| Gravity | 5 kg and 12 kg | 2 m | Not required | U = −Gm₁m₂/r |
| Electrostatic | 5 µC and 8 µC | 0.25 m | Vacuum, εr = 1 | U = −k|q₁q₂|/(εrr) |
| Electrostatic | 2 nC and 3 nC | 5 cm | Material, εr = 4 | Higher εr lowers the magnitude |
Understanding Energy of Attraction
Attraction energy describes a bound interaction between two objects. It is usually expressed as potential energy. The value is negative when the objects attract. A negative value means the pair has less energy together than apart. Energy must be supplied to separate them completely.
This calculator handles two common cases. Gravity attracts every pair of masses. Electrostatic attraction occurs between opposite electric charges. Both interactions become weaker as separation increases. Both become stronger when the object values increase.
Potential energy depends on the chosen reference level. This calculator sets zero energy at infinite separation. That standard reference makes comparisons simple. It also explains why attractive cases have negative values. Always state the reference when reporting potential energy in scientific work.
Formula Used
For gravity, the calculator uses U = −Gm₁m₂/r. Here, U is potential energy. G is the gravitational constant. The terms m₁ and m₂ are masses in kilograms. The distance r is measured in metres. The related attraction force is F = Gm₁m₂/r².
For opposite electric charges, the calculator uses U = −k|q₁q₂|/(εrr). The constant k is the Coulomb constant. The values q₁ and q₂ are charge magnitudes in coulombs. Relative permittivity εr describes the material between charges. Vacuum has εr equal to one. The related force is F = k|q₁q₂|/(εrr²).
How to Use This Calculator
Select gravitational or electrostatic attraction first. Enter the initial separation and its unit. Supply both masses for gravity. Supply both charge magnitudes for electrostatics. For an electric case, enter the relative permittivity. Use one for air or vacuum approximations. Choose a display precision. Then select the calculation button.
You can add a final separation. This optional value calculates the energy change. A larger final separation needs positive external work. A smaller final separation releases energy. Leave this field blank when only one separation is needed.
Reading the Results
The initial potential energy appears first. Its negative sign is important. Its magnitude equals the energy needed to separate the pair to infinity. The attraction force is also shown. This force points toward the other object. It is positive here because the display reports magnitude.
When a final separation is entered, the calculator reports ΔU. Positive ΔU means the system gained potential energy. That occurs when attractive objects move apart. Negative ΔU means energy was released. That occurs when attractive objects move closer.
Practical Limits
Use centre-to-centre separation for point-like objects. Large extended objects need more detailed models. Gravity calculations assume spherical symmetry or sufficiently large distances. Electric calculations assume stationary point charges. Material properties can vary with temperature and frequency.
Very small distances need quantum or atomic models. Very high speeds need relativistic corrections. Real systems may include friction, radiation, or external fields. Those effects are not included here. Use consistent units and review every input before relying on a result.
Frequently asked questions
1. Why is attraction energy negative?
Negative energy means the objects form a bound system. The pair has less potential energy together than when separated infinitely far away. External energy is required to pull an attractive pair apart.
2. Does gravity always produce attractive energy?
For ordinary positive masses, yes. Gravitational potential energy is negative under the common zero reference at infinite separation. The gravitational force pulls each mass toward the other.
3. Can this calculate repulsive electric energy?
This page is designed for opposite charges and attraction. Like charges have positive electrostatic potential energy using U = kq₁q₂/(εrr). Their force is repulsive rather than attractive.
4. What distance should I enter?
Enter centre-to-centre separation. For small objects treated as points, this is straightforward. For spheres, measure between their centres. Do not use surface spacing unless a problem specifically requests it.
5. What is relative permittivity?
Relative permittivity measures how a material changes electric interactions compared with vacuum. A larger value reduces the electric force and potential-energy magnitude. Use one for vacuum or a close air approximation.
6. Why does energy change with distance?
Both supported potential-energy formulas are inversely proportional to separation. Increasing distance makes the negative value closer to zero. Decreasing distance makes the negative value larger in magnitude.
7. What does the attraction force result mean?
It is the force magnitude at the initial separation. The force points along the line joining the objects. In an attractive case, each object is pulled toward the other object.
8. What does a positive ΔU show?
A positive potential-energy change means the system gained energy. This happens when attractive objects are moved farther apart. An outside agent must normally provide this energy as work.
9. What does a negative ΔU show?
A negative potential-energy change means the system lost potential energy. This happens when attractive objects move closer. That energy can appear as kinetic energy, heat, light, or another form.
10. Are the constants fixed?
The gravitational and Coulomb constants are fixed standard values in this calculator. The electrostatic result also depends on relative permittivity. That input changes with the chosen medium.
11. When are these formulas less accurate?
They are less accurate for extended irregular objects, changing charge distributions, strong external fields, extremely small separations, or relativistic motion. More complete physical models may be required in those situations.