Inverse square is ruthless
If you move two charges 10 times farther apart, the Coulomb force becomes 100 times smaller. Most big result changes come from distance, not from tweaking the charges slightly.
Scaling
Coulomb's Law Calculator
Inputs
1 µC.
A larger
εr weakens the force in this idealized model.
Enter a positive relative permittivity.
Used for displayed output only.
Tip: Press Ctrl/Cmd + Enter to calculate. The URL updates with your values, but no inputs are sent to a server.
Results
Force Magnitude
-
Electrostatic force magnitude
Direction
-
Attractive or repulsive
Electric Field from q1 at q2
-
Magnitude only; sign noted below
Potential Energy
-
Electrostatic potential energy
| Equation used | - |
|---|---|
| Signed force scalar | - |
| q1 in coulombs | - |
| q2 in coulombs | - |
| Distance in meters | - |
| Relative permittivity | - |
| Inverse-square factor | - |
Coulomb's Law Formula, Assumptions, and What the Output Means
Coulomb's law describes the electrostatic force between two stationary charges. In SI units the magnitude is F = k |q1 q2| / (εr r2), where k is Coulomb's constant, q1 and q2 are the charges in coulombs, r is their center-to-center separation in meters, and εr is the relative permittivity of a uniform medium. The inverse-square structure is the key scaling rule: double the separation and the force falls to one quarter; cut the separation in half and the force becomes four times larger. The interaction acts along the line joining the charges.
The sign of q1 q2 determines whether the force is attractive or repulsive. If the signs are opposite, the charges attract. If the signs are the same, they repel. This calculator reports both the force magnitude and a plain-language direction label because most practical questions are really about both: “How large is the force?” and “Are the charges pulling together or pushing apart?” It also reports the electric field due to q1 at the location of q2, using E = k q1 / (εr r2), and the electrostatic potential energy using U = k q1 q2 / (εr r).
Those extra outputs matter because force alone does not tell the whole story. The electric field describes how strongly space around a charge would push on a positive test charge, while potential energy tells you whether the charge configuration is energetically bound or resistant to compression. Negative potential energy corresponds to an attractive configuration; positive potential energy corresponds to a repulsive one. If you are comparing Coulomb's law with the inverse-square ideas in our Gravity & Newton's Second Law tool or force scaling in the Centripetal Force Calculator, the mathematical pattern will look familiar even though the physical source differs.
This page uses the standard idealization of point charges in electrostatic equilibrium. That is appropriate for homework checks, back-of-the-envelope reasoning, and many clean lab examples. It is not a full simulator for finite-sized conductors, corona discharge, dielectric breakdown, polarization effects, or moving charges. Very small separations, very large charges, or real engineered assemblies can violate the assumptions behind the simple formula. Treat the result as an ideal electrostatics estimate rather than design approval or safety guidance.
F = k q1 q2 / (εr r^2)
|F| = k |q1 q2| / (εr r^2)
E(q1 at q2) = k q1 / (εr r^2)
U = k q1 q2 / (εr r)
k = 8.9875517923 x 10^9 N·m^2/C^2
Worked example
Suppose q1 = +1 µC, q2 = -1 µC, and r = 0.10 m in air. The product of the charges is negative, so the interaction is attractive. The force magnitude is about 0.899 N, the field magnitude from q1 at q2 is about 8.99 x 105 N/C, and the potential energy is roughly -0.0899 J. If you kept the charges the same but doubled the distance to 0.20 m, the force and field would each drop to one quarter of those values.
Assumption note: The dielectric presets are simple relative-permittivity approximations. They are
useful for educational comparison, but real materials can be frequency-dependent, temperature-dependent, and
geometry-dependent.
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5 Quick Facts About Coulomb's Law
Gravity is tiny by comparison
The electric force between elementary particles is enormously stronger than their gravitational attraction. That is one reason electrostatic effects dominate atomic structure.
Force comparison
Water screens charge strongly
Because water has a large relative permittivity, idealized Coulomb interactions are much weaker in water than in air or vacuum. That matters in chemistry and biology.
Dielectrics
Potential energy keeps the sign
Opposite charges give negative electrostatic potential energy, while like charges give positive potential energy. The sign tells you whether the configuration is naturally bound or self-separating.
Energy intuition
The point-charge model has limits
Real electrodes, sparks, humidity, finite conductor size, and material polarization can make real setups depart from the simple equation. Coulomb's law is the clean starting point, not the full engineering model.
Assumptions
Frequently Asked Questions
Does this calculator show attraction or repulsion?
Yes. It uses the signs of q1 and q2 to label the interaction. Opposite signs attract; like signs repel.
What unit should I use for charge?
You can enter charges in coulombs, millicoulombs, microcoulombs, nanocoulombs, picocoulombs, or elementary charges. The calculator converts everything internally to SI units before evaluating the formulas.
Why is the force so small for tiny charges?
In everyday static-electricity problems the charges are often in the nanocoulomb or picocoulomb range. Those are extremely small amounts of charge, so even with a large constant k, the final force may still be modest unless the distance is also very small.
Can I use this for real hardware or safety limits?
Only as an ideal estimate. Real hardware may involve distributed charge, conductive geometry, field concentration, discharge paths, humidity, insulation failure, and moving charges. Use a detailed engineering model when the consequences matter.