Coulombs Law Calculator
Calculate the electrostatic force between two point charges with Coulomb's law, from both charge magnitudes and the distance separating them.
Coulombs Law Calculator
Calculator
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Formula: F = kq₁q₂/r²
Worked example — 1.798 N (repulsive)
Formula
F = kq₁q₂/r²
Electrostatic force between two point charges. k = 8.9875×10⁹ N·m²/C².
Worked Examples
Example 1: Two charges
Problem:q₁=1μC, q₂=2μC, r=0.1m
Solution:F=8.99e9×1e-6×2e-6/0.01=1.798 N
Result:1.798 N (repulsive)
Frequently Asked Questions
What is Coulomb's law?
Coulomb's law states that the electrostatic force between two point charges is F = kq₁q₂/r², where k = 8.9875×10⁹ N·m²/C² is Coulomb's constant, q₁ and q₂ are the charges in coulombs, and r is the separation in meters. Like charges repel; opposite charges attract.
How do you calculate Coulomb's law force?
Use F = kq₁q₂/r². For q₁ = 1 μC and q₂ = 2 μC separated by 0.1 m: F = 8.9875×10⁹ × 1×10⁻⁶ × 2×10⁻⁶ / 0.01 = 1.798 N (repulsive, since both charges are positive). Doubling the distance reduces the force by a factor of 4.
What units does the Coulomb's law calculator use?
Charges q₁ and q₂ are entered in coulombs (C). Use scientific notation for small charges, e.g. 1e-6 for 1 microcoulomb (μC) or 1e-9 for 1 nanocoulomb (nC). Distance r is in meters (m). The output force is in Newtons (N).
How does Coulomb force compare to gravity?
For two electrons (q = 1.6×10⁻¹⁹ C, m = 9.1×10⁻³¹ kg) separated by 1 nm, Coulomb force ≈ 2.3×10⁻¹⁰ N while gravitational force ≈ 5.5×10⁻⁵² N — electrostatics is about 10⁴² times stronger. Gravity dominates at large scales only because macroscopic matter is nearly electrically neutral.
What is the difference between the Coulomb force and the electrostatic potential energy of a charge pair?
The force is k q1 q2 divided by r squared and is a vector; the potential energy of the pair is k q1 q2 divided by r and is a scalar, falling off one power of r more slowly. Energy is the work needed to bring the charges from infinity to separation r, and force is the negative rate of change of that energy with r. Like charges give positive energy, opposite charges negative.
What is the electric field of a point charge, and how does it relate to this force?
The field of a point charge is E = k q / r squared, in newtons per coulomb or equivalently volts per metre, directed away from a positive charge. The force on a second charge placed there is simply q times E. Splitting the problem this way is useful because the field describes the surrounding space without reference to whatever test charge you later introduce.
How do I handle more than two charges?
Use the superposition principle: compute the Coulomb force from each other charge separately, treating each pair as if the rest were absent, then add those forces as vectors. Resolve each into components along your axes, sum the components and recombine. Superposition holds exactly for electrostatics, which is what makes the two-charge result in Coulombs Law Calculator a building block for any arrangement.
What is the permittivity of free space and how does it relate to Coulomb's constant?
Coulomb's constant equals 1 divided by 4 pi times the permittivity of free space. With epsilon nought at about 8.854e-12 in units of C squared per newton per square metre, that gives roughly 8.9875e9 N m squared per C squared. Many textbooks write Coulomb's law with the 4 pi epsilon nought form because it keeps the geometry of the inverse-square spreading explicit.
How does the surrounding medium change the electrostatic force?
Immersing the charges in a dielectric reduces the force by the relative permittivity of the medium, because the material polarises and partially screens the charges. Water has a relative permittivity around 80 near room temperature, so the attraction between two ions is roughly eighty times weaker in water than in vacuum. That screening is a large part of why ionic solids dissolve so readily in water.
When does Coulomb's law stop being valid?
It applies to point charges, or to spherically symmetric charge distributions treated from outside, and only when the charges are static. Extended or irregular bodies need the field to be integrated over the distribution. Moving charges add magnetic forces and finite propagation delays, so full electrodynamics is required, and at nuclear separations the strong interaction overwhelms electrostatic repulsion altogether.
Background & Theory
Coulomb Force by the Numbers
Coulomb's law describes one of the four fundamental forces of nature, and it's structurally identical to Newton's law of gravitation — both fall off as 1/r² — but electrostatic force is vastly stronger at the particle scale. The elementary charge is 1.602×10⁻¹⁹ C, so everyday "point charges" in a physics problem (microcoulombs, nanocoulombs) already represent trillions of electrons.
| Charge pair / distance | Approx. force |
|---|---|
| Two electrons, 1 nm apart | ~2.3×10⁻¹⁰ N (repulsive) |
| Proton and electron in a hydrogen atom (0.0529 nm, Bohr radius) | ~8.2×10⁻⁸ N (attractive) |
| Two 1 μC charges, 1 cm apart | ~90 N |
| A charged balloon (~1 nC) near hair, a few cm away | micronewton range — enough to visibly lift hair strands |
The inverse-square dependence means doubling the separation cuts the force to a quarter, and halving it quadruples the force — this rapid falloff is why static electricity effects (like a balloon sticking to a wall) are only noticeable over short ranges.
Reviewed for accuracy by Manoj Kumar, Mathematics Educator · Editorial policy
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