Coulombs Law Calculator
The force between charges: F = k·q₁q₂/r² with the attraction verdict live, the inverse square shown exactly, and the coulomb's true size confessed on its own card.
Coulombs Law Calculator
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What this result does not account for
- Point charges or uniform spheres, electrostatic
- No medium shielding or dielectric screens
In short: Two microcoulombs, a hand's width apart (0.1 m): F = k·q₁q₂/r² = 0.898755 N, pushing them apart — like charges repel, and the page takes the verdict from the sign of the product. The giant card confesses the unit's true size: two FULL coulombs a metre apart push with 8.988e+9 N — about 916,475,228 kg of force. The coulomb is enormous; everyday static lives in micro-worlds for a reason. Double the gap to 0.2 m and the force quarters to 0.224689 N — the inverse square, exact.
Formula
F = k·q₁q₂/r² · k ≈ 8.988×10⁹ N·m²/C² · like repel, unlike attract · double r, quarter F
Coulomb's law is the electric inverse square: the product of the charges, discounted by the square of the gap, scaled by a constant so large it teaches its own lesson — a coulomb is a giant, and chemistry happens in micro- and nanocoulombs precisely because the electric force dwarfs everything it meets. The sign of the product keeps the verdict: positive repels, negative attracts.
Worked Example
- Enter both charges WITH their signs and the gap.
- Read the force and the repel/attract verdict.
- Check the giant card before quoting coulombs casually.
- Use the inverse-square card before 'just moving it a bit further'.
Defaults: 0.898755 N, repelling; two full coulombs at 1 m: 8.988e+9 N; double the gap, quarter the force.
Strengths & Limits Of This Model
Where this engine is strong
- Verdict from the sign, printed with the magnitude
- The coulomb's true size confessed on its own card
Where it stops
- No polarization or induction effects
- No relativistic or quantum corrections
Practical Use Cases
Electrostatics
sensors, sprayers, precipitators
Teaching
the inverse square, electric edition
Atomic reasoning
why chemistry is electric
Methodology & Editorial Standards
Computation runs in IEEE-754 double precision at full internal precision; rounding to two decimal places occurs strictly at the display layer, so no cumulative drift enters the result. All monetary outputs use accounting presentation — grouped thousands, two decimals, negatives in parentheses — so figures can be transcribed directly into a model or working paper. Division-by-zero and out-of-domain inputs return an em-dash rather than a misleading number.
This engine was reconciled against an independent reference implementation and hand-verified for the worked example above before release. Our full five-stage review process is published on the About Us page.
Disclaimer. This calculator is provided for informational and modelling purposes only and does not constitute financial, tax, legal, medical, or engineering advice. Verify all figures with a qualified professional before acting on them.
Coulombs Law Calculator — 8 Expert FAQs
8 analyst-written answers to the questions practitioners actually ask — optimised for voice and answer-engine retrieval.
Why is k so enormous?
Because the coulomb is enormous: k is small in fundamental terms, but one coulomb is some 6.24×10¹⁸ elementary charges — chemistry-scale objects carry micro- and nanocoulombs. The giant card prices the mismatch: two whole coulombs a metre apart fight with billions of newtons.
Why an inverse SQUARE?
Geometry, again: the field spreads over a sphere whose area grows as r², so the same influence thins as 1/r². Gravity obeys the same law for the same reason — and both are exact consequences of living in three spatial dimensions.
How is the attraction verdict decided?
From the sign of the product q₁q₂: positive means the charges are alike and push apart; negative means they differ and pull together. The page prints the magnitude with the word, because a force without a direction is only half an answer.
Is zero charge an error?
No — it is an honest zero: a neutral body feels no Coulomb force at all (though a charged neighbor will still polarize and nudge it; that subtlety is beyond the point-charge law). Zero here is 'nothing to push on'.
Why is r = 0 refused?
Because two point charges at the same place is not a small force, it is no reading at all — the formula divides by zero and physics declines. Real charges have size; the point-charge law stops where the gap does.
How exact is k?
k = 1/(4πε₀) is now a measured constant, about 8.9875517923×10⁹ N·m²/C² (CODATA, quoted approximately). For tabletop and teaching work its uncertainty is irrelevant; for metrology, the quote matters and the page says approximate.
Does this law survive at atomic scales?
Remarkably well as the FORCE law — chemistry is Coulomb attraction dressed in quantum rules. What fails is the classical picture of little spheres: electrons orbit nothing, they occupy states. The inverse square itself carries into the quantum framework intact.
How does this pair with the voltage page?
Through the per-charge bookkeeping: voltage is energy per coulomb, and this page prices what one coulomb does to another at a distance. Move a charge against this force and the work done is exactly the voltage page's promise, banked.