Coulomb's Law Calculator
Compute electrostatic force F = k·|q1·q2|/r² between point charges. Runs locally in your browser.
Trust summary CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance
- Input interpretation
- Enter values to calculate.
- Result
- —
- Assurance
- Engineering
- Declared partition coverage
- PASS · 2/2 declared partitions (force, invalid-domain) · Matrix
- Known limitations
- Point charges in free space
- Core CVP does not include live graph, viewport, or pointer interaction.
- Model
- Electrostatic force between point charges.
- Scope
- Point charges; εr=1
- Verification
- Engine tested · Source checked · v1.0.0 · CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance· View Manifest · CVP overview · Specification
- Versions
- Calculation 1.0.0 · CVP protocol 1.0.0-proposed
- CVP identity
- 1/1 property · digest 232339ac4ad2
- Legacy regression
- 4/4 tests · Production surface contract 4/4
- Reference
- O1 model · O2 expected_values · O2 numerical_behavior
- Interfaces
- PASS · UI (SSR) / REST / MCP
- Supplemental domain review
- Internal · Pass · electrical-engineer
- Named expert review
- Not performed
- CVP suite
- 1/1 golden · 1/1 CVP boundary · 1/1 invalid · 1/1 property · 1/1 cross-interface · 1/1 CVP contract · Manifest
- Sources
- SI / electrostatics textbooks
- CODATA / NIST — Coulomb constant
- Evidence
- 2 legacy golden · 1 legacy boundary · legacy regression suite · 1/1 oracle-backed golden · 1/1 invalid · Artifact integrity PASS · CalculatorX electrical review
- Semantic contract
- PASS
Full verification
Formulas
Core equations used by this calculator.
How to use
Enter the two charges
q1 and q2 in coulombs (signs set attraction vs repulsion).
Enter separation distance r
Distance must be greater than zero (meters).
Read the force magnitude
F = k·|q1·q2|/r² with k = 8.99×10⁹ N·m²/C².
Example calculations
Common configurations with formula and result.
1 µC · 1 µC · 0.1 m
like charges
Coulomb's Law calculator specification
Version 1.0.0 · Engine tested · Supplemental domain review · Internal · 2026-08-08
- Engine tested 4/4 tests · Production surface contract 4/4
- Supplemental domain review Internal · Pass · electrical-engineer · 2026-08-08
- Named expert review Not performed
- Calculation version 1.0.0
Review policy · Evidence · Reviewed by CalculatorX electrical review (electrical-engineer)
- Definition
- Coulomb's law: F = k·|q1·q2|/r² with k ≈ 8.9875517923×10⁹ N·m²/C². Opposite signs attract.
- What it calculates
- Electrostatic force between point charges.
- Inputs
- q1_C
- q2_C
- r_m
- Outputs
- F_N
- attractive
- Formula
F=k|q1q2|/r²- Assumptions
- Point charges; εr=1
- Units
- C, m → N
- Boundary conditions
- r≤0 → VALUE_MUST_BE_POSITIVE
- Example
- 1µC,1µC,0.1m → ~0.899N
- Validation cases
1 published on this page · 4/4 tests · Production surface contract 4/4 · View evidence
- q1=1e-6 q2=1e-6 r=0.1 → F≈0.899
- Sources
- SI / electrostatics textbooks — Coulomb's lawSupports: F=k|q1q2|/r²
- CODATA / NIST — Coulomb constant — k = 1/(4πε₀)Supports: Pinned k = 8.9875517923×10⁹
- SI / electrostatics textbooks — Coulomb's law
- Last reviewed
- 2026-08-08
- Reviewed by
- CalculatorX electrical review (electrical-engineer)
- Calculation version
- 1.0.0
Background
Interpretation and common distinctions.
Compute Coulomb's law force.
Supported and not supported
Supported — Magnitude and attractive flag · API physics.em.coulomb
Not supported — Multipoles, dielectrics, continuous charge distributions
Agent / API notes
Capability id: physics.em.coulomb · tool id: coulomb · pin 1.0.0.
Related tools
Other calculators in this family: Capacitance, Ohm's Law .
Frequently asked questions
Key distinctions behind the calculation.
Vacuum or material?
v1 uses vacuum k. In a dielectric, divide by εr (not modeled here).