Laplace's Equation Potential Calculator (Plates, Cylinders, Spheres)
Solve ∇²V = 0 between two conducting boundaries: potential, electric field and capacitance for parallel plates, coaxial cylinders or concentric spheres.
How to use the Laplace's Equation Potential Calculator
- Enter or select: Geometry, Inner boundary a, Outer boundary b, Potential at a, Potential at b, Evaluate at position.
- The results (Potential V, Electric field E, Capacitance (per m² / per m / total), General solution) are calculated instantly as you type.
- Use “Copy link” to share the calculation with the same input values.
Formula
- ∇²V = 0
- Plates: V = c₁x + c₂
- Cylinders: V = c₁ ln ρ + c₂
- Spheres: V = c₁/r + c₂
- E = −∇V
About this tool
For a sign convention check: E points from the higher towards the lower potential.