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Spherical Capacitor Calculator — result sheet
Calculate ideal capacitance and stored energy for two concentric spherical conductors with a specified dielectric.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: For concentric spheres, C = 4πε₀εᵣR₁R₂/(R₂ − R₁); stored energy U = ½CV².
The spherical geometry makes the radius gap part of the capacitance rather than an afterthought. The page reports both farads and picofarads while stating the ideal dielectric and voltage boundary.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Inner conductor radius — cm; minimum 1.0E-6; maximum 1000000000
- Outer conductor radius — cm; minimum 1.0E-6; maximum 1000000000
- Relative permittivity εᵣ — dimensionless; minimum 1.0E-6; maximum 1000000
- Potential difference — V; minimum 0; maximum 1000000000000
Worked example
| Input | Value |
|---|---|
| Inner conductor radius | 5 |
| Outer conductor radius | 10 |
| Relative permittivity εᵣ | 1 |
| Potential difference | 1000 |
A 5 cm and 10 cm vacuum spherical capacitor has C ≈ 11.1265 pF and stores about 0.00000556325 J at 1,000 V.
Assumptions and limits
- The conductors are concentric spherical shells with negligible finite-thickness and edge effects.
- The dielectric is uniform and represented by a constant relative permittivity.
- Radii are converted from centimetres to metres before the SI formula is applied.
- Dielectric breakdown, leakage, stray capacitance, charging current, and construction safety are excluded.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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