Free · Physics models
Concentric Sphere Capacitance
Calculate capacitance and inverse radii for two concentric conducting spheres with a uniform dielectric.
- Formula & worked example
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Calculator inputs
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How to use this calculator
- Enter the known values in the units shown. Results update as you type.
- Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
- Use the worked example to check the method. Reset restores the starting fields.
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Formula and method
Capacitance = 3.3379502. The worked example lists its inputs and unit conventions.
C = 4π ε₀ εr ab/(b−a).
Worked example
Enter these known values and leave the other values blank.
- Inner sphere radius
- 1 cm
- Outer sphere radius
- 3 cm
- Relative permittivity
- 2
- Capacitance
- 3.338 pF
Assumptions and limitations
- The dielectric completely fills the gap between positive radii with b > a. The retained ε₀ = 8.854187817×10⁻¹² F/m is a historical rounded constant, not a current exact SI definition. Supported relative permittivity is at least one.
- Clear the quantity to solve an inverse; keep known quantities fixed with locks. Some inverses are singular or ambiguous and require further known values.
- Unit selectors convert the same physical quantity. Rounded reference constants and presets limit physical accuracy even when arithmetic displays more digits.
Common questions
What does this model assume?
The dielectric completely fills the gap between positive radii with b > a. The retained ε₀ = 8.854187817×10⁻¹² F/m is a historical rounded constant, not a current exact SI definition. Supported relative permittivity is at least one.
Can I solve for an input?
Editable calculated fields support the captured inverse relationships. Clear the unknown and supply enough independent known values; an inverse must remain within the declared physical domain.
References
The dielectric completely fills the gap between positive radii with b > a. The retained ε₀ = 8.854187817×10⁻¹² F/m is a historical rounded constant, not a current exact SI definition. Supported relative permittivity is at least one.