Parallel Plate Capacitor Calculator (Capacitance from Area, Gap and Dielectric)
Capacitance, charge, stored energy and electric field of two parallel plates from their area, the gap, the insulator between them and the voltage.
Results
The dashed line marks the value you entered.
What this tool does
Capacitance grows with plate area and with the permittivity of the insulator, and falls as the plates move apart: halve the gap and the capacitance doubles. Two plates of 100 cm² with 1 mm of air between them hold only about 88 pF; a dielectric with εr = 4 multiplies that by four. The formula ignores the fringing field at the edges, so it works best when the gap is much smaller than the plate. Keep the field well below the breakdown strength of the insulator — roughly 3 kV/mm for dry air.
Formula
C = ε₀ εr A ÷ d (ε₀ = 8.854 × 10⁻¹² F/m) · Q = C V · E = ½ C V² · field = V ÷ d
Variables
| Symbol | Meaning | Unit |
|---|---|---|
ar | Area of each plate | cm² |
dg | Gap between the plates | mm |
er | Relative permittivity of the insulator (εr) | — |
vv | Voltage across the plates | V |
C | Capacitance | pF |
Q | Charge on the plates | nC |
E | Energy stored in the gap | nJ |
F | Electric field in the gap | V/mm |
Worked example
- Area of each plate100 cm²
- Gap between the plates1 mm
- Relative permittivity of the insulator (εr)4
- Voltage across the plates100 V
- Capacitance354.17 pF
- Charge on the plates35.417 nC
- Energy stored in the gap1770.84 nJ
- Electric field in the gap100.0 V/mm
Limitations
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.