Case 1
- Plate area A (m²)
- 0.01m²
- Plate separation d (mm)
- 1mm
- Relative permittivity εr
- 1
88.5419pF
Open with these valuesParallel-Plate Capacitor Calculator
88.5419pF
Result: 88.5419 pFCapacitance grows with plate area and shrinks with the gap: C = ε₀ × εr × A ÷ d. Two plates of 0.01 m² one millimetre apart in air hold 88.54 pF. Halving the gap doubles the capacitance, which is why real capacitors use very thin dielectric films.
The numbers at a glance
Held fixed: Plate area A (m²) 0.010000 m², Plate separation d (mm) 1.000 mm.
| Relative permittivity εr | Result (pF) |
|---|---|
| 1.00Your value | 88.5419 |
| 1.20 | 106.2503 |
| 1.40 | 123.9586 |
| 1.60 | 141.6670 |
| 1.80 | 159.3754 |
| 2.00 | 177.0838 |
Worked examples
Case 2
- Plate area A (m²)
- 0.05m²
- Plate separation d (mm)
- 2mm
- Relative permittivity εr
- 4.5
996.0961pF
Open with these valuesCase 3
- Plate area A (m²)
- 0.005m²
- Plate separation d (mm)
- 0.1mm
- Relative permittivity εr
- 3
1,328.1282pF
Open with these valuesHow it's calculated
C = ε₀ × εr × A ÷ d
- StepEnter the overlapping area of one plate in square metres.
- StepEnter the gap between the plates in millimetres, usually the dielectric thickness.
- StepEnter the relative permittivity: 1 for air, higher for any insulator.
- ResultRead the capacitance in picofarads; divide by 1000 for nanofarads.
Reference table
| A (m²), d (mm), εr | In nF | Capacitance in pF |
|---|---|---|
| 0.005, 0.1, 3 | 1.3281 nF | 1328.1282 |
| 0.01, 1, 1 | 0.0885 nF | 88.5419 |
| 0.02, 0.5, 2.2 | 0.7792 nF | 779.1685 |
| 0.05, 2, 4.5 | 0.9961 nF | 996.0961 |
| 0.1, 5, 1 | 0.1771 nF | 177.0838 |
Questions
How do I calculate the capacitance of a parallel-plate capacitor?
Multiply the electric constant ε₀, about 8.854 × 10⁻¹² F/m, by the relative permittivity and the plate area, then divide by the gap in metres. For 0.01 m², a gap of 1 mm and air between the plates that gives 88.541878 pF.
What is relative permittivity?
Also called the dielectric constant, it says how much better a material stores electric field energy than a vacuum, and it has no unit. Vacuum and air are about 1, paper around 3, glass and mica roughly 5 to 10, and many ceramics reach the hundreds. A higher value multiplies the capacitance by the same factor.
Why does a smaller gap increase capacitance?
Capacitance is inversely proportional to the plate separation, so halving the gap doubles it. A smaller gap lets the same voltage create a stronger field, which pulls more charge onto the plates.
What is the difference between picofarads and nanofarads?
They are two scales for the same quantity: 1 nF is 1000 pF, and one farad is 10¹² pF. Small air-gap capacitors are usually quoted in pF, larger film types in nF.
Which units do I enter?
Plate area in square metres, separation in millimetres, and the relative permittivity as a plain number. The calculator converts the gap to metres itself and returns picofarads.
Sources and last check
Information, not professional advice.