Parallel Plate Capacitor Calculator
Calculate the capacitance of a parallel plate capacitor from plate area, separation and dielectric constant. Enter the overlap area, gap distance and relative permittivity to get C in farads, µF, nF and pF.
Find Capacitance from Plate Area, Separation and Dielectric
Parallel Plate Capacitor Formula
Where:
- \(C\) — capacitance (farads, F)
- \(\varepsilon_0 = 8.854 \times 10^{-12}\ \text{F/m}\) — vacuum permittivity
- \(\varepsilon_r\) — relative permittivity (dielectric constant) of the material between the plates, dimensionless
- \(A\) — area of one plate, i.e. the overlap area of the two plates (m²)
- \(d\) — separation between the plates (m)
The formula says that capacitance grows with plate area and with the dielectric constant, and shrinks as the gap widens. It comes from \(C = Q/V\) applied to the uniform electric field \(E = \sigma/\varepsilon\) between two infinite charged plates.
Parallel Plate Capacitor – Calculation Example
Example: two plates, each with an overlap area of 100 cm², separated by a 1 mm air gap (\(\varepsilon_r \approx 1\)).
Convert to SI units: \(A = 100\ \text{cm}^2 = 0.01\ \text{m}^2\), \(d = 1\ \text{mm} = 0.001\ \text{m}\).
\[ C = 8.854 \times 10^{-12} \times 1 \times \frac{0.01}{0.001} = 8.854 \times 10^{-11}\ \text{F} \]
Result: \(C \approx 88.5\ \text{pF}\) (about 0.0885 nF). This matches the calculator's default values, so you can reproduce it directly.
How to use the calculator
- Enter the Plate Area (A) — the area of one plate, or the overlap area if the plates are offset — and choose its unit (mm², cm², m², in² or ft²).
- Enter the Plate Separation (d), the distance between the plates, and choose its unit (µm, mm, cm, m, mil or in).
- Enter the Relative Permittivity (εr) of the material filling the gap. Use 1 for vacuum or air, ≈2.2 for PTFE, ≈4.7 for glass, ≈80 for water.
- Read the Capacitance in farads, together with the same value converted to picofarads, nanofarads and microfarads. The Calculation Details panel shows the substituted formula step by step.
What is a parallel plate capacitor?
A capacitor stores electric charge and energy in the electric field between its conductors. The simplest and most instructive model is the parallel plate capacitor: two flat conducting plates of area \(A\), facing each other at a distance \(d\), with an insulating material (the dielectric) between them. When a voltage is applied, charge \(+Q\) accumulates on one plate and \(-Q\) on the other, creating a nearly uniform field in the gap.
Capacitance measures how much charge the plates hold per volt: \(C = Q/V\). A larger plate area gives more room for charge, and a smaller gap means a stronger field for the same voltage, so both increase capacitance. The dielectric multiplies capacitance by \(\varepsilon_r\) because its molecules polarize and partially cancel the field between the plates. This is why real capacitors are wound into rolls or stacked in layers — more overlapping area in a compact volume.
The result is typically tiny in farads: everyday capacitors range from picofarads (RF circuits, filters) to microfarads and millifarads (power supplies, motor start circuits). A 100 cm² air-gap capacitor at 1 mm yields only ~88.5 pF, which shows why practical capacitors use thin films (µm and sub-µm gaps) and high-permittivity ceramics.
If you are studying electrostatics more broadly, the field between charged conductors follows an inverse-square law at a distance — you can explore this with our point charge electric field calculator.
Dielectric constants of common materials
| Material | Relative permittivity εr (approx.) |
|---|---|
| Vacuum | 1 (exact) |
| Air (dry, 1 atm) | 1.0006 |
| PTFE / Teflon | 2.1 |
| Polyethylene | 2.3 |
| Paper | 3–4 |
| Glass | 4.7–7 |
| Mica | 5–7 |
| Alumina (ceramic) | 9–10 |
| Water (20 °C) | 80 |
Values vary with frequency, temperature and grade, so check a datasheet for precision work.
Assumptions, limitations and practical tips
- Uniform field, no fringing: the formula assumes the field is perfectly uniform between the plates. This holds when the plate dimensions are much larger than the separation (ideally \(A \gg d^2\)). For small plates or wide gaps, edge fields (fringing) make the real capacitance slightly higher than calculated.
- Dielectric fills the whole gap: the material must completely and uniformly fill the space between the plates. Air pockets or partial filling reduce the effective permittivity.
- Linear, homogeneous dielectric: \(\varepsilon_r\) must be constant and independent of voltage. At very high fields, dielectrics become nonlinear and eventually break down — the gap must also withstand the applied voltage (check the dielectric strength, typically given in kV/mm).
- Conducting, flat plates: thin films, curved plates or rough surfaces deviate from the ideal model.
- Units matter: the calculator converts everything to SI automatically, but if you compute by hand, use m² for area and m for distance — mixing mm and cm is the most common source of order-of-magnitude errors.
- Charged plates attract each other with a force per unit area related to the electrostatic pressure in the gap — relevant when designing mechanical supports for large capacitors or electrostatic actuators.
Frequently Asked Questions
How do I calculate parallel plate capacitance by hand?
Multiply the vacuum permittivity \( \varepsilon_0 = 8.854 \times 10^{-12}\ \text{F/m} \) by the relative permittivity \( \varepsilon_r \), then by the plate area in square meters, and divide by the gap in meters. For example, a 0.02 m² plate area, a 0.5 mm gap and \( \varepsilon_r = 2.2 \) gives \( C = 8.854 \times 10^{-12} \times 2.2 \times 0.02 / 0.0005 \approx 780\ \text{pF} \). Always convert area and distance to SI units first.
What is a typical or good capacitance value for a parallel plate capacitor?
There is no single "good" value — it depends on the application. RF and filter circuits use picofarads (pF), timing and audio circuits use nanofarads (nF), and power supplies use microfarads (µF) or more. Because vacuum permittivity is so small, even large plates with a millimeter air gap give only tens of pF. Practical capacitors reach µF values by using micro-meter thin dielectric films and high-permittivity ceramics.
Why is my hand calculation off by a factor of 10, 100 or 1000?
The most common cause is a unit mix-up: area must be in m² (not cm² or mm²) and distance in m (not mm). Remember that 1 cm² = 10⁻⁴ m² and 1 mm² = 10⁻⁶ m², because both length dimensions convert. Also double-check whether you entered the plate area or the total area of both plates — the formula uses only one plate's overlap area, not the sum.
Does the calculator account for fringing fields at the plate edges?
No. The formula \( C = \varepsilon_0 \varepsilon_r A/d \) assumes a perfectly uniform field, which holds only when the plate dimensions are much larger than the gap. Real capacitors have edge (fringing) fields that make the actual capacitance slightly higher than calculated. For square plates, the error stays below roughly 1% when the side length is more than about 40 times the separation.
Can I use this calculator for a capacitor with two different dielectrics or a partial air gap?
Only if you first compute an effective permittivity. For dielectric layers stacked in series (perpendicular to the plates), the gap behaves like capacitors in series: with thicknesses \( d_1 \) and \( d_2 \), use \( d / \varepsilon_{eff} = d_1/\varepsilon_1 + d_2/\varepsilon_2 \). For side-by-side materials (parallel to the plates), treat them as capacitances in parallel and add the results. Air pockets in the gap effectively lower the overall permittivity.
How does temperature and frequency affect the result?
Relative permittivity is not a fixed constant — it varies with temperature, frequency and material grade. Water drops from about 80 at low frequencies to far less at microwave frequencies; ceramic dielectrics can shift tens of percent over their rated temperature range. For precision timing or filter circuits, check the dielectric's datasheet at your operating frequency and temperature rather than relying on a table value.
What else should I check besides capacitance when designing a real capacitor?
Check the dielectric strength (breakdown field, typically given in kV/mm) so the gap can withstand your working voltage with a safety margin, and the equivalent series resistance and leakage current for the material. Also remember that charged plates attract each other with a mechanical force, which matters for electrostatic actuators or large flexible-plate designs where the gap could deform under voltage.