⚡ Parallel Plate Capacitor Calculator
Calculate C = ε₀·A/d for a parallel plate capacitor.
Result
How to Use This Calculator
This calculator finds the capacitance of a parallel plate capacitor from its geometry. Enter the plate area, the separation between the plates, and the relative permittivity of the material between them.
Enter the plate area A in square meters. This is the overlapping area of the two plates, not the total surface.
Enter the separation d in meters. For a 0.5 mm gap, enter 0.0005.
Enter the relative permittivity of the dielectric. Use 1 for air or vacuum, or look up your material: paper is about 3.5, glass runs 4 to 10, ceramic can exceed 100.
Click Calculate. The capacitance appears in farads, with picofarad and nanofarad equivalents so small values are easy to read.
The Parallel Plate Capacitance Formula
Capacitance measures how much charge a capacitor holds per volt: C = Q/V. For two flat parallel plates, the geometry alone determines it. Bigger plates hold more charge, so capacitance grows with area. A tighter gap concentrates the electric field, so capacitance grows as separation shrinks. Slip a dielectric material between the plates and its molecules polarize, letting the plates store even more charge, which is what the relative permittivity captures.
The formula assumes the plates are much wider than the gap between them. When that holds, the electric field is nearly uniform and edge effects are tiny. It also assumes the dielectric fills the gap completely and the plates are parallel. Real capacitors deviate a little, but for homework and first-pass design this formula is the standard starting point.
Worked Example
Where This Comes Up
You will use this formula whenever you size a capacitor from scratch. Touch sensors, capacitive proximity switches, and MEMS microphones all behave like tiny parallel plate capacitors, and their sensitivity comes straight from C = e0 x er x A / d. In power electronics, snubber capacitors across switching transistors are chosen with this math. It is also the standard first calculation in electromagnetism homework before moving on to cylindrical and spherical capacitors.
Watch your units: area in square meters and separation in meters, or the powers of ten will punish you. A 1 cm^2 plate is 0.0001 m^2, and a 0.1 mm gap is 0.0001 m. Also remember the result is usually picofarads to nanofarads for hand-sized plates. If your answer comes out in whole farads, you probably entered centimeters instead of meters.
Frequently Asked Questions
What is the permittivity of free space?
It is a physical constant, 8.854 x 10^-12 F/m. It appears in the capacitance formula because it describes how easily electric fields form in a vacuum.
What is relative permittivity?
Relative permittivity measures how much a material between the plates increases capacitance compared to vacuum. Air is about 1.0006, so roughly 1. Paper is around 3.5 and ceramic can exceed 100.
Why does bringing the plates closer increase capacitance?
A smaller gap means a stronger electric field for the same voltage, so the plates hold more charge. Capacitance is inversely proportional to separation: halve the gap and capacitance doubles.
What units does this calculator use?
Enter area in square meters and separation in meters. The result is in farads. Small capacitors give tiny farad values, so convert: multiply by 10^9 for nanofarads or 10^12 for picofarads.
Does plate shape matter?
Only the overlapping area counts. The formula assumes flat, parallel plates that are large compared to their separation, so edge effects are negligible.