Capacitance Calculator

What the capacitance calculator does

The capacitance of a parallel-plate capacitor depends on its plate area, the gap between the plates, and the material in between. This calculator finds the capacitance from these, and can also solve backward for the area or the spacing needed to reach a target capacitance.

Below is what capacitance is, the equation behind it, how the geometry sets the value, and a worked example.

How to use it

1. Choose what to calculate: capacitance, plate area, or separation distance.
2. Enter the known values, using simple mode for air or advanced mode to set the permittivity.
3. Press Calculate for the result, or Reset to clear it.

What capacitance is

Capacitance is a measure of how much electric charge a component can store for a given voltage. A capacitor with high capacitance holds a lot of charge at a modest voltage, while a low-capacitance one holds little. It is the defining property of a capacitor, one of the most common components in electronics, used to store energy, smooth out voltage, filter signals, and set timing. Capacitance is measured in farads, though practical capacitors are usually a tiny fraction of a farad, in the range of microfarads, nanofarads, or picofarads.

The most basic kind of capacitor is two parallel conducting plates separated by a small gap, and its capacitance is set entirely by its physical construction: how large the plates are, how far apart they sit, and what fills the space between them. This calculator works with that parallel-plate arrangement, the foundation for understanding capacitance. By relating the capacitance to the area, the spacing, and the material, it lets you find any one of these from the others, which is useful both for understanding how capacitors work and for designing one to a target value.

The equation it uses

The capacitance of a parallel-plate capacitor is the permittivity times the plate area, divided by the gap:

C = ε × A ÷ d

Here C is the capacitance, ε is the permittivity of the material between the plates, A is the area of the plates, and d is the separation between them. Capacitance grows with larger plates and shrinks with a wider gap, while the permittivity of the filling material scales the whole thing. The calculator can rearrange this to solve for any of the three geometric quantities: the capacitance from area and spacing, the area needed for a target capacitance, or the spacing that gives a desired value.

How area and spacing set the capacitance

The geometry of a parallel-plate capacitor controls its capacitance in two opposite ways. Larger plates mean more capacitance, because there is more surface on which charge can accumulate; double the area and you double the capacitance. This is why high-capacitance capacitors often pack in a very large plate area, sometimes by rolling long strips of foil into a compact cylinder.

The spacing works the other way: a smaller gap means more capacitance. Bringing the plates closer together strengthens the attraction between the opposite charges on them, letting more charge be stored at the same voltage, so halving the gap doubles the capacitance. This is why capacitors use very thin insulating layers between their plates. The two effects together explain the design of real capacitors, which chase high capacitance through large areas and tiny gaps. The calculator makes the trade-offs concrete, showing how changing the area or the spacing moves the capacitance up or down.

Permittivity and dielectrics

The third ingredient is the material between the plates, captured by its permittivity. Permittivity describes how readily a material permits an electric field to store energy within it, and a higher permittivity gives a higher capacitance for the same plate area and spacing. The calculator defaults to the permittivity of empty space, which is also very close to that of air, suitable for a simple air-gap capacitor.

Real capacitors usually fill the gap with an insulating material called a dielectric, such as ceramic, plastic film, or metal oxide, chosen because it has a permittivity several times higher than air, boosting the capacitance considerably. In advanced mode, the calculator lets you enter the permittivity of whatever material you are using, so you can model a capacitor with a dielectric rather than just air. The permittivity to enter is the absolute permittivity of the material, the permittivity of free space multiplied by the material's relative figure. This makes the calculator flexible enough to handle both the textbook air-gap case and practical capacitors with real dielectrics.

Units and precision

The calculator takes the plate area in units from square millimetres to square yards, the separation in units from millimetres to yards, and the capacitance in farads or its smaller multiples, with the permittivity in farads per metre. It applies the parallel-plate relationship exactly. The default permittivity is that of free space, which suits an air gap; for a dielectric, enter the material's absolute permittivity in advanced mode. The calculation is an idealisation that ignores edge effects at the plate borders, which are small for closely spaced plates.

A worked example

Suppose a parallel-plate capacitor has plates of 1 square metre separated by 1 millimetre, with air between them.

Using the permittivity of free space, the capacitance is C = ε × A ÷ d ≈ 8.85 nanofarads. This shows how small the capacitance of a simple air-gap capacitor is even with sizeable plates: a full square metre of plate, just a millimetre apart, gives only a few nanofarads. Filling the gap with a dielectric of higher permittivity, or shrinking the spacing, would raise this considerably.

Questions people ask

How do you calculate capacitance?

For a parallel-plate capacitor, use C = ε × A ÷ d, from the permittivity, the plate area, and the gap. More fundamentally, capacitance is charge divided by voltage.

How does plate area affect capacitance?

Directly: larger plates give more capacitance, because more surface stores more charge. Doubling the area doubles the capacitance.

How does the gap affect capacitance?

Inversely: a smaller gap gives more capacitance. Halving the separation doubles the capacitance, which is why capacitors use very thin insulating layers.

What is a dielectric?

An insulating material placed between the plates, with a higher permittivity than air, which raises the capacitance. Ceramics and plastic films are common dielectrics.

References

A quick note on where the physics comes from. Capacitance, the parallel-plate formula, and dielectrics are standard physics, set out in OpenStax's University Physics and in Georgia State University's HyperPhysics. The permittivity of free space follows NIST. The HyperPhysics link is worth a quick click to confirm it lands where you expect.

1. OpenStax, University Physics Volume 2, Section 8.1, Capacitors and Capacitance. https://openstax.org/books/university-physics-volume-2/pages/8-1-capacitors-and-capacitance
2. HyperPhysics, Capacitance and the Parallel Plate Capacitor. http://hyperphysics.phy-astr.gsu.edu/hbase/electric/pplate.html
3. National Institute of Standards and Technology (NIST), Fundamental Physical Constants, vacuum electric permittivity. https://physics.nist.gov/cgi-bin/cuu/Value?ep0