The capacitance calculator above works out how much charge a structure stores per volt applied to it, starting from its physical dimensions and the material between its conductors. This is the design question rather than the arithmetic one: not what a capacitor labelled 100 nF will do, but what capacitance a given pair of plates, a length of coaxial cable or a stack of metallised film will actually have.
Arb Digital builds free tools that stay in their lane and link to the neighbours. This page computes capacitance from geometry. If you already have capacitor values and want to combine them, our capacitor combination calculator handles series and parallel networks. If you want the energy in a capacitor you already know the value of, the capacitor energy calculator is the shorter route, and the capacitance converter simply rescales between farads, microfarads, nanofarads and picofarads.
What This Capacitance Calculator Does
Capacitance is defined as charge divided by voltage. Put a potential difference across two conductors and charge accumulates, positive on one and negative on the other; the ratio of that charge to the voltage is the capacitance, measured in farads. A farad is an enormous unit in practical terms, which is why real components are labelled in microfarads, nanofarads and picofarads.
For a pair of parallel plates the geometry gives a simple result. The capacitance is the permittivity of the material multiplied by the plate area and divided by the separation. Larger plates hold more charge at the same voltage; a smaller gap makes the field stronger for the same voltage and pulls in more charge; a dielectric with a higher permittivity polarises and partly cancels the field, allowing still more charge for the same applied voltage.
The coaxial and spherical modes handle the two other geometries that have closed-form answers. A coaxial capacitor is a wire inside a tube, which is exactly what a length of screened cable is, and it is why cable capacitance per metre appears on every datasheet. A spherical capacitor is two concentric shells, more useful as a teaching case than a component, but it gives the cleanest illustration of why capacitance depends on the ratio of the radii rather than their difference alone.
Alongside the capacitance itself, the panel reports what the structure does at a working voltage you choose. The charge follows from Q = CV, the energy from a half of C times V squared, and the electric field from the voltage divided by the gap. That field figure is the one that decides whether the design survives, because every dielectric has a voltage gradient beyond which it breaks down.
How to Use It
- Choose the geometry first. The inputs that matter change with it: plates use area and separation, coaxial uses two radii and a length, spherical uses two radii alone.
- Set the dielectric constant. Use the preset list or type a value from a datasheet. It is dimensionless and always at least one, because a vacuum is the reference.
- Watch the units on the separation. Practical gaps are microns, not metres, and getting this wrong is the single easiest way to be out by a factor of a thousand.
- Use the plate count for stacked designs. A multilayer ceramic or an interleaved variable capacitor with N plates behaves like N−1 single capacitors in parallel.
- Check the field strength against the dielectric's rating. If it exceeds the material's breakdown strength, the design fails no matter how attractive the capacitance is.
The Formula: How Capacitance Is Calculated
Section 8.1 of OpenStax University Physics Volume 2, on capacitors and capacitance, derives the parallel-plate result as C = ε₀A ÷ d, where A is the plate area, d is the separation and ε₀ is the permittivity of free space. Inserting a dielectric multiplies that by the material's relative permittivity, giving C = εrε₀A ÷ d.
The constant comes from measurement. The 2022 CODATA value for the vacuum electric permittivity, published by NIST, is 8.854187 8188 × 10⁻¹² farads per metre, and the farad itself is the SI derived unit of capacitance defined in the BIPM SI Brochure as one coulomb per volt.
Work the default values. The plates are 100 cm², which is 0.01 square metres, separated by 0.1 mm, which is 0.0001 metres, with a polyester dielectric at 3.5. The capacitance is 8.8541878 × 10⁻¹² × 3.5 × 0.01 ÷ 0.0001 = 3.0990 × 10⁻⁹ farads, which is 3,099 picofarads or 3.099 nanofarads. At 100 volts it holds 310 nanocoulombs, stores 15.5 microjoules, and sits in a field of 1,000,000 volts per metre, which is one kilovolt per millimetre.
The coaxial formula is C = 2πεrε₀L ÷ ln(b/a), with a the inner radius, b the inner radius of the shield and L the length. The spherical formula is C = 4πεrε₀ab ÷ (b − a). Both depend on the ratio of the radii rather than their absolute size, which is why a thin coaxial cable and a thick one can share the same capacitance per metre.
Why a Thinner Dielectric Is Not Always Better
Halving the gap doubles the capacitance, which makes thin dielectrics look like free performance. They are not, because halving the gap also doubles the electric field at any given voltage, and every insulator has a field strength beyond which it conducts. Air breaks down at roughly 3 megavolts per metre, polypropylene film at around 500, and thin oxide layers at more still, but no material is unlimited.
This is why capacitors are specified by a voltage rating as well as a capacitance, and why the two trade against each other in a given volume. Doubling the working voltage of a design generally means doubling the dielectric thickness, which halves the capacitance, so the product of capacitance and voltage rating for a given plate area is roughly fixed by the material. Choosing a better dielectric is the only way to move that product, and it is why capacitor technology is largely a materials story.
The field figure in the result panel is the number to check. Compare it against the dielectric strength quoted for your material and leave real margin, because the published figure is measured on pristine samples under controlled conditions. Voids, contamination, sharp edges and moisture all reduce it, and a capacitor that punctures once is usually destroyed permanently.
Choosing a Dielectric, and the Trap in Ceramics
Relative permittivity ranges over several orders of magnitude. Air is essentially one. Common plastic films sit between 2 and 3.5. Mica is around 6.5. Water is above 80, which is why it is such an effective solvent but useless as a capacitor dielectric. Some ceramic formulations reach into the thousands, which is how a physically small multilayer ceramic capacitor can offer microfarads.
The trap is that high-permittivity ceramics are not stable. Class 1 ceramics such as C0G and NP0 have modest permittivity and are effectively constant with temperature, voltage and age. Class 2 ceramics such as X7R and Y5V achieve their much higher values through a ferroelectric mechanism that varies with all three. A Y5V part can lose most of its rated capacitance at its rated voltage, and X7R parts routinely lose a third or more under DC bias.
The practical consequence is that a capacitance calculated from geometry describes the structure, not necessarily the component's behaviour in circuit. For film, mica and Class 1 ceramic parts the calculated figure is close to reality. For Class 2 ceramics you have to consult the manufacturer's bias and temperature curves, and design for the derated value rather than the printed one.
Fringing Fields, Stray Capacitance and Real Boards
The parallel-plate formula assumes the field is uniform between the plates and zero everywhere else. That is only true for plates that are large compared with their separation. Real plates have field lines that bulge outward at the edges, and those fringing fields store extra charge, so the true capacitance is always a little higher than the formula suggests. For plates a hundred times wider than their gap the error is well under one per cent; for plates only a few times wider it can be several per cent.
The same physics creates stray capacitance everywhere in a circuit. Any two conductors separated by an insulator form a capacitor, so adjacent PCB traces, a trace over a ground plane, the windings of a transformer and even a pair of hands near a sensitive input all contribute. A trace running above a ground plane on standard FR-4 has a capacitance of roughly a picofarad per centimetre, which is negligible at audio frequencies and decisive at radio frequencies.
Cable capacitance is the version that bites most often. Screened cable is a coaxial capacitor, typically around 100 picofarads per metre, and it appears directly across the signal. Combined with the source impedance it forms a low-pass filter, which is why a long run from a high-impedance sensor loses high frequencies. Our capacitor charge time calculator gives the time constant that combination produces, and the Ohm's law calculator and voltage divider calculator cover the resistive side of the same network.
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Browse All Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Entering the separation in millimetres while thinking in metres — a factor of a thousand in the gap is a factor of a thousand in the answer, and it is the most common error on this calculation.
- Assuming capacitance depends on voltage — it does not, for an ideal capacitor. It depends on geometry and material only, though real Class 2 ceramics behave otherwise for a different reason.
- Ignoring the electric field — a design with attractive capacitance and a field above the dielectric's breakdown strength does not work at all.
- Trusting the formula for small plates — fringing at the edges adds capacitance, and the error grows as the plates get closer in size to their separation.
- Using a permittivity below one — the relative value is measured against vacuum, so it is always at least one and normally well above it.
Related Free Tools From Arb Digital
Combine known values with the capacitor combination calculator, find stored energy with the capacitor energy calculator, and time a charging curve with the capacitor charge time calculator. Unit changes are handled by the capacitance converter and the area converter. For the resistive parts of the same circuit, use the Ohm's law calculator, the voltage divider calculator and the resistor combination calculator. The full free online tools hub lists everything Arb Digital publishes.
Frequently Asked Questions
Capacitance equals the relative permittivity multiplied by the permittivity of free space and the plate area, divided by the separation. The permittivity of free space is about 8.854 times ten to the minus twelve farads per metre, so practical capacitances come out very small.
Not for an ideal capacitor, because it depends only on geometry and the dielectric. Class 2 ceramic capacitors are the practical exception: their ferroelectric dielectric loses permittivity under DC bias, so a real part can measure well below its printed value in circuit.
Use a dielectric with a higher permittivity, reduce the gap, or stack more plates in parallel. All three have limits: high-permittivity materials are less stable, a smaller gap raises the electric field toward breakdown, and stacking adds cost and physical height.
It follows from two pi times the permittivity times the length, divided by the natural log of the shield radius over the conductor radius. Typical screened cable comes out near 100 picofarads per metre, which loads a high-impedance signal source noticeably over a long run.
Fringing fields. The formula assumes the electric field exists only between the plates, but real field lines bulge out at the edges and store additional charge. The discrepancy is small for plates much wider than their separation and grows as they get closer in size.
It depends on the material. Air breaks down near 3 megavolts per metre and plastic films are typically in the hundreds. Published figures are measured on clean samples, so real designs need margin for voids, contamination, moisture and sharp conductor edges.
A stack of N plates with alternating connections behaves as N minus 1 capacitors in parallel, so the capacitance scales with that count. This is how multilayer ceramic capacitors reach useful values in a very small package.
This tool is provided for educational and design-estimating use. It models ideal geometry with no fringing, no dielectric loss and no bias dependence, and it is not a substitute for manufacturer data or safety testing.
