Capacitor Calculator

Dielectric preset:

Choose Custom to enter another dielectric constant.

Relative permittivity:

Use 1 for vacuum; material values vary with formulation, frequency, temperature, and bias.

Plate area:

Use the overlapping face area, not the combined area of both plates.

Plate separation:

Smaller gaps raise both capacitance and electric-field stress.

Applied voltage:

Negative voltage reverses the charge sign; capacitance and stored energy remain nonnegative.

Fringe correction:

Leave at 0% unless a measured or simulated correction is available.

Dielectric strength:

Use a verified value and appropriate derating; 0 means not evaluated.

kV/mm

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Two conductors separated by insulation can store electric charge. Capacitance describes how much charge is stored per volt, and the farad is its SI unit. Most simple plate arrangements produce values far below one farad, so picofarads and nanofarads are common scales in geometry exercises and early design estimates.

A parallel-plate model makes the physical tradeoffs visible. Capacitance rises when the facing plate area grows, when the dielectric's relative permittivity grows, or when the gap becomes thinner. Applied voltage does not change ideal capacitance, but it does change stored charge, stored energy, and electric-field stress.

Effects of changing parallel plate capacitor quantities
Change	Capacitance	Other consequence at fixed voltage
Double plate area	Doubles	Charge and stored energy double.
Double relative permittivity	Doubles	Charge and stored energy double in the ideal linear model.
Halve plate separation	Doubles	Electric field also doubles.
Double voltage	Unchanged	Charge doubles and stored energy becomes four times larger.

The gap deserves special attention. A thinner dielectric can improve capacitance while reducing the distance available to withstand voltage. Breakdown strength is therefore a material and construction limit, not a bonus value to infer from the capacitance result.

Real capacitors are not infinite flat plates with a perfectly uniform dielectric. Edge fields, electrode shape, multilayer or wound construction, frequency, leakage, equivalent series resistance, tolerance, temperature, aging, defects, and voltage derating all matter. The ideal model is useful for learning and first-pass comparison, not for approving a real component or high-voltage design.

How to Use This Tool:

Start with the physical geometry, check every unit, and add a voltage-stress comparison only when you have a defensible dielectric-strength value.

Choose a Dielectric preset or enter a positive Relative permittivity for the material and operating conditions you intend to model.
Enter the overlapping area of one facing plate under Plate area, then choose m², cm², mm², or in².
Enter the dielectric thickness under Plate separation and select m, mm, µm, or in. A unit mistake here changes capacitance and field stress together.
Set Applied voltage. A negative value reverses stored-charge polarity but leaves capacitance, energy, and field magnitude nonnegative.
Leave Fringe correction at 0% unless a measurement or simulation supports an uplift. Enter Dielectric strength greater than zero only to enable the simple voltage-margin check.
Read Capacitance ledger for the main quantities and Stress audit for field and margin. Use the gap rows to compare 50%, 100%, 150%, and 200% of the entered separation.

Interpreting Results:

Parallel-plate capacitance is the geometry-and-material estimate. Stored charge follows voltage polarity, while Stored energy depends on voltage squared. A negative voltage therefore produces negative charge but never negative energy.

Electric field is voltage magnitude divided by gap. The voltage margin is evaluated only when dielectric strength is above zero and applied voltage is nonzero. A missing margin means no finite operating-stress ratio was calculated, not that the construction is safe.

Margin below 1.0 means the entered voltage exceeds the calculated breakdown voltage.
Margin from 1.0 up to but not including 1.5 is labeled Thin margin.
Margin from 1.5 up to but not including 3.0 is labeled Working margin.
Margin of 3.0 or more is labeled Comfortable margin, but it is still only an ideal comparison against a user-supplied strength.

Technical Details:

The model assumes two large, flat, parallel conductors with a uniform dielectric completely filling the separation. Area and gap are converted to square metres and metres before calculation. Vacuum permittivity uses the 2022 CODATA value of 8.8541878188 × 10⁻¹² F/m.

Formula Core:

Geometry determines capacitance first. Voltage then determines charge, energy, electric field, and the optional breakdown comparison.

\begin{array}{lcl} C & = & \frac{ε_{0} ε_{r} A}{d} (1 + p / 100) \\ Q & = & C V \\ U & = & \frac{1}{2} C V^{2} \\ E & = & \frac{| V |}{d} \\ V_{breakdown} & = & S d \\ m & = & \frac{V_{breakdown}}{| V |} \end{array}

C is capacitance in farads, ε₀ is vacuum permittivity, ε_r is relative permittivity, A is plate area in m², d is separation in metres, p is fringe correction in percent, V is applied voltage, S is dielectric strength, and m is voltage margin. Strength entered in kV/mm is converted consistently with the gap before breakdown voltage is reported in volts.

With relative permittivity 2.2, plate area 25 cm², separation 0.5 mm, 12 V, and no fringe correction, capacitance is about 97.396 pF. Charge is about 1.169 nC, stored energy is about 7.013 nJ, and field magnitude is 0.0240 kV/mm.

Rule Core:

Capacitor calculation rules and boundaries
Quantity	Rule	Meaning
Relative permittivity	Greater than 0, up to 100,000	Preset values are representative and can be replaced by a custom value.
Area and separation	Strictly greater than 0	Zero geometry is rejected rather than clamped.
Fringe correction	0% to 25%, inclusive	Applies a direct percentage multiplier to capacitance and its dependent results.
Dielectric strength	0 disables the check	A positive value enables breakdown voltage and margin.
Gap sweep	0.5×, 1×, 1.5×, and 2×	Every other input stays fixed while separation changes.

Surface charge density is charge divided by area. Ideal energy density is stored energy divided by the dielectric volume, A × d. Results retain full precision internally and are formatted with engineering prefixes for display.

Engineering Limits:

This electrostatic estimate does not certify a material, insulation system, or commercial capacitor. Use verified datasheets, applicable standards, conservative derating, and qualified engineering review for real hardware.

Relative permittivity can vary with formulation, frequency, temperature, bias, and aging.
Breakdown strength depends on thickness, defects, humidity, contamination, waveform, electrode geometry, and test method.
The percentage fringe correction does not replace field simulation or measurement for unusual shapes.
Leakage, equivalent series resistance, ripple current, dielectric absorption, heating, tolerances, and failure energy are outside the model.

Worked Examples:

Halving the gap

Starting from the 25 cm² polypropylene example above, reducing the 0.5 mm gap to 0.25 mm raises capacitance from about 97.396 pF to 194.792 pF. At the same 12 V, field magnitude also doubles from 0.0240 to 0.0480 kV/mm. The larger capacitance is therefore paired with greater dielectric stress.

References:

CODATA value: vacuum electric permittivity, National Institute of Standards and Technology, 2022.
Capacitors and Capacitance, OpenStax, 2016.
Chapter 8 Key Equations, OpenStax, 2016.