Quick answer
Capacitance C = ε₀ εr A ÷ d, with ε₀ = 8.8541878128 × 10⁻¹² F/m. Plates of 10 cm² separated by 1 mm in vacuum (εr = 1) give 8.8542 pF.
Enter the plate area, separation and relative permittivity. The calculator returns the capacitance. Use this parallel plate capacitor calculator to check your own figures.
Related tools: Voltage Divider Calculator: Output voltage of a two-resistor divider. RLC Impedance Calculator: Impedance and phase angle of a series RLC circuit. RMS Voltage Calculator: Convert between RMS, peak and peak-to-peak voltage of a sine wave.
How to use the Parallel Plate Capacitor Calculator
- Enter plate area (cm²) (above 0).
- Enter plate separation (mm) (above 0).
- Enter relative permittivity εr (above 0). It starts at 1.
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Plate area | A number, in cm² | > 0 |
| Plate separation | A number, in mm | > 0 |
| Relative permittivity εr | A number | > 0, starts at 1 |
Formula and method
Formula
C = ε₀ εr A ÷ d, ε₀ = 8.8541878128×10⁻¹² F/m
IEEE-754 double precision; shown to the decimals indicated.
Ignores fringing fields, which matter when the gap is not small compared with the plates.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Plate area = 10; Plate separation = 1; Relative permittivity εr = 1.
| Result | Value |
|---|---|
| Capacitance | 8.8542 pF |
Example 2
Inputs: Plate area = 25; Plate separation = 0.5; Relative permittivity εr = 4.5.
| Result | Value |
|---|---|
| Capacitance | 199.2192 pF |
Example 3
Inputs: Plate area = 100; Plate separation = 2; Relative permittivity εr = 2.2.
| Result | Value |
|---|---|
| Capacitance | 97.3961 pF |
The first line is the headline result (capacitance). IEEE-754 double precision; shown to the decimals indicated.
Scaling
Capacitance rises with area and with permittivity and falls with separation. A dielectric with εr = 4 quadruples the capacitance to about 35.4 pF. Halving the gap doubles it.
Validity
The formula assumes the separation is much smaller than the plate size, so edge (fringing) effects are small. Real capacitors also have a breakdown voltage that limits how thin the dielectric can be.
How the result changes with plate area
Holding every other input at the first worked example, this table changes only plate area. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Plate area | Capacitance |
|---|---|
| 5 | 4.4271 pF |
| 10 | 8.8542 pF |
| 20 | 17.7084 pF |
| 40 | 35.4168 pF |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Plate area: entering "0" shows "Plate area must be greater than 0." beside that field and no result.
- Relative permittivity εr: entering "0" shows "Relative permittivity εr must be greater than 0." beside that field and no result.
Choosing between the Parallel Plate Capacitor Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Voltage Divider Calculator](/engineering/voltage-divider-calculator/) | input voltage, r1 and r2 | Output voltage |
| [RLC Impedance Calculator](/engineering/rlc-impedance-calculator/) | resistance, inductance and capacitance | Impedance |
| [RMS Voltage Calculator](/engineering/rms-voltage-calculator/) | i know the and voltage | RMS voltage |
| [Current Divider Calculator](/engineering/current-divider-calculator/) | total current, r1 and r2 | Current through R1 |
| [Inductive Reactance Calculator](/engineering/inductor-reactance-calculator/) | inductance and frequency | Inductive reactance |
Background: electrical circuits
Ohm's law links voltage, current and resistance: V = I × R, so I = V ÷ R and R = V ÷ I. Power is P = V × I, which also equals I² × R and V² ÷ R.
These relations hold for ohmic components, where resistance is constant. Diodes and transistors are non-linear, and in AC circuits with reactive parts impedance (Z) takes the place of resistance. Check component ratings and local electrical code before relying on any calculation.
Assumptions and limitations
- Valid when d is much smaller than the plate size
Use results as engineering estimates and check them against the governing standards, safety factors and a qualified engineer's judgement before relying on them.
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for plate area and relative permittivity εr to confirm this.
Frequently asked questions
What is permittivity?
A material's ability to store electric energy in a field.
What is a picofarad?
A picofarad is 10⁻¹² farad, so the 8.8542 pF in the example is 0.0000000000088542 F.
How can I increase capacitance?
Increase area or reduce the gap.
What does the Parallel Plate Capacitor Calculator calculate?
Capacitance of two parallel plates. It returns Capacitance.
What formula does the Parallel Plate Capacitor Calculator use?
C = ε₀ εr A ÷ d, ε₀ = 8.8541878128×10⁻¹² F/m. Ignores fringing fields, which matter when the gap is not small compared with the plates.
What do I need to enter in the parallel Plate Capacitor Calculator?
You enter Plate area (cm²), Plate separation (mm) and Relative permittivity εr.
How is the result rounded or limited?
IEEE-754 double precision; shown to the decimals indicated. Valid when d is much smaller than the plate size.
What is an example of a parallel Plate Capacitor result?
With plate area 10, plate separation 1 and relative permittivity εr 1, the capacitance is 8.8542 pF.
Where does the method come from?
The method follows: CODATA 2018 / SI exact constants.
Can I rely on this calculator for a decision?
Use results as engineering estimates and check them against the governing standards, safety factors and a qualified engineer's judgement before relying on them. For this calculator in particular: Valid when d is much smaller than the plate size.
Related calculators
- Voltage Divider Calculator — Output voltage of a two-resistor divider.
- RLC Impedance Calculator — Impedance and phase angle of a series RLC circuit.
- RMS Voltage Calculator — Convert between RMS, peak and peak-to-peak voltage of a sine wave.
- Current Divider Calculator — Current through each of two parallel resistors.
- Inductive Reactance Calculator — Reactance of an inductor at a frequency.
- RC Circuit Calculator — Time constant, cutoff frequency and charge level of an RC circuit.
- Series Resistance Calculator — Total resistance of resistors in series.
Sources
- CODATA 2018 / SI exact constants
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.