HomeCalculatorsElectricalCircuitsCapacitance Calculator
Electrical calculator

Capacitance Calculator

Compute parallel-plate capacitance C=εA/d or combine series/parallel capacitors. Runs locally in your browser.

Instant result
Result
—

Enter values to calculate.

Inputs—
Mode—
Formula—
Trust summary CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance
Input interpretation
Enter values to calculate.
Result
—
Assurance
Engineering
Declared partition coverage
PASS · 4/4 declared partitions (plate, parallel, series, invalid-domain) · Matrix
Known limitations
  • Ideal parallel plates with a homogeneous isotropic dielectric fully filling the gap. εr is a scalar ≥ 1. Fringing, frequency dependence, dielectric loss, leakage, ESR/ESL and parasitics are neglected.
  • Core CVP does not include live graph, viewport, or pointer interaction.
Model
Parallel-plate C or series/parallel combination.
Scope
Ideal parallel plates with a homogeneous isotropic dielectric fully filling the gap
Verification
Engine tested · Source checked · v1.1.0 · CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance· View Manifest · CVP overview · Specification
Versions
Calculation 1.1.0 · CVP protocol 1.0.0-proposed · Evidence 2026-09-11.url-canonical-mode
Verification revision
2026-09-11.url-canonical-mode · 5/5 property · digest 2e5db26b1665
Legacy regression
17/17 tests · Production surface contract 4/4
Trust layers
Verification VERIFIED · Production CURRENT · overall VERIFIED
Reference
O1 model · O2 expected_values · O2 numerical_behavior
Interfaces
PASS · UI (SSR) / REST / MCP — ui-ssr is query-result HTML, not a live browser session. Error-path engine·REST·MCP 2/2 (status, code, calculation_version). SSR compared on URL-canonical requested calculations; empty query is idle (not an error) and JSON-typed object/array inputs are REST/MCP-only.
Supplemental domain review
Internal · Pass · electrical-engineer
Named expert review
Not performed
CVP suite
3/3 golden · 9/9 CVP boundary · 12/12 invalid · 5/5 property · 5/5 metamorphic · 7/7 cross-interface · 4/4 CVP contract · Manifest
Sources
Sources
Evidence
3 legacy golden · 8 legacy boundary · legacy regression suite · 3/3 oracle-backed golden · 12/12 invalid · Artifact integrity PASS · CalculatorX electrical review
This calculator CURRENT · Public schema 1.1.0 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓
Semantic contract
PASS
Full verification

Manifest identity, reference classes, interfaces, suite, and production records.

Formulas

Core equations used by this calculator.

Parallel plateC = ε0·εr·A/d
ParallelC = C1+C2+…
Series1/C = 1/C1+1/C2+…
iEngine constant ε0 = 8.8541878188×10⁻¹² F/m (NIST CODATA 2022). Ideal parallel plates; fringing neglected.

How to use

1

Choose plate, parallel, or series mode

Plate uses geometry; parallel/series combine discrete capacitors.

2

Enter geometry or capacitor values

Plate needs A, d, and εr ≥ 1. Parallel/series need at least two capacitances > 0.

3

Read C or Ceq

Plate: C = ε0·εr·A/d with the engine ε0 shown under Formulas. Series uses 1/C = Σ 1/Ci.

Example calculations

Common configurations with formula and result.

ϟ

Illustrative PCB dielectric (εr = 4)

A=0.01 m² · d=1 mm · εr=4 — FR-4-like example only; use laminate datasheet Dk for design.

ε0·4·A/d
≈354.17 pF

Capacitance calculator specification

Version 1.1.0 · Engine tested · Supplemental domain review · Internal · 2026-09-11

Calculation status

Review policy · Evidence · Reviewed by CalculatorX electrical review (electrical-engineer)

Definition
Capacitance relates charge and voltage (C=Q/V). A parallel-plate capacitor is C=ε0·εr·A/d. Parallel capacitors add; series combine as reciprocals.
What it calculates
Parallel-plate C or series/parallel combination.
Inputs
  • mode plate|parallel|series
  • plate: A_m2, d_m, er≥1
  • parallel/series: capacitors_F[] (≥2); UI aliases C1, C2, …
Outputs
  • C_F
  • C_uF / C_nF / C_pF
Formula
C=ε0·εr·A/d with ε0=8.8541878188e-12 F/m (CODATA 2022)
Assumptions
  • Ideal parallel plates with a homogeneous isotropic dielectric fully filling the gap
  • Relative permittivity is a scalar constant (no frequency dependence or dielectric loss)
  • Fringing, leakage, ESR/ESL and parasitic capacitance are neglected
  • Scope is vacuum or conventional passive dielectric: εr ≥ 1
Units
  • m², m, F
Boundary conditions
  • A, d, Ci ≤ 0 → VALUE_MUST_BE_POSITIVE
  • εr ≤ 0 → VALUE_MUST_BE_POSITIVE; 0 < εr < 1 → VALUE_OUT_OF_RANGE (εr ≥ 1 required)
  • parallel/series with fewer than two capacitances → NEEDS_TWO_INPUTS
  • unknown mode → INVALID_MODE
Example
A=0.01 m², d=0.001 m, er=4 → 354.17 pF
Validation cases

1 published on this page · 17/17 tests · Production surface contract 4/4 · View evidence

  • plate A=0.01 d=0.001 er=4 → C=3.54167512752e-10 F (354.17 pF)
Sources
Last reviewed
2026-09-11
Reviewed by
CalculatorX electrical review (electrical-engineer)
Calculation version
1.1.0

Background

Interpretation and common distinctions.

Increasing plate area increases capacitance linearly; increasing plate spacing reduces it inversely. Relative permittivity scales capacitance when a homogeneous dielectric fully fills the gap.

Supported and not supported

Supported — Parallel-plate · series/parallel · API electrical.capacitance

Not supported — Coaxial/cylindrical exact models, fringing, frequency-dependent or complex permittivity, ESR/ESL, leakage

Agent / API notes

Capability id: electrical.capacitance · tool id: capacitance · pin 1.1.0.

Canonical agent input uses mode with oneOf:

  • plate — required A_m2, d_m, er (≥ 1)
  • parallel / series — required capacitors_F (array of farads, minItems 2)

Human UI still shows C1, C2, … and normalizes to capacitors_F before the engine.

Share URLs keep only the active mode’s inputs (mode decides the parameter set). Extra query fields such as C1/C2 on mode=plate are ignored by the engine and stripped from the canonical share link.

Other calculators in this family: 555 Timer Calculator, Current Divider Calculator, High-Pass Filter Calculator, Kirchhoff's Law Calculator, LED Resistor Calculator, Low-Pass Filter Calculator, Ohm's Law Calculator, Parallel Resistor Calculator . Explore all Circuits.

→ 555 Timer Calculator Astable frequency, period, high/low times and duty — or monostable pulse width — for the classic 555 timer from R and C. ln(2)-canonical NE555 timing with device-applicability warnings. › → Current Divider Calculator Split a total current between two parallel resistors: I1 = It·R2/(R1+R2), I2 = It·R1/(R1+R2). Runs locally in your browser. › → High-Pass Filter Calculator First-order RC high-pass cutoff fc=1/(2πRC) and optional |H(f)|. Twin of the LPF calculator. › → Kirchhoff's Law Calculator Apply Kirchhoff’s voltage law to a series loop or current law to a parallel node with N resistors. › → LED Resistor Calculator Size the series resistor for one or more LEDs: R = (Vs − n·Vf) / If. › → Low-Pass Filter Calculator Design a first-order RC low-pass filter: solve any two of R, C, and cutoff fc = 1/(2πRC), and evaluate magnitude |H(f)| in linear and dB. Runs locally in your browser. › → Ohm's Law Calculator Enter any two of voltage, current, resistance, and power to solve the remaining values. Runs locally in your browser. Free online tool — no sign-up. › → Parallel Resistor Calculator Compute equivalent resistance of two or more resistors in parallel. Runs locally in your browser. ›
}

Frequently asked questions

Key distinctions behind the calculation.

What is relative permittivity εr?

A dimensionless ratio of the dielectric’s permittivity to vacuum. This calculator treats εr as a scalar constant ≥ 1. Use the datasheet value at the relevant frequency when it is available.

When is the parallel-plate formula inaccurate?

Whenever fringing, incomplete dielectric fill, frequency-dependent Dk, loss, leakage, or parasitics matter — for example when the gap is not small compared with the plate dimensions.

Why do parallel capacitors add, and why is series capacitance smaller?

Parallel networks share voltage, so charges (and C = Q/V) add. Series networks share charge, so voltages add and 1/Ceq = Σ 1/Ci, which is always smaller than the smallest Ci.

Does plate mode include fringing?

No — ideal parallel-plate only.