Parallel-Plate Capacitor Permittivity, Charge & Stored Energy Calculator

Compute dielectric plate capacitance (pF/nF) and stored joules at voltage.

Parallel-Plate Capacitance
389.58 pF
Stored Electrostatic Energy 0.01 mJ
Stored Charge (Q = CV) 77.92 nC
Electric Field Strength (V/d) 400 kV/m
Inputs
cm²
Overlapping conductive plate area in square centimeters (cm²).
mm
Separation thickness between plates in millimeters (mm).
ε_r
Dielectric constant ε_r (1.0 air, 4.4 FR-4 fiberglass).
V
DC voltage applied across the capacitor terminals.
Results & Graph
Parallel-Plate Capacitance
389.58 pF
Stored Electrostatic Energy
0.01 mJ
Stored Charge (Q = CV)
77.92 nC
Electric Field Strength (V/d)
400 kV/m

Parallel-Plate Capacitance

Graph 1 • Plate Area Cm2 Sensitivity Recalculates the domain equation across 50% to 150% of the primary input while holding other parameters constant.
0 pF 315.6 pF 631.1 pF 50%: 194.79 pF 194.8 50% 75%: 292.19 pF 292.2 75% 100%: 389.58 pF 389.6 100% 125%: 486.98 pF 487.0 125% 150%: 584.38 pF 584.4 150%
Graph 2 • Primary & Supporting Metric Comparison Compares the primary output alongside supporting domain benchmarks.
Parallel-Plate Capacitance 389.58 pF Stored Electrostatic Energy 0.01 mJ Stored Charge (Q = CV) 77.92 nC Electric Field Strength (V/d) 400 kV/m
Graph 3 • Exact Output Table & Units Displays each calculated output in its exact domain unit.
Parallel-Plate Capacitance389.58 pFStored Electrostatic Energy0.01 mJStored Charge (Q = CV)77.92 nCElectric Field Strength (V/d)400 kV/m
Summary: Plates of 50 cm² separated by 0.5 mm (ε_r=4.4) yield 389.58 pF and store 0.0078 mJ at 200 V.
Summary: Plates of 50 cm² separated by 0.5 mm (ε_r=4.4) yield 389.58 pF and store 0.0078 mJ at 200 V.
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Formula & Mathematical Methodology: Capacitor Energy & Plate Physics & Engineering Equation

C = ε₀ × εr × Area / Gapd
Q = C × V
EnergyJ = 0.5 × C × V²
C = ε₀ × ε_r × Area / Gap_d; Q = C × V; Energy_J = 0.5 × C × V²
  • plateAreaCm2: Plate Area Cm2 (cm²)
  • dielectricGapMm: Dielectric Gap Mm (mm)
  • relativePermittivityEr: Relative Permittivity Er (ε_r)
  • appliedVoltageV: Applied Voltage V (V)

Rounding: Physical constants follow CODATA/NIST values; output quantities display to 2 decimal places.

Worked Example: Physics & Engineering Benchmark: Capacitor Energy & Plate

Compute dielectric plate capacitance (pF/nF) and stored joules at voltage.

  1. Enter the physical dimensions, electrical parameters, or thermodynamic state variables.
  2. Apply the governing equation: C = ε₀ × ε_r × Area / Gap_d; Q = C × V; Energy_J = 0.5 × C × V².
  3. Inspect the primary SI output, derived quantities, and 3 visual SVG graphs.
Result: Computes Capacitor Energy & Plate via C = ε₀ × ε_r × Area / Gap_d; Q = C × V; Energy_J = 0.5 × C × V².

Frequently Asked Questions

What equation powers the Parallel-Plate Capacitor Permittivity, Charge & Stored Energy Calculator?

It evaluates C = ε₀ × ε_r × Area / Gap_d; Q = C × V; Energy_J = 0.5 × C × V² using IEEE-754 double precision and renders three synchronized SVG plots.

Can I test parameter sensitivity across multiple values?

Yes. Graph 1 automatically plots a 50%–150% parameter response curve, and you can pin up to 3 custom scenarios.

Are all units consistent with SI standards?

Yes. Each input field specifies its exact SI or engineering unit and converts internally where needed.

Science & Engineering · Electrical & RF Engineering

Parallel-Plate Capacitor Permittivity, Charge & Stored Energy Calculator: inputs, method, and how to read the result

Compute dielectric plate capacitance (pF/nF) and stored joules at voltage.

Choose inputs for the case you are checking

The defaults are illustrative. Replace them with values for your case and keep the units shown beside each field.

  • Plate Area Cm2: Overlapping conductive plate area in square centimeters (cm²).
  • Dielectric Gap Mm: Separation thickness between plates in millimeters (mm).
  • Relative Permittivity Er: Dielectric constant ε_r (1.0 air, 4.4 FR-4 fiberglass).
  • Applied Voltage V: DC voltage applied across the capacitor terminals.

What the calculation includes

With the default values shown, Parallel-Plate Capacitance is 389.58 pF. The calculation follows Capacitor Energy & Plate Physics & Engineering Equation; the formula and variable definitions above show how the inputs combine.

One-input check: With the other defaults held constant, changing Plate Area Cm2 from 50 cm² to 55 cm² changes Parallel-Plate Capacitance from 389.58 pF to 428.54 pF. This is a comparison inside the calculator's stated model, not a prediction.

Where to use caution

  • Uses standard SI physical constants (g = 9.80665 m/s², c = 299,792,458 m/s, σ = 5.670374×10⁻⁸ W·m⁻²·K⁻⁴).
  • Engineering reference model; apply appropriate safety factors and empirical calibration for critical hardware designs.

Scope: SI / NIST Physics & Engineering Standard Check the assumptions and limitations against your situation before relying on the estimate.

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