What is the formula for a parallel plate capacitor?

C = ε₀ × εᵣ × A / d, where ε₀ = 8.854×10⁻¹² F/m is the permittivity of free space, εᵣ is the relative permittivity of the dielectric, A is the plate area in m², and d is the separation in meters.

What is relative permittivity (εᵣ)?

Relative permittivity, also called the dielectric constant, is a dimensionless ratio describing how much a material increases capacitance compared to a vacuum. Air ≈ 1.0, paper ≈ 3.7, glass ≈ 4.7, mica ≈ 5.4, and water ≈ 80.

How does plate area affect capacitance?

Capacitance is directly proportional to plate area. Doubling the plate area doubles the capacitance, because twice the area can store twice the charge at the same voltage.

How does separation distance affect capacitance?

Capacitance is inversely proportional to separation. Halving the gap doubles the capacitance, because the electric field between closer plates is stronger for the same charge.

Why are results often in picofarads?

Practical parallel plate capacitors with plate areas of a few cm² and millimeter gaps have capacitances in the picofarad to nanofarad range. Very large plates or very thin gaps (or high-εᵣ dielectrics) can reach the nanofarad range.

Parallel Plate Capacitance Calculator

Compute C = ε₀ × εᵣ × A / d for a parallel plate capacitor — choose plate area, separation, and dielectric material.

Capacitor Parameters

Enter plate area, separation, and dielectric to calculate capacitance.

Plate Area (A)

Plate Separation (d)

Dielectric Material

Result

Enter values and click Calculate.

Formula

C = ε₀ × εᵣ × A / d
ε₀ = 8.854187817 × 10⁻¹² F/m | εᵣ = relative permittivity | A = plate area (m²) | d = separation (m)

Larger area → higher capacitance (more charge per volt)
Smaller gap → higher capacitance (stronger field)
Higher εᵣ → higher capacitance (material polarizes, stores more energy)

Summary

Compute C = ε₀ × εᵣ × A / d for a parallel plate capacitor — choose plate area, separation, and dielectric material.

How it works

Enter the plate area in cm² or m² using the unit selector.
Enter the plate separation in mm or m using the unit selector.
Select the dielectric material from the dropdown or enter a custom relative permittivity (εᵣ).
Click Calculate to get the capacitance auto-scaled to pF, nF, or µF.
The substituted formula is shown so you can verify each step.

Use cases

Design parallel plate capacitors for electronics and RF circuits.
Estimate capacitance of PCB trace pairs separated by a dielectric substrate.
Verify capacitor sizing in sensor and MEMS design.
Solve physics homework problems on electrostatics and capacitance.
Compare dielectric materials for a fixed plate geometry.
Understand how plate area and gap affect capacitance in touchscreen design.

Frequently Asked Questions

Last updated: 2026-09-22 · Reviewed by Nham Vu