⚡ Parallel Plate Capacitor
Calculate capacitance, charge, voltage, and stored energy.
Capacitance
How to Use This Calculator
Enter the plate area A in m², the plate separation d in metres, and optionally the voltage V across the capacitor. The calculator returns capacitance in farads, and if voltage is provided, also gives the stored charge Q and the energy E. Select a dielectric material from the dropdown to automatically set the relative permittivity εᵣ.
Select the dielectric material between the plates. Air gives εᵣ = 1, ceramic gives εᵣ ≈ 6, and water gives εᵣ = 80. Higher εᵣ means more capacitance.
Enter the plate area A in m². A 10 cm × 10 cm plate has an area of 0.01 m².
Enter the plate separation d in metres. A 1 mm gap is 0.001 m. Smaller gaps give larger capacitance.
Optionally enter the voltage V across the plates to also calculate stored charge Q = CV and energy E = ½CV².
Parallel Plate Capacitance Formula
ε₀ is fixed at 8.854 × 10⁻¹² F/m. εᵣ is the relative permittivity of the dielectric material (dimensionless). A is the overlapping plate area in m² and d is the separation in metres. Doubling A doubles C; doubling d halves C. Inserting a high-εᵣ dielectric is how compact capacitors pack large capacitance into small components.
Worked Examples
Where This Comes Up in Real Life
Capacitors in electronic circuits are typically described in picofarads (pF), nanofarads (nF), or microfarads (µF). The parallel plate formula shows why real capacitors use thin dielectric films with high εᵣ: a ceramic capacitor with εᵣ = 2000, plate area 1 cm² (0.0001 m²), and 10 µm separation gives C = 8.854×10⁻¹² × 2000 × 0.0001 / 0.00001 = 177 nF. That is a reasonable value for a small surface-mount component.
MEMS pressure sensors and touchscreens use capacitance changes for measurement. A touchscreen detects a finger because the finger (a conductor) changes the effective εᵣ near the sensor plate, shifting C by a detectable amount. The closer the finger, the more C changes. Capacitive proximity sensors in industrial machinery use the same physics to detect objects without physical contact, making them ideal for counting items on a production line or detecting liquid levels inside sealed tanks.
Frequently Asked Questions
What is the formula for parallel plate capacitance?
C = ε₀ × εᵣ × A / d, where ε₀ = 8.854×10⁻¹² F/m (permittivity of free space), εᵣ is the relative permittivity (dielectric constant), A is plate area (m²), and d is separation (m).
What is a dielectric material?
A dielectric is an insulating material between capacitor plates that increases capacitance by reducing the effective electric field. Common dielectrics: air (εᵣ≈1), paper (3.5), ceramic (6–8), water (80).
How much energy is stored in a capacitor?
E = ½CV² = Q²/(2C) = ½QV. Energy is stored in the electric field between the plates.
What happens when you double the plate area?
Capacitance doubles. Doubling plate separation halves capacitance. Capacitance is directly proportional to area and inversely proportional to distance.
What is the charge on a capacitor?
Q = C × V, where Q is charge in coulombs, C is capacitance in farads, and V is voltage across the capacitor in volts.