MotionLab

Capacitance Calculator

How much charge a capacitor can store for a given voltage — the foundation of energy storage in circuits.

Plate area (m²)

Plate separation (m)

Dielectric constant κ

Capacitance (F)

C = κε₀A/d

What you entered

Plate area (m²): 0.01Plate separation (m): 0.001Dielectric constant κ: 1

1
C = κε₀A ÷ d
1 × 8.854e-12 × 0.01 ÷ 0.001= 8.8542e-11 F
2
Charge Q = CV (at 1 V)
8.8542e-11 × 1= 8.8542e-11 C
3
Energy E = ½CV² (at 1 V)
0.5 × 8.8542e-11 × 1²= 4.4271e-11 J

Result

Capacitance (F): 0

A parallel-plate capacitor with 0.01 m² plates, 0.001 m gap, and κ = 1 has a capacitance of 8.8542e-11 F.

Parallel plate capacitance, charge and stored energy

Capacitance is the dielectric constant times the permittivity of free space times area over separation.

Plate area (m2)	Separation (m)	Dielectric constant	Capacitance (F)	Charge (C)	Energy (J)
0.01	0.001	1	8.8542e-11	8.8542e-11	4.4271e-11
0.01	0.001	4	3.5417e-10	3.5417e-10	1.7708e-10
0.05	0.0005	3	2.6563e-9	2.6563e-9	1.3281e-9
0.1	0.0001	1	8.8542e-9	8.8542e-9	4.4271e-9
1	0.001	2	1.7708e-8	1.7708e-8	8.8542e-9

Rows one and two are identical plates with and without a dielectric, and the material alone quadruples the capacitance - which is why real capacitors are filled rather than air-gapped. Row four shows the other lever: cutting the separation tenfold multiplies capacitance by ten, and squeezing plates close together is how practical capacitors reach useful values in small packages. Even so the figures here are in nanofarads at best, which shows how large a farad really is. Reducing the gap also raises the field strength for a given voltage, so there is a breakdown limit on how close the plates can go.

Three knobs to tune capacitance

Capacitance increases with larger plate area (more room for charge), smaller gap (stronger field), and higher dielectric constant (the insulating material between plates polarizes and effectively multiplies the capacitance) — real capacitor design is about optimizing all three.

Why dielectrics matter

Inserting a dielectric material (κ > 1) between the plates increases capacitance without changing the physical size — water has κ ≈ 80, which is why it's such a good solvent for ionic compounds, and ceramic capacitors use materials with κ in the thousands.

Frequently asked questions

A parallel-plate capacitor has plates 10 cm × 10 cm, separated by 1 mm of air. What's its capacitance?

C = ε₀A/d = 8.854×10⁻¹² × 0.01 / 0.001 = 88.54 pF. That's picofarads — small. Inserting a ceramic dielectric (κ = 1000) increases it to 88.54 nF, which is why ceramic capacitors pack so much capacitance into tiny packages.

How much energy does a capacitor store?

Energy = ½CV². A 100 μF capacitor at 400 V stores ½ × 10⁻⁴ × 160000 = 8 J. A camera flash capacitor (300 μF, 300V) stores 13.5 J — released in milliseconds, which is how a small battery can produce a brilliant flash.

Why does reducing plate separation increase capacitance?

Closer plates create a stronger electric field for the same voltage (E = V/d), which stores more charge per volt. Halving the gap doubles the capacitance. This is why manufacturers make the dielectric as thin as possible — but too thin risks dielectric breakdown (sparking through the insulator).

How are capacitors different from batteries?

Capacitors store energy in an electric field and discharge in microseconds to seconds. Batteries store energy chemically and discharge over hours. Capacitors have much lower energy density but much higher power density — they excel at delivering short bursts of energy (camera flash, defibrillators).