Leyden Jar Capacitance Calculator

Calculator

Capacitance model

Inner jar diameter

Wall thickness

Foil overlap height

Custom overlap area

Relative dielectric constant

Edge correction percent

Applied bank voltage

Jars in parallel

Jars in series

Leakage resistance

MΩ

Dielectric strength

kV/mm

Formula Used

Parallel plate model: C = ε₀ × εᵣ × A ÷ d

Cylindrical jar model: C = 2π × ε₀ × εᵣ × L ÷ ln(b ÷ a)

Stored charge: Q = C × V

Stored energy: E = 0.5 × C × V²

Electric field: field = voltage per jar ÷ dielectric thickness

Here, ε₀ is vacuum permittivity. εᵣ is relative dielectric constant. A is overlap area. d is wall thickness. L is foil height. a is inner radius. b is outer radius.

How to Use This Calculator

Select the model. Use the cylindrical model for round jars.
Enter measured inner diameter, wall thickness, and foil overlap height.
Add custom overlap area only when you already measured it.
Enter dielectric constant for the jar material.
Add voltage, jar count, leakage resistance, and dielectric strength.
Press Calculate. Results appear above the form.
Use CSV or PDF buttons to save the current result.

Example Data Table

Example	Inner Diameter	Foil Height	Thickness	Dielectric Constant	Voltage	Use Case
Small classroom jar	60 mm	80 mm	2 mm	5	3000 V	Low energy demonstration
Medium bottle jar	85 mm	120 mm	2.5 mm	5.5	5000 V	Historical experiment
Two jars in parallel	80 mm	110 mm	2 mm	5	4000 V	Higher capacitance bank
Two jars in series	80 mm	110 mm	2 mm	5	8000 V	Higher voltage sharing

Understanding Leyden Jar Capacitance

A Leyden jar is an early capacitor. It stores charge on two conductive coatings. Glass, plastic, or another insulator separates those coatings. The inner coating is one plate. The outer coating is the second plate. The dielectric controls how strongly electric field lines pass through the wall.

The useful capacitance depends on overlap area, wall thickness, and dielectric constant. A taller foil band gives more area. A wider jar also gives more area. Thin glass raises capacitance, but it also raises stress. A higher dielectric constant raises capacitance without changing size.

Why Geometry Matters

A jar is not a perfect flat capacitor. Its plates curve around a cylinder. For thin walls, the flat plate formula works well. For thicker walls, the cylindrical formula is better. This calculator offers both ideas. It also lets you add a small edge correction. That correction estimates fringing near foil edges.

Voltage is another key input. Capacitance alone does not show stored energy. Energy rises with the square of voltage. Doubling voltage makes four times the energy. This is why even small jars can shock, spark, or damage instruments. Treat every charged jar as hazardous.

Design and Safety Notes

Real jars have losses. Damp glass, fingerprints, dust, and poor foil contact reduce performance. Leakage resistance controls how quickly charge fades. A clean, dry jar holds charge longer. Rounded terminals can reduce unwanted corona. Good insulation around the top rim also helps.

Use the calculated electric field as a warning value. Compare it with a realistic dielectric strength. Old glass can be uneven. Recycled bottles may have bubbles and thin spots. Leave a wide safety margin. Never test unknown jars near people, electronics, or flammable vapors.

Practical Use

This tool is useful for demonstrations and design checks. Enter measured dimensions rather than labels. Measure only the region where inner and outer foil overlap. Select series jars for higher voltage tolerance. Select parallel jars for higher capacitance. Then compare charge, energy, and time constant before building.

Record each build carefully. Note the dielectric, foil height, wall thickness, and test voltage. Recheck values after cleaning the jar. Small changes can shift results. Careful notes make later comparisons easier and safer for every future test.

FAQs

What is a Leyden jar?

A Leyden jar is an early capacitor. It uses conductive coatings separated by glass or another dielectric. It can store electric charge and release it suddenly.

Which formula should I use?

Use the cylindrical model for normal round jars. Use the parallel plate formula when you know the exact overlap area or when the wall is very thin.

What dielectric constant should I enter?

Common glass often falls near 4 to 10. Plastic values vary. Use a measured or manufacturer value when accuracy matters.

Why does thickness reduce capacitance?

Greater thickness separates the conductive plates more. Wider separation weakens the electric field coupling. That lowers capacitance, but may improve voltage tolerance.

Why does energy rise so quickly?

Stored energy equals one half times capacitance times voltage squared. Because voltage is squared, small voltage increases can greatly increase stored energy.

Can I connect jars in parallel?

Yes. Parallel jars add capacitance. Two equal jars in parallel give about twice the capacitance, while voltage rating stays similar.

Can I connect jars in series?

Yes. Series jars reduce equivalent capacitance, but they can share voltage. Use careful construction because uneven leakage can make voltage sharing unequal.

Is a Leyden jar dangerous?

Yes. It can store high voltage and release charge suddenly. Discharge it safely before touching conductors. Keep experiments away from people and electronics.