Capacitance Calculator

Category: Physics
- March 23, 2025
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Calculate the capacitance of various capacitor types and configurations. This calculator supports parallel plate, cylindrical, spherical capacitors and capacitors in series or parallel connections.

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About Capacitance

Capacitance is a measure of a capacitor's ability to store electric charge for a given potential difference (voltage). The SI unit of capacitance is the farad (F), which is equal to one coulomb per volt (C/V).

Parallel Plate Capacitor

A parallel plate capacitor consists of two parallel conductive plates separated by a dielectric material.

  • Formula: C = ε₀εᵣA/d
  • ε₀: Permittivity of free space (8.85 × 10⁻¹² F/m)
  • εᵣ: Relative permittivity (dielectric constant) of the material between plates
  • A: Overlapping area of the plates
  • d: Distance between plates
Cylindrical Capacitor

A cylindrical capacitor consists of two coaxial cylindrical conductors separated by a dielectric material.

  • Formula: C = 2πε₀εᵣL/ln(b/a)
  • L: Length of the cylinders
  • a: Radius of the inner cylinder
  • b: Radius of the outer cylinder
  • ln(b/a): Natural logarithm of the ratio of outer to inner radius
Spherical Capacitor

A spherical capacitor consists of two concentric spherical conducting shells separated by a dielectric material.

  • Formula: C = 4πε₀εᵣab/(b-a)
  • a: Radius of the inner sphere
  • b: Radius of the outer sphere
Capacitors in Series

When capacitors are connected in series, the reciprocal of the equivalent capacitance is equal to the sum of the reciprocals of the individual capacitances.

  • Formula: 1/C_eq = 1/C₁ + 1/C₂ + ... + 1/Cₙ
  • The equivalent capacitance is always less than the smallest individual capacitance
Capacitors in Parallel

When capacitors are connected in parallel, the equivalent capacitance is the sum of the individual capacitances.

  • Formula: C_eq = C₁ + C₂ + ... + Cₙ
Energy Stored in a Capacitor

The energy stored in a charged capacitor is:

  • Formula: E = ½CV²
  • C: Capacitance
  • V: Voltage across the capacitor
Common Dielectric Materials
Material Dielectric Constant (εᵣ) Breakdown Voltage (MV/m)
Vacuum 1.0 -
Air 1.0006 3
Paper 2.0-4.0 16
Polyethylene 2.1 50
Polypropylene 2.2 40
PVC 3.4 14
Mica 5.0 100
Glass 5.0-10.0 14
Ceramic 20-12000 8
Water 80.0 -
Applications of Capacitors
  • Energy Storage: Storing and releasing electrical energy quickly, as in camera flashes
  • Power Conditioning: Smoothing voltage fluctuations in power supplies
  • Signal Coupling/Decoupling: Blocking DC while allowing AC to pass
  • Filters: Creating frequency-selective circuits
  • Tuning: Selecting specific frequencies in radio circuits
  • Timing: Creating time delays in circuits
  • Sensors: Detecting changes in position, pressure, or humidity

What Is a Capacitance Calculator?

The Capacitance Calculator is an easy-to-use online tool that helps you determine the capacitance of different types of capacitors. Whether you're working with a basic parallel plate capacitor or a more complex cylindrical or spherical configuration, this tool provides quick and clear results.

It also calculates the total capacitance for combinations of capacitors connected in series or parallel, and even estimates the energy stored when a voltage is applied.

Capacitance Formulas Used

Parallel Plate Capacitor:
\( C = \varepsilon_0 \varepsilon_r \frac{A}{d} \)
Cylindrical Capacitor:
\( C = 2\pi \varepsilon_0 \varepsilon_r \frac{L}{\ln(b/a)} \)
Spherical Capacitor:
\( C = 4\pi \varepsilon_0 \varepsilon_r \frac{ab}{b - a} \)
Capacitors in Series:
\( \frac{1}{C_{eq}} = \frac{1}{C_1} + \frac{1}{C_2} + \dots + \frac{1}{C_n} \)
Capacitors in Parallel:
\( C_{eq} = C_1 + C_2 + \dots + C_n \)
Energy Stored:
\( E = \frac{1}{2} C V^2 \)

Key Features

  • Supports multiple capacitor types: parallel plate, cylindrical, spherical
  • Handles series and parallel combinations
  • Lets you select or enter dielectric material values
  • Customizable output with unit and decimal options
  • Shows detailed calculation steps
  • Estimates stored energy based on voltage input

How to Use the Calculator

  1. Select the type of capacitor or connection you want to calculate.
  2. Enter the required dimensions and values:
    • For geometric capacitors: input area, distance, radius, or length
    • For combined capacitors: enter individual capacitance values
  3. Choose the dielectric material or enter a custom dielectric constant.
  4. Adjust advanced settings like output units, decimal places, and display options.
  5. Click Calculate to view the results.
  6. Use the voltage input to see how much energy the capacitor can store.

Who Is This Useful For?

This calculator is helpful for students, educators, electronics hobbyists, and professionals working on circuit design or component selection. Whether you're learning about how capacitors work or need accurate results for your project, it offers a fast and reliable solution.

Frequently Asked Questions (FAQ)

Q: What is capacitance?

A: Capacitance is the ability of a component to store electrical energy in an electric field. It is measured in farads (F).

Q: What does the dielectric constant (εᵣ) represent?

A: It represents how much a material increases a capacitor’s ability to store charge compared to a vacuum. Higher values generally lead to higher capacitance.

Q: What happens when I connect capacitors in series or parallel?

A: In series, the total capacitance is less than the smallest individual capacitor. In parallel, the total capacitance is the sum of the individual capacitors.

Q: Can I use this tool to estimate energy storage?

A: Yes, enter a voltage value to see the energy stored using the formula \( E = \frac{1}{2}CV^2 \).

Q: What units does this calculator support?

A: You can choose from a wide range of units including farads (F), millifarads (mF), microfarads (μF), nanofarads (nF), and picofarads (pF), along with length and area units.

Why Use This Calculator?

It provides fast and reliable results without the need for manual formulas or conversions. Whether you're checking your homework, building a circuit, or just curious, this tool helps you understand and work with capacitors more easily.