Capacitance Calculator

Category: Physics
- April 04, 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.

Select Capacitor Type

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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 a user-friendly online tool that helps you find out the capacitance of various types of capacitors. Whether you're dealing with a simple parallel plate capacitor or a more intricate cylindrical or spherical design, this tool gives you quick and straightforward results.

It also computes 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 various capacitor types: parallel plate, cylindrical, spherical
  • Handles series and parallel combinations
  • Allows you to select or input dielectric material values
  • Customisable output with unit and decimal options
  • Displays detailed calculation steps
  • Estimates stored energy based on voltage input

How to Use the Calculator

  1. Select the type of capacitor or connection you wish to calculate.
  2. Input the necessary dimensions and values:
    • For geometric capacitors: enter area, distance, radius, or length
    • For combined capacitors: input 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 see the results.
  6. Use the voltage input to find out how much energy the capacitor can store.

Who Is This Useful For?

This calculator is beneficial for students, educators, electronics enthusiasts, and professionals involved in circuit design or component selection. Whether you're learning how capacitors function or need precise results for your project, it provides a quick and dependable solution.

Frequently Asked Questions (FAQ)

Q: What is capacitance?

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

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

A: It indicates how much a material enhances a capacitor’s ability to store charge compared to a vacuum. Higher values typically result in higher capacitance.

Q: What occurs 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 variety 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 quick and reliable results without needing manual formulas or conversions. Whether you're checking your homework, building a circuit, or just curious, this tool makes it easier to understand and work with capacitors.