Capacitance Calculator

- May 10, 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

Understanding the Capacitance Calculator

The Capacitance Calculator is a handy tool that helps users find the capacitance of different types of capacitors. Whether you're working with parallel plate, cylindrical, or spherical capacitors, this calculator makes it easy to input your specifications and get results. It also accommodates configurations for capacitors connected in series or parallel, making it versatile for various electrical projects.

Why Use the Capacitance Calculator?

This calculator is designed for both students and professionals who need to quickly compute capacitance. It reduces the chance of errors in manual calculations and helps users understand the relationships between different parameters. With this tool, you can learn about the capacitance of various configurations without complex formulas getting in the way.

Types of Capacitors You Can Calculate

  • Parallel Plate Capacitors: Commonly used in many applications, these consist of two plates separated by a dielectric material.
  • Cylindrical Capacitors: Made up of two coaxial cylinders, these are often used in applications requiring a compact design.
  • Spherical Capacitors: These consist of two concentric spheres and are useful in certain electrical contexts.
  • Capacitors in Series: When connected in series, their overall capacitance can be calculated easily.
  • Capacitors in Parallel: The total capacitance of capacitors in parallel is simply the sum of their capacitances.

Input Options for Accurate Results

The Capacitance Calculator offers various input options to ensure accurate results. Users can enter specific details for each capacitor type, including plate area, distance between plates, and dielectric constants. The interface allows you to select units from the metric system, ensuring the calculations fit your preferences. This flexibility makes the tool user-friendly and suitable for different needs.

Understanding Dielectric Materials

Dielectric materials play an important role in how capacitors function. The calculator allows you to choose from common dielectric materials or enter a custom value. Each material has a specific dielectric constant, which affects the overall capacitance. Some typical dielectric materials include:

  • Vacuum (1.0)
  • Air (1.0006)
  • Polyethylene (2.1)
  • PVC (3.4)
  • Water (80.0)

Calculation Results You Can Trust

Once you've entered all the necessary values, the calculator provides clear and precise results. You’ll see not only the calculated capacitance but also the energy storage at a specified voltage. The results are presented in an easy-to-understand format, with options to view the calculation steps for deeper learning.

Advanced Features for Detail-Oriented Users

The Capacitance Calculator includes advanced options for users who need more control over their results. You can choose the number of decimal places, opt for scientific notation, and even select the output unit that best fits your project. These features cater to both casual users and professionals who require precision in their calculations.

Learning More About Capacitance

This calculator is not just a tool; it’s also an educational resource. Each calculation includes explanations of the formulas used, helping users understand the theory behind capacitance. Whether you’re learning for school or enhancing your skills for work, this calculator provides valuable insights into electrical engineering concepts.