Induction Calculator

Solenoid Inductance Calculator

Understanding inductance is crucial in electronics and electrical engineering. An inductor is a passive two-terminal electrical component that stores energy in a magnetic field when electric current flows through it. The most common form of an inductor is a solenoid, which is a coil of wire wound into a tightly packed helix.

What is Inductance?

Inductance is the property of an electrical conductor by which a change in current flowing through it induces an electromotive force (voltage) in both the conductor itself (self-inductance) and in any nearby conductors (mutual inductance). It is a measure of how much magnetic flux is produced per unit of current. The standard unit of inductance is the Henry (H).

The Solenoid Inductance Formula

The inductance of a solenoid can be calculated using the following formula:

L = (μ₀ * μr * N² * A) / l

Where:

  • L is the inductance in Henrys (H).
  • μ₀ (Mu naught) is the permeability of free space, a fundamental physical constant approximately equal to 4π × 10⁻⁷ H/m (Henrys per meter).
  • μr (Mu relative) is the relative permeability of the core material. This dimensionless value indicates how much more permeable a material is compared to a vacuum. For an air core, μr = 1.
  • N is the number of turns in the coil.
  • A is the cross-sectional area of the solenoid in square meters (m²). If you input the radius, the calculator will convert it to area using A = π * R².
  • l is the length of the solenoid in meters (m).

This formula assumes a long solenoid where the length is significantly greater than its diameter, and the magnetic field is uniform inside the coil and negligible outside.

How to Use the Solenoid Inductance Calculator

Our calculator simplifies the process of determining the inductance of a solenoid. Simply input the required parameters:

  1. Number of Turns: Enter the total number of wire turns in your solenoid.
  2. Core Relative Permeability (μr): Input the relative permeability of the material inside your coil. Use '1' for an air core.
  3. Solenoid Radius (mm): Enter the radius of your solenoid's cross-section in millimeters.
  4. Solenoid Length (mm): Enter the total length of your solenoid in millimeters.

Click the "Calculate Inductance" button, and the calculator will provide the inductance value in both Henrys (H) and microHenrys (μH).

Example Calculation

Let's calculate the inductance for a common scenario:

  • Number of Turns (N): 150 turns
  • Core Relative Permeability (μr): 1 (air core)
  • Solenoid Radius (R): 15 mm (0.015 m)
  • Solenoid Length (l): 75 mm (0.075 m)

First, calculate the cross-sectional area (A):

A = π * R² = π * (0.015 m)² ≈ 3.14159 * 0.000225 m² ≈ 0.00070685 m²

Now, apply the inductance formula:

L = (μ₀ * μr * N² * A) / l

L = (4π × 10⁻⁷ H/m * 1 * 150² * 0.00070685 m²) / 0.075 m

L = (1.2566 × 10⁻⁶ * 1 * 22500 * 0.00070685) / 0.075

L = (1.2566 × 10⁻⁶ * 15904.125) / 0.075

L ≈ 0.020000000000000004 / 0.075

L ≈ 0.000266666 H

L ≈ 266.67 μH

Using the calculator with these values should yield approximately 266.67 μH.

Solenoid Inductance Calculator

function calculateInductance() { var numTurns = parseFloat(document.getElementById("numTurns").value); var relativePermeability = parseFloat(document.getElementById("relativePermeability").value); var solenoidRadius_mm = parseFloat(document.getElementById("solenoidRadius").value); var solenoidLength_mm = parseFloat(document.getElementById("solenoidLength").value); // Validate inputs if (isNaN(numTurns) || numTurns <= 0 || !Number.isInteger(numTurns)) { document.getElementById("result").innerHTML = "Please enter a valid positive integer for Number of Turns."; return; } if (isNaN(relativePermeability) || relativePermeability < 1) { // Relative permeability cannot be less than 1 (vacuum) document.getElementById("result").innerHTML = "Please enter a valid positive number for Core Relative Permeability (μr ≥ 1)."; return; } if (isNaN(solenoidRadius_mm) || solenoidRadius_mm <= 0) { document.getElementById("result").innerHTML = "Please enter a valid positive number for Solenoid Radius."; return; } if (isNaN(solenoidLength_mm) || solenoidLength_mm <= 0) { document.getElementById("result").innerHTML = "Please enter a valid positive number for Solenoid Length."; return; } // Convert mm to meters var solenoidRadius_m = solenoidRadius_mm / 1000; var solenoidLength_m = solenoidLength_mm / 1000; // Permeability of free space (μ₀) = 4π × 10⁻⁷ H/m var mu_naught = 4 * Math.PI * Math.pow(10, -7); // Calculate cross-sectional area (A = π * R²) var area_m2 = Math.PI * Math.pow(solenoidRadius_m, 2); // Calculate Inductance (L = (μ₀ * μr * N² * A) / l) var inductance_H = (mu_naught * relativePermeability * Math.pow(numTurns, 2) * area_m2) / solenoidLength_m; // Convert to microHenrys for common display var inductance_uH = inductance_H * Math.pow(10, 6); document.getElementById("result").innerHTML = "Calculated Inductance: " + inductance_H.toFixed(9) + " H " + inductance_uH.toFixed(3) + " μH"; }

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