Multi-Layer Coil Inductance Calculator

The Formula

The formula for calculating the inductance of a multi-layer coil is:

\[L = \frac{0.31460 \times r^2 \times N^2}{9r + 10l}\]

Where:

• L: Inductance (in microhenries, µH)
• r: Coil radius (in centimeters, cm)
• l: Coil length (in centimeters, cm)
• N: Total number of turns (turns per layer * number of layers)

Calculation Steps

1. Convert the coil diameter from mm to cm and calculate the radius
2. Convert the coil length from mm to cm
3. Calculate the total number of turns by multiplying turns per layer by number of layers
4. Insert these values into the formula
5. Perform the calculation to get the result in microhenries (µH)

Example Calculation

Let's calculate the inductance for a multi-layer coil with these parameters:

• Diameter: 20 mm
• Length: 30 mm
• Turns per layer: 100
• Number of layers: 3

Step 1: r = 20 mm / 20 = 1 cm

Step 2: l = 30 mm / 10 = 3 cm

Step 3: N = 100 * 3 = 300 turns

Step 4: L = (0.31460 * 1² * 300²) / (9 * 1 + 10 * 3)

Step 5: L ≈ 705.90 µH

Visual Representation

This visual shows a multi-layer coil with its estimated inductance based on our example calculation.