Coil Inductance Calculator

How to Use the Circular Winding Coil Inductance Calculator

To determine the inductance of a circular single-layer coil, follow these steps:

1. 1
   Enter Turns: Input the total integer number of winding turns (N).
2. 2
   Enter Radius: Input the average radius of the coil loop, choosing inches (in), millimeters (mm), or centimeters (cm).
3. 3
   Enter Length: Input the total axial length of the coil.
4. 4
   Calculate: Click the "Calculate Coil Inductance" button.

How to Calculate Circular Winding Coil Inductance

Circular single-layer coils are common in RF networks and transmitters. Wheeler's classic single-layer solenoid equation is used to calculate their self-inductance based on the loop geometry and length.

Real-Life Sizing Scenarios

Scenario 1: Sizing an RF Winding with 10 Turns
An RF amateur winding a transmitter coil uses 10 turns on an air core with a radius of 1.0 inch and an axial length of 2.0 inches:
L = (r² × N²) ÷ (9r + 10l) = (1.0² × 10²) ÷ (9×1.0 + 10×2.0) = 100 ÷ 29 = 3.448 µH

Formula and step-by-step Manual Sizing

The calculation uses Wheeler's formula:
L = (r² × N²) ÷ (9r + 10l)
where r is radius in inches, l is length in inches, and L is inductance in microhenries (µH).

How to Use the Planar PCB Spiral Inductance Calculator

To determine planar spiral PCB trace inductance, follow these steps:

1. 1
   Enter Outer Diameter: Input the total outer boundary dimension and choose millimeters (mm) or mils.
2. 2
   Enter Track Width: Input the copper trace width.
3. 3
   Enter Track Spacing: Input the track-to-track separation clearance.
4. 4
   Enter Turns: Input the total designed turns count.
5. 5
   Calculate: Click the "Calculate Coil Inductance" button.

How to Calculate Planar PCB Spiral Inductance

Planar PCB coils are designed directly onto copper trace layers for NFC nodes, RFID antennas, and RF circuits. Wheeler's flat spiral approximation is the standard formula used to verify their self-inductance.

Real-Life Sizing Scenarios

Scenario 1: Sizing an NFC Antenna on FR4 Board
An engineer layouts a flat circular circular spiral with Dout = 40 mm, trace width = 0.5 mm, spacing = 0.3 mm, and 8 turns. The inner diameter is computed as Din = Dout − 2×N×w − 2×(N−1)×s = 27.8 mm. Converting to inches yields rout = 0.7874 in and rin = 0.5472 in. Average radius ravg = 0.6673 in, winding width w = 0.2402 in:
L = (31.33 × ravg² × N²) ÷ (8ravg + 11w) = (31.33 × 0.6673² × 8²) ÷ (8×0.6673 + 11×0.2402) ≈ 111.90 µH

How to Use the Multi-Layer Winding Coil Inductance Calculator

To determine multi-layer coil inductance, follow these steps:

1. 1
   Enter Turns: Input the total turns count (N).
2. 2
   Enter Average Radius: Input the average radius of the winding cross-section.
3. 3
   Enter Length: Input the axial winding length.
4. 4
   Enter Depth: Input the radial winding depth.
5. 5
   Calculate: Click the "Calculate Coil Inductance" button.

How to Calculate Multi-Layer Winding Coil Inductance

Multi-layer coils consist of stacked wire turns, which increases the total inductance. The calculation uses Wheeler's multi-layer formula.

Real-Life Sizing Scenarios

Scenario 1: Sizing a stacked crossover choke coil
An audio engineer designs a multi-layer speaker crossover choke using 100 turns, an average radius of 1.5 inches, length of 2.0 inches, and depth of 0.5 inches:
L = (0.8 × a² × N²) ÷ (6a + 9b + 10c) = (0.8 × 1.5² × 100²) ÷ (6×1.5 + 9×2.0 + 10×0.5) = 18000 ÷ 32 = 562.50 µH

How to Use the Rectangular Winding Coil Inductance Calculator

To determine rectangular winding coil inductance, follow these steps:

1. 1
   Enter Turns: Input the total turns count.
2. 2
   Enter Average Side Length: Input the average side dimension of the winding.
3. 3
   Enter Average Side Width: Input the average width dimension.
4. 4
   Enter Winding Thickness: Input the thickness of the wire buildup.
5. 5
   Calculate: Click the "Calculate Coil Inductance" button.

How to Calculate Rectangular Winding Coil Inductance

Rectangular coils are common in magnetic sensors, yoke coils, and induction heating configurations. An adaptation of Wheeler's multi-layer formula is applied by using an equivalent average side radius.

Real-Life Sizing Scenarios

Scenario 1: Sizing a magnetic loop receiver coil
A technician winds a rectangular coil loop with 50 turns. The average side dimensions are length = 3.0 inches, width = 2.0 inches, and winding thickness = 0.5 inches:
aIn = (3.0 + 2.0) ÷ 2 = 2.5 in, bIn = 2.0 in, cIn = 0.5 in
L = (0.8 × aIn² × N²) ÷ (6aIn + 9bIn + 10cIn) = (0.8 × 2.5² × 50²) ÷ (6×2.5 + 9×2.0 + 10×0.5) = 12500 ÷ 38 ≈ 328.95 µH

How to Use the Single-Layer Cylindrical Coil Inductance Calculator

To determine single-layer cylindrical coil inductance, follow these steps:

1. 1
   Enter Turns: Input the total turns count.
2. 2
   Select Input Type: Choose Coil Radius or Coil Diameter.
3. 3
   Enter Dimension: Input the radius or diameter value.
4. 4
   Enter Length: Input the axial winding length.
5. 5
   Calculate: Click the "Calculate Coil Inductance" button.

How to Calculate Single-Layer Cylindrical Coil Inductance

Single-layer cylindrical coils are classic air-core solenoids. Sizing calculations use Wheeler's solenoid equation.

Real-Life Sizing Scenarios

Scenario 1: Sizing an RF Tuning Coil
An engineer winds 20 turns on a 1.0-inch diameter coil former (radius = 0.5 inches) with a winding length of 1.0 inch:
L = (r² × N²) ÷ (9r + 10l) = (0.5² × 20²) ÷ (9×0.5 + 10×1.0) = 100 ÷ 14.5 ≈ 6.90 µH

How to Use the Relay Solenoid Winding Coil Inductance Calculator

To determine relay solenoid winding coil inductance, follow these steps:

1. 1
   Enter Turns: Input the total turns count.
2. 2
   Enter Diameter: Input the inner core diameter.
3. 3
   Enter Length: Input the axial core length.
4. 4
   Select Core Material: Choose Soft Iron, Ferrite, or Air.
5. 5
   Calculate: Click the "Calculate Coil Inductance" button.

How to Calculate Relay Solenoid Winding Coil Inductance

Relay coils utilize high-permeability magnetic cores (like soft iron or ferrite) to concentrate the magnetic flux, generating strong magnetic forces at lower turns counts. The calculation uses the fundamental solenoid inductance equation.

Real-Life Sizing Scenarios

Scenario 1: Sizing an iron-core relay actuator
An engineer designs an actuator winding with 1000 turns on a soft iron core (diameter = 10 mm, length = 30 mm, mu_r = 2000):
d = 0.01 m, l = 0.03 m, A = π × d² ÷ 4 = 7.854 × 10^−5 m²
L = (mu_0 × mu_r × N² × A) ÷ l = ((4π×10^−7) × 2000 × 1000² × 7.854×10^−5) ÷ 0.03 ≈ 6.58 H (or 6580 mH)

How to Use the Flat Winding Spiral Coil Inductance Calculator

To determine flat winding spiral coil inductance, follow these steps:

1. 1
   Enter Outer Diameter: Input the outer dimension of the spiral.
2. 2
   Enter Inner Diameter: Input the inner dimension.
3. 3
   Enter Turns: Input the total turns count.
4. 4
   Enter Conductor Width: Input the width of the wire conductor.
5. 5
   Calculate: Click the "Calculate Coil Inductance" button.

How to Calculate Flat Winding Spiral Coil Inductance

Flat spiral coils, also known as pancake coils, are flat spiral wire windings. Sizing calculations use Wheeler's flat spiral formula.

Real-Life Sizing Scenarios

Scenario 1: Sizing an induction cooker heater coil
An appliance designer winds a flat pancake coil with OD = 200 mm, ID = 100 mm, conductor width = 2 mm, and 20 turns:
avgRadius = (100 + 50) ÷ 2 = 75 mm (2.9528 in)
windingWidth = 100 − 50 = 50 mm (1.9685 in)
L = (r² × N²) ÷ (8r + 11w) = (2.9528² × 20²) ÷ (8×2.9528 + 11×1.9685) = 3487.6 ÷ 45.276 ≈ 77.03 µH