What Is a Coil Turn?

A turn is one complete loop of wire around the coil former. The total number of turns strongly affects the inductance of a coil.

       ┌───────────────┐
       │   Coil wire   │
       │ ((((((((((((  │
       └───────────────┘
             ↑
           Turns

For a simple air-core solenoid, inductance depends mainly on the number of turns, coil diameter, coil length and the magnetic permeability of the core.

Air-Core Coil Formula

For a long air-core solenoid, the approximate inductance is:

       μ₀ N² A
L = ─────────────
          l

where:

• L = inductance in henries
• μ₀ = permeability of free space
• N = number of turns
• A = cross-sectional area in m²
• l = coil length in metres

For an air core:

μ₀ = 4π × 10⁻⁷ H/m

The cross-sectional area of a cylindrical coil is:

A = πr²

where r is the coil radius.

Calculating the Number of Turns

Rearranging the solenoid formula gives:

        √(L × l)
N = ───────────────
       √(μ₀ × A)

This calculator uses this relationship to estimate the number of turns for an air-core coil.

Coil Turns Calculator

Example — 100 µH Air-Core Coil

Suppose we want to make an approximately 100 µH air-core coil with:

Inductance = 100 µH

Diameter = 25 mm

Length = 50 mm

The calculator determines the approximate number of turns required using the air-core solenoid equation.

The actual inductance can differ because the simple solenoid equation assumes an idealized geometry. For shorter coils, winding arrangement, wire diameter and spacing can have a significant effect.

Why Number of Turns Matters

For an ideal solenoid, inductance is proportional to the square of the number of turns:

L ∝ N²

Therefore, doubling the number of turns does not merely double the inductance. Ideally, it increases the inductance by approximately four times.

N × 2

L × 4

Similarly, reducing the number of turns reduces the inductance significantly.

Turns Calculator From Existing Coil

If the inductance, diameter and length of an existing air-core coil are known, the same equation can be used to estimate its number of turns.

Wire Length

Once the number of turns is known, the approximate wire length can also be estimated.

For a simple single-layer coil, the circumference of one turn is approximately:

C = πD

Therefore, the approximate wire length is:

Wire length ≈ N × πD

This is only an approximation because the wire follows a helical path and the actual length is slightly greater than the simple circumference calculation.

Wire Length Calculator

Wire Diameter and Turns per Layer

For a single-layer coil, the approximate number of turns that fit along the coil length is:

Turns per layer ≈ Coil length / Wire diameter

For example, if a coil is 50 mm long and the insulated wire occupies approximately 0.5 mm per turn:

Turns per layer ≈ 50 / 0.5

≈ 100 turns

The actual number depends on how tightly the wire is wound and on the total insulated wire diameter.

Turns per Layer Calculator

Multi-Layer Coils

If the required number of turns is greater than the number that can fit on one layer, the winding can be constructed using multiple layers.

Layer 1  ((((((((((
Layer 2   ))))))))))
Layer 3  ((((((((((

The simple long-solenoid equation becomes less accurate as the coil becomes short and its diameter becomes large compared with its length.

For practical coil construction, the winding geometry should therefore be considered when high accuracy is required.

Air-Core vs Magnetic-Core Coils

This calculator is intended primarily for air-core cylindrical coils. A magnetic-core inductor requires the core's magnetic properties and geometry to be taken into account.

Inductance and Coil Diameter

For a given number of turns and coil length, increasing the coil diameter increases its cross-sectional area and therefore generally increases the inductance.

However, changing the diameter also changes the physical winding geometry, so practical coils may not follow the ideal equation exactly.

Inductance and Coil Length

For a long air-core solenoid:

L ∝ 1 / l

For the same number of turns and diameter, increasing the coil length generally reduces the inductance.

This is one reason the physical dimensions of a coil are important when designing an inductor.

Practical Coil Construction

When winding a real coil, several dimensions should be considered:

• Coil diameter
• Coil length
• Number of turns
• Wire diameter
• Insulation thickness
• Number of layers
• Spacing between turns
• Core material

The calculator provides an initial theoretical estimate. The finished coil should be measured if an accurate inductance value is required.

Measuring the Finished Coil

An LCR meter can be used to measure the inductance of the finished coil.

For higher-frequency applications, the measured inductance can depend on the test frequency because practical coils contain parasitic resistance and capacitance.

Common Mistakes

• Using millimetres as metres in the formula.
• Using diameter instead of radius when calculating area manually.
• Using the air-core formula for a magnetic-core inductor.
• Ignoring wire insulation when calculating turns per layer.
• Assuming a short coil behaves like an ideal long solenoid.
• Ignoring spacing between turns.
• Ignoring parasitic capacitance at high frequencies.
• Expecting the calculated value to exactly match the finished coil.

Key Points

• An air-core coil's inductance depends strongly on turns, diameter and length.
• For an ideal solenoid, L is proportional to N².
• Doubling the turns can approximately quadruple the inductance.
• The coil cross-sectional area is based on radius, not diameter.
• Wire diameter determines how many turns fit in each layer.
• Multi-layer coils require consideration of their actual geometry.
• Magnetic-core inductors require a different design approach.
• Measuring the finished coil is recommended when accuracy matters.