What is the Nagaoka coefficient?

A correction factor (< 1) that accounts for the magnetic flux leaking out the ends of a finite-length solenoid. Short, fat coils have a lower Nagaoka coefficient.

Does wire diameter affect inductance?

Marginally — thicker wire slightly increases the effective coil diameter. The main effect is on resistance and Q factor.

What is self-resonant frequency?

The frequency at which the coil's parasitic inter-turn capacitance resonates with its inductance. Above the SRF, the coil behaves as a capacitor.

How does a ferrite core change the inductance?

The inductance is multiplied by the relative permeability µᵣ of the core material. Ferrite cores have µᵣ from 100 to 10,000.

What Q factor is considered good?

For RF coils, Q > 100 is good; Q > 300 is excellent. For power inductors, Q is less critical than saturation current.

How do I wind a close-wound coil?

Set the winding length equal to N × wire diameter. The pitch equals the wire diameter, giving adjacent turns with no gap.

Helical Coil Inductance Calculator

Calculate the inductance, wire length, DC resistance, Q factor, and self-resonant frequency of a helical (solenoid) coil using the Nagaoka correction.

Coil Diameter (outer)

Wire Diameter

Number of Turns

Coil Length (winding length)

Dimension Unit

Core Relative Permeability (µr)

Inductance (Wheeler/Nagaoka)

1.645 µH

Corrected inductance using Nagaoka coefficient

Inductance (Solenoid ideal)

2.632 µH

L = µ₀µᵣN²A/l — ideal infinite solenoid

Nagaoka Coefficient

0.6250

Correction factor for finite-length solenoid (< 1)

Wire Length

0.628 m

Total wire needed = N × π × D

Winding Pitch

0.750 mm

Spacing between adjacent turns

DC Resistance

0.055 Ω

Copper resistance at DC (ρ = 1.72×10⁻⁸ Ω·m)

Q Factor (est. @ 1 MHz)

187.8

Quality factor = 2πfL / R (DC resistance only)

Self-Resonant Freq (est.)

27.7 MHz

Approximate SRF from parasitic capacitance

Cross-Section Area

78.54 mm²

Coil cross-section area π(D/2)²

Inductance: Ideal vs Corrected

Ideal

Corrected

AWG	Diameter	Resistance	Max Current
18	1.024 mm	21.0 mΩ/m	5 A
20	0.812 mm	33.3 mΩ/m	3.3 A
22	0.644 mm	53.0 mΩ/m	2.1 A
24	0.511 mm	84.2 mΩ/m	1.3 A
26	0.405 mm	134 mΩ/m	0.83 A
28	0.321 mm	213 mΩ/m	0.52 A
30	0.255 mm	339 mΩ/m	0.33 A

Planning notes, formulas, and examples

About the Helical Coil Inductance Calculator

Helical coils — cylindrical solenoids wound with wire — are the most common form of inductor in electronics. They appear in RF circuits, power supplies, filters, sensors, and Tesla coils. Calculating their inductance accurately requires more than the simple solenoid formula; the Nagaoka correction factor accounts for the finite length of real coils.

This Helical Coil Inductance Calculator computes the inductance using both the ideal solenoid formula and the Nagaoka-corrected formula, along with the total wire length, DC resistance, estimated Q factor at 1 MHz, self-resonant frequency, and winding pitch. Simply enter the coil diameter, wire diameter, number of turns, winding length, and core permeability.

Whether you are designing an RF tank coil, winding a power inductor, or building a Tesla coil secondary, This calculator gives you the essential parameters in seconds. Preset buttons cover common coil types, and a wire gauge reference table helps you select the right magnet wire for your application.

When This Page Helps

Use this page to estimate air-core or simple-core coil inductance, wire length, resistance, and rough RF behavior from the winding geometry you plan to build. It is a quick pre-build check for whether a coil will land near the inductance and frequency range you need. That helps you compare winding choices before buying wire or winding the coil.

How to Use the Inputs

Enter the outer diameter of the coil form.
Enter the wire diameter (bare conductor).
Enter the total number of turns.
Enter the winding length (the axial extent of the winding, not the wire length).
Select the dimension unit (mm, cm, inches, or meters).
Set the core relative permeability (1 for air, ~2000 for ferrite).
Review inductance, wire length, resistance, Q factor, and self-resonant frequency.

Formula used

Solenoid (ideal): L = µ₀ × µᵣ × N² × A / l
Nagaoka correction: L_corr = L × k_N, where k_N ≈ 1 / (1 + 0.9 × D/l)
Wire Length: l_wire = N × π × D
DC Resistance: R = ρ × l_wire / A_wire (ρ_Cu = 1.72 × 10⁻⁸ Ω·m)
Q at f: Q = 2πfL / R

Example Calculation

Result: L_corrected = 0.65 µH, Wire Length = 0.628 m, R = 0.095 Ω

A 20-turn air-core coil on a 10 mm form spanning 15 mm yields about 0.65 µH of inductance with 63 cm of wire.

Tips & Best Practices

Short wide coils deviate more from the ideal long-solenoid model, which is why the correction factor matters.
Thicker wire lowers resistance and can improve Q, but it also changes winding pitch and effective geometry.
Self-resonant frequency matters in RF work because an inductor stops behaving like a simple inductor above that region.
If you are winding on a real core, verify the permeability range for the actual operating frequency rather than assuming a DC-style value.

Why Coil Geometry Matters

Inductance grows with turn count and magnetic coupling, but the exact geometry determines how efficient that turn count really is. Real coils are finite in length, so some flux leaks out of the ends and the ideal long-solenoid equation tends to overstate inductance for short windings.

Electrical Tradeoffs

The same winding that increases inductance also increases wire length and resistance. In RF designs, that affects Q factor and resonance. In power designs, the priorities may shift toward copper loss, current handling, and core saturation instead.

Use As A First-Pass Design Tool

This calculator is useful for coil planning and quick comparison, but parasitic capacitance, skin effect, proximity effect, and real core losses can move the built result away from the estimate. Prototype and measure if the coil is part of a frequency-critical design.

Sources & Methodology

Last updated: January 15, 2025

Frequently Asked Questions

A correction factor (< 1) that accounts for the magnetic flux leaking out the ends of a finite-length solenoid. Short, fat coils have a lower Nagaoka coefficient.