What is the formula for Air-Coil Inductance (Wheeler)?

The Air-Coil Inductance (Wheeler) formula is L = µ0 × N² × π × r² / (l + 0.9 × r), where L—Inductance (H); N—Number of turns; r—Coil radius (m); l—Coil length (m).

Air-Coil Inductance (Wheeler)

Q: How do you calculate Air-Coil Inductance (Wheeler)?

Use the formula L = µ0 × N² × π × r² / (l + 0.9 × r). Wheeler’s short-coil approximation gives the inductance of a single-layer air-core solenoid from its turns, radius, and length, correcting the ideal-solenoid formula for the finite length of real coils. Enter the values you know in the calculator above and it solves for the remaining variable.

L = µ0·N²·π·r² / (l + 0.9·r)

Calculator

Inductance

Number of Turns

Coil Radius

Coil Length

Result

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Formula

L = µ0 × N² × π × r² / (l + 0.9 × r)

Description

Wheeler’s short-coil approximation gives the inductance of a single-layer air-core solenoid from its turns, radius, and length, correcting the ideal-solenoid formula for the finite length of real coils. It is the standard hand-calculation for winding RF coils, Tesla-coil secondaries, and air-core chokes, accurate to about 1% when the coil length is at least 0.4 times its diameter.

Variables

L — Inductance (H)
N — Number of turns
r — Coil radius (m)
l — Coil length (m)

Practical Notes

The 0.9·r term accounts for the field spilling out the ends of a short coil; as l ≫ r it reduces to the ideal solenoid µ0N²A/l. Accuracy degrades for very short, fat coils.

Related Concepts

All Inductors formulas →

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