Single-layer air-core coils
An air-core solenoid — enamelled wire wound in a single layer on a non-magnetic form — is the workhorse inductor of RF work: tuned circuits, antenna matching networks, crystal-radio tanks, and QRP filters. With no ferrite to saturate or shift with temperature, its inductance is set purely by geometry, which makes it easy to calculate and easy to trim by spreading or squeezing the turns.
Wheeler's formula
The standard approximation is Wheeler's 1928 formula. With the diameter d and length ℓ in inches and n turns:
L (µH) = d²·n² / (18·d + 40·ℓ)
It is accurate to about 1% as long as the coil is not too short — roughly length ≥ 0.4·diameter. For very short "pancake" coils a different formula is needed, but the vast majority of practical solenoids fall comfortably in Wheeler's range.
Worked example
Take a coil 1 inch (25.4 mm) in diameter, 1 inch long, with 20 turns: L = (1²·20²)/(18·1 + 40·1) = 400/58 = 6.90 µH. To go the other way — say you want 6.9 µH on a 1-inch form with 24 AWG wire wound close (pitch = one wire diameter ≈ 0.51 mm) — the calculator solves the quadratic that appears when the length itself depends on the turn count, giving about 14.3 turns over a 7.3 mm winding length.
Winding notes
Close-wound coils pack the most inductance into a given length but couple turn-to-turn capacitance; spacing the turns by roughly 1.5× the wire diameter lowers that self-capacitance and raises the self-resonant frequency, at the cost of a longer coil for the same inductance. The wire-length and DC resistance figures help you check that a design is practical before you start winding.
Related tools: once you know the inductance, the reactance & LC resonance calculator tells you what capacitor resonates with it and at what frequency, and the antenna length calculator covers the radiating side of an RF project.