How the helical coil formulas work
A helical coil is wire wound in a helix: each turn climbs one pitch while circling the coil diameter once. Unwrap a single turn and it becomes the hypotenuse of a right triangle — that is why the wire length per turn is √((πD)² + p²), not just πD.
H = N · (p + Dw) // coil axial height
L = D² · N² / (18 · D + 40 · H) // Wheeler 1928, D & H in inches, L in µH
f = 1 / (2π √(L · C)) // LC resonant frequency
Worked example (matches published calculator references): D = 10 mm, Dw = 0.5 mm, N = 15, spacing = 0.3 mm → pitch = 0.8 mm, wire length ≈ 471.3 mm, coil height = 12 mm, L ≈ 1.342 µH, and with C = 0.46 pF the resonant frequency is ≈ 202,553 kHz.
What this helical coil calculator covers
Wire length. As a helical coil length calculator and coil winding length calculator, it answers how to calculate coil winding length from the helix coil length formula Lw = N·√((πD)² + p²). It works equally as a coil wire length calculator, a helical coil winding calculator, a spring coil length calculator and a solenoid wire length calculator — any single-layer helix winding.
Inductance. As an air core inductor calculator (also searched as air core coil calculator, air core coil inductance calculator, single layer coil inductance calculator and single layer air core inductor calculator), it implements Harold Wheeler's 1928 formula — a wheeler formula calculator / wheeler inductance formula calculator for the helix coil inductance calculator case (coil inductance calculator air core). Looking for a solenoid inductance calculator? A solenoid is just a long helical coil, so this tool covers that geometry too, including the classic inductance of a helical coil formula.
Turns design. The reverse tab is a number of turns calculator inductor tool — a coil turns calculator, inductor turns calculator and inductance to turns calculator: it tells you how many turns for inductor calculator searches mean — the exact turns (turns needed for inductor calculator, target inductance turns calculator) by solving Wheeler's formula numerically.
Resonance. Enter a capacitor and it becomes an LC resonant frequency calculator — a coil resonant frequency calculator for the self resonant frequency calculator coil question, reporting the helical coil resonant frequency of your winding, plus tank circuit frequency calculator use for Tesla primaries.
Wire & geometry. The AWG tab is an AWG wire diameter chart and magnet wire diameter table (AWG to mm calculator built in), and the forward results act as a coil pitch calculator, coil spacing calculator, coil height calculator, wire volume calculator coil and coil DC resistance calculator.
Applications. RF builders use it as a helical antenna calculator and rf choke calculator; high-voltage builders as a tesla coil primary calculator. Every input accepts mm or inch — a true helical coil calculator mm workflow — and it is a free coil inductance calculator online with no sign-up.
Scope boundary
Frequently asked questions
How do you calculate the length of a helical coil?
Unwrap one turn of the helix: it forms the hypotenuse of a right triangle with base πD (one circumference) and height p (the pitch). So one turn uses √((πD)² + p²) of wire, and N turns use Lw = N · √((πD)² + p²). D is the coil diameter measured to the center of the wire.
What is Wheeler's formula for coil inductance?
Harold Wheeler's 1928 formula for a single-layer air-core coil is L(µH) = D² · N² / (18·D + 40·l), where D is the coil diameter in inches, l is the coil axial length in inches, and N is the number of turns. It is accurate to about 1% when D/l is less than 3.
How accurate is Wheeler's formula?
Wheeler's single-layer formula is accurate to roughly 1% when the ratio of coil diameter to coil length (D/l) is below 3. This calculator shows the D/l ratio for your coil and warns you when it leaves the reliable range. Real coils also differ due to lead length, nearby metal, and self-capacitance.
How do I calculate the number of turns for a target inductance?
Use the reverse solver tab: enter your target inductance plus the coil diameter, wire diameter and turn spacing. Because N appears in both the numerator and denominator of Wheeler's formula, the tool solves for N numerically with bisection, then rounds up to a whole turn and shows the inductance you will actually get.
What is coil pitch, and how is it different from spacing?
Pitch is the axial distance from the center of one turn to the center of the next. Spacing (gap) is the empty distance between adjacent wires. Pitch = spacing + wire diameter. For a close-wound coil the spacing is zero and the pitch equals the wire diameter.
Does wire diameter affect inductance in Wheeler's formula?
Not directly: Wheeler's formula uses only coil diameter, coil length and turns. Wire diameter matters indirectly because a thicker wire with the same spacing makes the coil longer, which changes the denominator. It also sets the minimum possible pitch (turns cannot be closer than the wire diameter).
How do I find the resonant frequency of a helical coil?
Resonate the coil with a known capacitor and use f = 1 / (2·π·√(L·C)). Enter a tank or stray capacitance in picofarads in the forward calculator and it will compute the LC resonant frequency. Above the self-resonant frequency the coil stops behaving as an inductor.
What AWG wire should I use for winding a coil?
It depends on current and frequency: thicker wire (lower AWG number) handles more current with lower DC resistance, while thinner wire lets you pack more turns in a short coil. The AWG table tab lists bare-wire diameters from AWG 10 to 40 so you can pick a wire and see the minimum pitch it allows.
Can this helical coil calculator work in inches and millimeters?
Yes. Every length input has a mm / inch unit selector, and the inductance can be entered in nH, µH or mH in the reverse solver. All internal math is done consistently and results are shown in the unit you chose plus meters.
What is the difference between a helical coil and a solenoid?
A helical coil is the general geometric shape: wire wound in a helix. A solenoid is a helical coil used specifically to produce a magnetic field, usually longer than it is wide. This tool computes the geometry and inductance of the helical winding itself, which applies to solenoids, RF chokes, Tesla coil primaries and antenna loading coils alike.
Why is my measured inductance different from the calculated value?
Common causes: lead wires add inductance, metal objects near the coil change the field, the D/l ratio is outside Wheeler's accurate range, the coil is not a true single layer, or you are measuring near the self-resonant frequency where the coil no longer looks inductive. Verify with the resonance method using a known capacitor.
How much wire do I need to wind a helical coil?
Use the forward calculator: enter coil diameter, turns and pitch and it returns the exact helical wire length Lw = N·√((πD)² + p²), plus a little guidance to add 5–10% extra for leads and the first/last partial turns.
What is a good length-to-diameter ratio for an air-core coil?
A classic rule of thumb is a coil length roughly equal to the diameter (l ≈ D), which gives a good balance of inductance per wire length and Q factor. Very short, fat coils (D/l above 3) leave Wheeler's accurate range and waste wire on end turns.
Is this calculator suitable for Tesla coil primaries and RF chokes?
Yes, as a starting point: both are single-layer air-core helical coils, exactly what Wheeler's formula models. Enter the primary diameter, tubing diameter and spacing, then use the resonant frequency section with your tank capacitor to check the primary resonance. Always verify the finished coil by measurement.