Inductance Calculator
This inductance calculator finds L from the number of turns and the dimensions for air-core coils, toroids and cores with an AL value. Example: an air-core coil with 500 turns, 20 mm diameter and 100 mm length has about 0.90 mH.
Example: What do you want to calculate: Cylindrical coil (air core) · Coil diameter 20 mm · Coil length 100 mm · Number of turns N 500 · Core factor µr 1 · Frequency for the reactance 100 kHz → Result: L ≈ 902.98 µH (Wheeler); ideal long solenoid: 986.96 µH. Source: Wikipedia – Spule (Elektrotechnik), Induktivität. Updated: .
How it is calculated
The inductance L of a coil describes how much magnetic flux it produces per ampere; it grows with the square of the number of turns. It is given in henry (H), usually in millihenry or microhenry. The calculator covers four typical cases.
The formulas
For a long cylindrical coil, L = µ₀·µr·N²·A / l, with the number of turns N, cross-section A, length l and the magnetic constant µ₀ = 1.2566·10⁻⁶ H/m. For short single-layer air-core coils the Wheeler approximation L[µH] = N²·r² / (9r + 10l), with r and l in inches, gives better values. A toroidal coil has L = µ₀·µr·N²·A / l with A = h·(Do − Di) / 2 and l = π·(Do + Di) / 2. For cores with an AL value simply L = AL·N²; conversely you need N = √(L / AL) turns.
Example and reactance
The air-core coil with 500 turns, 20 mm diameter and 100 mm length gives 0.99 mH by the ideal formula and 0.90 mH by Wheeler. At 100 kHz that is a reactance X_L = 2π·f·L of about 567 Ω. With an AL value of 1000 nH, 30 turns give 900 µH, and 900 µH also needs 30 turns.
- Twice the turns means four times the inductance.
- An iron or ferrite core raises L by the factor µr as long as it does not saturate.
- Thick wire, several layers and high frequencies (skin effect, self-capacitance) change the value.
Frequently asked questions
How do you calculate the inductance of a coil?
For a long coil with L = µ₀·µr·N²·A / l. With 500 turns, 20 mm diameter and 100 mm length that is about 0.99 mH without a core; short coils are better calculated by Wheeler.
How many turns do I need for a given inductance?
With the core’s AL value: N = √(L / AL). For 900 µH at AL = 1000 nH that is 30 turns. Without an AL value, rearrange the coil formula for N.
What is the AL value?
The AL value tells which inductance a core gives per turn squared, usually in nH. It combines core material and shape and is in the datasheet.
Sources and legal basis
- Wikipedia – Spule (Elektrotechnik), Induktivität
- Wikipedia – Inductance (Solenoid, Toroid)
- Wheeler, H. A. (1928): Simple Inductance Formulas for Radio Coils, Proc. IRE 16
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