EngineeringFormula

Electrical

Inductor Calculator

Calculate inductive reactance, stored energy, series/parallel equivalent inductance, or air-core coil inductance from turns and geometry.

Formula XL = 2 pi f LReviewed Sep 8, 2026

Inductors show up in filters, power supplies, RF coils, relays, motors, and energy-storage circuits. This calculator covers the practical checks users search for most: reactance from L and frequency, stored magnetic energy from L and current, uncoupled series/parallel combinations, and a Wheeler single-layer air-core coil estimate from turns, diameter, and winding length.

Calculation Bench
Mode
01

L · Component inductance or calculated coil inductance.

02

f · Signal, ripple, or operating frequency.

Air-core coil mode estimates single-layer solenoids only. For ferrite cores, use the core maker's AL value.

Solution

Enter the known inductor values to calculate reactance, energy, equivalent L, or coil inductance.

XL = 2 pi f L

Formula Sheet

XL=2πfLX_L=2\pi fL
E=12LI2E=\dfrac{1}{2}LI^2
Ls=L1+L2+L3+...L_s=L_1+L_2+L_3+...
1Lp=1L1+1L2+...\dfrac{1}{L_p}=\dfrac{1}{L_1}+\dfrac{1}{L_2}+...
LμH=D2N218D+40ℓL_{\mu H}=\dfrac{D^2N^2}{18D+40\ell}
  • LInductance
  • XLInductive Reactance
  • fFrequency
  • ICurrent
  • NTurns
  • DCoil Diameter
  • lCoil Length

Variables & Units

SymbolVariableDescriptionCommon Units
LInductanceComponent inductance or calculated coil inductance.nH, µH, mH, H
XLInductive ReactanceAC opposition caused by inductance at a given frequency.Ω, kΩ
fFrequencySignal, ripple, or operating frequency.Hz, kHz, MHz
ICurrentCurrent through the inductor for stored-energy checks.mA, A
NTurnsNumber of turns in the single-layer air-core coil.
DCoil DiameterDiameter measured to the centerline of the winding.mm, in
lCoil LengthAxial winding length of the solenoid.mm, in

How to Use This Calculator

  • 01Choose Reactance when you need XL at a specific frequency.
  • 02Choose Stored Energy when you know inductance and current.
  • 03Choose Series/Parallel when combining uncoupled inductors; coupled coils and transformers need a mutual-inductance model.
  • 04Choose Air-Core Coil for a single-layer solenoid estimate using turns, coil diameter, and coil length.
  • 05For coil work, measure diameter to the winding centerline and winding length along the coil axis; outside former diameter alone can shift the estimate.
  • 06Use the result notes to decide whether the output is a simple circuit value or a first-pass coil estimate that still needs measurement.

How the Formula Works

Inductive reactance is XL = 2 pi f L, so reactance rises linearly with frequency and inductance.

Stored magnetic energy is E = 1/2 L I^2. Doubling current stores four times as much energy.

Uncoupled inductors add like resistors in series. In parallel, the reciprocal inductances add.

The air-core coil mode uses Wheeler's single-layer solenoid approximation, L(uH) = D^2 N^2 / (18D + 40l), with D and l in inches. It is a practical estimate, not a guaranteed manufactured value.

Worked Example 01

10 mH inductor at 60 Hz

Known

  • Inductance: 10 mH
  • Frequency: 60 Hz

Formula

XL = 2 pi f L

Substitution

XL = 2 pi x 60 x 0.010

Result

XL = 3.77 ohms

At mains frequency, a 10 mH inductor has only a few ohms of reactance.

Worked Example 02

Energy in a 1 mH inductor at 2 A

Known

  • Inductance: 1 mH
  • Current: 2 A

Formula

E = 1/2 L I^2

Substitution

E = 1/2 x 0.001 x 2^2

Result

E = 0.002 J

Stored energy rises with current squared, so current rating matters in real inductors.

Worked Example 03

25-turn air-core coil

Known

  • Turns: 25
  • Diameter: 25.4 mm
  • Length: 25.4 mm

Formula

L(uH) = D^2 N^2 / (18D + 40l)

Substitution

L(uH) = 1^2 x 25^2 / (18 x 1 + 40 x 1)

Result

L = 10.8 uH

This is a first-pass Wheeler estimate for a single-layer air-core coil.

Applications

  • 01Checking inductor reactance in AC filters and impedance calculations
  • 02Estimating energy stored in power-supply inductors
  • 03Combining uncoupled inductors in series or parallel
  • 04Estimating a single-layer air-core RF coil before winding and measuring it

Assumptions

  • 01Series/parallel mode assumes inductors are uncoupled and far enough apart that mutual inductance is negligible.
  • 02Air-core coil mode assumes a single-layer solenoid and uses Wheeler's empirical approximation.
  • 03Reactance mode assumes sinusoidal steady-state AC at the entered frequency.
  • 04Stored-energy mode uses ideal inductance and does not include saturation or core loss.

Where This Model Stops

  • 01Does not model ferrite core AL values, toroids, coupled inductors, transformers, saturation current, DC resistance, Q factor, SRF, or skin/proximity effects.
  • 02Air-core coil output is an estimate; RF coils and power inductors should be measured or checked against manufacturer data.
  • 03Does not check current saturation, DC copper loss, temperature rise, self-resonant frequency, insulation spacing, or voltage stress.
  • 04Parallel inductors with magnetic coupling can produce very different results from the uncoupled formula.
  • 05Does not select an inductor part number, wire gauge, thermal rating, or current rating.

References

  1. [1]
    Single layer air core inductor design calculator

    Circuits.dk

    Reference for Wheeler single-layer air-core formula and practical RF coil notes.

  2. [2]
    Solenoid Inductance Calculator

    RF Toolbox

    Reference for Wheeler current-sheet formula and ideal long-solenoid comparison.

  3. [3]
    Coil Inductance Calculator

    Tesla Scientific

    Reference for common Wheeler-style air-core coil formulas and geometry definitions.

Frequently Asked Questions

What does an inductor calculator usually calculate?

Common inductor calculators cover inductive reactance, stored energy, equivalent inductance in series or parallel, and coil inductance from turns and geometry.

Is this the same as a resistor or capacitor calculator?

No. Inductors depend on frequency in AC circuits: XL = 2 pi f L. They also store magnetic energy, E = 1/2 L I^2.

How accurate is the air-core coil result?

It is a practical Wheeler estimate for single-layer air-core solenoids. Real coils vary because of wire diameter, winding pitch, nearby metal, parasitic capacitance, and measurement frequency.

Can I use this for transformers or coupled coils?

No. Series/parallel mode assumes uncoupled inductors. Transformers and coupled coils require mutual inductance, coupling coefficient, and core data.

Why does frequency matter for an inductor?

Inductive reactance is XL = 2 pi f L, so the same inductor looks like a small impedance at low frequency and a much larger impedance at higher frequency, until parasitic effects become important.

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