Inductive Reactance Calculator
Enter any two of the three values (frequency, inductance, reactance) and this calculator solves for the third using the formula XL = 2 * pi * f * L. Switch solve mode to find inductance from reactance or frequency from reactance. Unit selectors cover Hz to GHz for frequency, H to nH for inductance, and milliohm to megaohm for reactance. The admittance BL = 1 / XL is also calculated automatically.
Formula
Worked example
A 14 mH coil at 1 kHz: XL = 2 * pi * 1000 Hz * 0.014 H = 87.96 Ohm. Admittance BL = 1 / 87.96 = 0.01137 S. To find inductance from those same values: L = 87.96 / (2 * pi * 1000) = 14 mH. To find frequency: f = 87.96 / (2 * pi * 0.014) = 1000 Hz.
What is inductive reactance?
Inductive reactance (XL) is the opposition an inductor offers to the flow of alternating current. Unlike resistance, it does not convert energy to heat. Instead, the inductor stores energy in its magnetic field during each half-cycle and returns it to the circuit. The result is a 90-degree phase shift: voltage leads current by a quarter cycle in a purely inductive circuit. Because reactance depends on frequency, inductors pass low-frequency (and DC) signals more easily than high-frequency ones, which is the foundation of low-pass filter design.
The formula and its derivations
The core formula is XL = 2 * pi * f * L, where f is the signal frequency in hertz and L is the inductance in henries. Rearranging gives L = XL / (2 * pi * f) to find the inductance needed for a target reactance at a known frequency, and f = XL / (2 * pi * L) to find the frequency at which an inductor reaches a target reactance. Admittance (BL), the reciprocal of reactance, equals 1 / XL and is measured in siemens (S). It expresses how readily current flows: a high admittance means low opposition.
How frequency and inductance affect XL
Inductive reactance is directly proportional to both frequency and inductance. Doubling either one doubles XL. A 1 mH inductor presents about 6.3 Ohm at 1 kHz, 628 Ohm at 100 kHz, and 6.28 kOhm at 1 MHz - a clean 10-fold increase for each decade of frequency. This linear relationship on a log-log scale (slope of +1) is a hallmark of inductive behaviour and is used to identify parasitic inductance in circuit measurements. Capacitors do the opposite: their reactance falls with frequency (slope of -1), which is why LC resonance occurs where the two slopes cross.
Practical applications and filter design
Knowing XL lets you pick an inductor for a specific job. In a simple RL circuit the impedance is Z = sqrt(R^2 + XL^2), and the cutoff frequency of an RL low-pass filter is f_c = R / (2 * pi * L). In an LC resonant circuit, the resonant frequency is f_0 = 1 / (2 * pi * sqrt(LC)), the point where XL equals XC (capacitive reactance). Power-supply chokes use large inductances (100 mH or more) to block audio-frequency ripple, audio crossover coils work in the 1-10 mH range, and RF inductors used in tuned circuits are often in the nH to low-uH range operating at MHz frequencies.
Typical inductive reactance at common frequencies
| Inductance | 60 Hz (mains) | 1 kHz (audio) | 100 kHz (RF) | 1 MHz (RF) |
|---|---|---|---|---|
| 1 nH | 0.000 Ohm | 0.000 Ohm | 0.001 Ohm | 0.006 Ohm |
| 1 uH | 0.000 Ohm | 0.006 Ohm | 0.628 Ohm | 6.28 Ohm |
| 100 uH | 0.038 Ohm | 0.628 Ohm | 62.8 Ohm | 628 Ohm |
| 1 mH | 0.377 Ohm | 6.28 Ohm | 628 Ohm | 6280 Ohm |
| 10 mH | 3.77 Ohm | 62.8 Ohm | 6280 Ohm | 62800 Ohm |
| 100 mH | 37.7 Ohm | 628 Ohm | 62800 Ohm | 628000 Ohm |
| 1 H | 377 Ohm | 6280 Ohm | 628 kOhm | 6.28 MOhm |
Reactance values (XL = 2 * pi * f * L) for standard inductor values across common frequency bands.
Frequently asked questions
What is inductive reactance and how is it different from resistance?
Reactance and resistance both oppose current flow, but resistance dissipates energy as heat while reactance stores it in a magnetic field and returns it. Reactance also depends on frequency; resistance does not. In a purely inductive circuit, voltage leads current by 90 degrees and no net power is consumed over a full cycle.
Why does inductive reactance increase with frequency?
An inductor opposes changes in current by generating a back-EMF proportional to the rate of change of current (V = L * dI/dt). Higher frequency means faster changes, so the back-EMF and the resulting opposition to current are larger. Mathematically, XL = 2 * pi * f * L, so a ten-fold increase in frequency causes a ten-fold increase in reactance.
Does an inductor block DC?
No. At DC (f = 0 Hz) the formula gives XL = 0 Ohm, so an ideal inductor is a short circuit for DC. Only its winding resistance (called DCR or RDC) limits DC current. This is the principle behind choke filters: they block AC ripple while passing steady DC current.
What is admittance and why does it matter?
Admittance (BL) is the reciprocal of reactance (BL = 1 / XL), measured in siemens (S). It tells you how easily current flows through the inductor at a given frequency. High admittance means low opposition. It is useful in parallel circuit analysis, where admittances add directly just as resistances do in series.
How do I find the inductance for a target reactance at a specific frequency?
Rearrange the formula: L = XL / (2 * pi * f). For example, to get 50 Ohm at 10 kHz, L = 50 / (2 * pi * 10000) = approximately 796 uH. Use the "Solve for Inductance" mode in this calculator to do this instantly without manual rearrangement.
What units are used for inductance in this calculator?
The calculator supports henries (H), millihenries (mH), microhenries (uH), nanohenries (nH), and picohenries (pH). Power electronics inductors are commonly in the mH range, audio coils in the mH to H range, and RF components in the nH to uH range.
At what frequency does an LC circuit resonate?
An LC circuit resonates when inductive reactance equals capacitive reactance (XL = XC). The resonant frequency is f_0 = 1 / (2 * pi * sqrt(L * C)). At resonance, impedance is at its minimum for a series circuit (or maximum for a parallel circuit) and current peaks sharply. Use the capacitive reactance calculator alongside this one to match XC to XL.