What is the formula for inductive reactance?
XL = 2πfL, with f in hertz, L in henries and XL in ohms. Reactance is proportional to both frequency and inductance: double either one and XL doubles.
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Inductive reactance calculator
Enter an inductance and a frequency in this inductive reactance calculator to get the reactance of an inductor, or solve for the inductance or frequency behind the reactance you need. Add the winding resistance for impedance, phase and Q, and the self-resonant frequency to see where a real part stops behaving like an inductor.
Solve for
Examples
H
Hz
Ω
Optional: gives |Z|, phase and Q.
Hz
Optional: from the datasheet; shows how the winding capacitance shifts the result.
Inductive reactance XL
6.283 Ω
- Angular frequency ω
- 628.3 krad/s
Ideal inductor: XL doubles each time the frequency doubles. Add the DCR for |Z| and Q, and the SRF from the datasheet to see where the model stops.
10 µH at decade steps around 100 kHz
| Frequency | XL |
|---|---|
| 100 Hz | 6.283 mΩ |
| 1 kHz | 62.83 mΩ |
| 10 kHz | 628.3 mΩ |
| 100 kHz | 6.283 Ω |
| 1 MHz | 62.83 Ω |
| 10 MHz | 628.3 Ω |
| 100 MHz | 6.283 kΩ |
How to calculate inductive reactance
Use XL = 2πfL. A 10 µH inductor has a reactance of 6.283 Ω at 100 kHz and 62.83 Ω at 1 MHz: reactance rises in proportion to frequency, and the voltage across the inductor leads the current by 90°. A real inductor follows this line from where XL passes its winding resistance up to somewhat below its self-resonant frequency.
Inductive reactance formula
Reactance is the ratio of the AC voltage across an inductor to the AC current through it. The faster the current changes, the larger the voltage the inductor develops to oppose it, so the reactance rises with frequency.
XL = 2π × f × L = ωL
- XL
- inductive reactance in Ω
- f
- frequency in Hz (ω = 2πf in rad/s)
- L
- inductance in H
Rearranged for the inductance or the frequency:
L = XL ÷ (2π × f) f = XL ÷ (2π × L)
With the winding resistance R in series, the impedance, phase and quality factor are:
|Z| = √(R² + XL²) φ = arctan(XL ÷ R) Q = XL ÷ R
The turn-to-turn capacitance Cp sits across the inductor and resonates with it at the SRF. From the datasheet SRF, Cp and the reactance of the lossless L ∥ Cp pair are:
Cp = 1 ÷ ((2π × SRF)² × L) X = XL ÷ (1 − (f ÷ SRF)²)
- SRF
- self-resonant frequency in Hz
- Cp
- distributed (parallel) capacitance in F
Inductive reactance examples
Example 1: a 10 µH buck inductor at 500 kHz
XL = 2π × 500 kHz × 10 µH = 31.42 Ω. With a 40 mΩ winding resistance, Q = 31.42 Ω ÷ 40 mΩ = 785 and XL only equals R at 637 Hz. At the switching frequency the reactance sets the ripple current; the DCR matters for the DC conduction loss, not for the AC behavior.
Example 2: a measured 33 µH power inductor near its SRF
OMICRON Lab measured a 33 µH power inductor with 44 mΩ of winding resistance and its first resonance at 13.238 MHz. That implies Cp = 1 ÷ ((2π × 13.238 MHz)² × 33 µH) = 4.38 pF. At 1 MHz the part looks like 33.2 µH (+0.6 %), at 5 MHz like 38.5 µH (+17 %), and above 13.2 MHz it is capacitive.
Example 3: an RF choke for 500 Ω at 13.56 MHz
L = 500 Ω ÷ (2π × 13.56 MHz) = 5.87 µH. The next E12 value up, 6.8 µH, gives 579.4 Ω. Pick a part whose SRF is well above 13.56 MHz: by the L ∥ Cp formula, an SRF of three times the operating frequency already makes the choke look 12.5 % larger than its label.
Inductive reactance table
XL = 2πfL for common inductors at common frequencies. These are ideal values; a real part only follows them below its self-resonant frequency.
| f \ L | 100 nH | 1 µH | 10 µH | 100 µH | 1 mH | 10 mH |
|---|---|---|---|---|---|---|
| 50 Hz | 31.4 µΩ | 314 µΩ | 3.14 mΩ | 31.4 mΩ | 314 mΩ | 3.14 Ω |
| 60 Hz | 37.7 µΩ | 377 µΩ | 3.77 mΩ | 37.7 mΩ | 377 mΩ | 3.77 Ω |
| 1 kHz | 628 µΩ | 6.28 mΩ | 62.8 mΩ | 628 mΩ | 6.28 Ω | 62.8 Ω |
| 10 kHz | 6.28 mΩ | 62.8 mΩ | 628 mΩ | 6.28 Ω | 62.8 Ω | 628 Ω |
| 100 kHz | 62.8 mΩ | 628 mΩ | 6.28 Ω | 62.8 Ω | 628 Ω | 6.28 kΩ |
| 1 MHz | 628 mΩ | 6.28 Ω | 62.8 Ω | 628 Ω | 6.28 kΩ | 62.8 kΩ |
| 10 MHz | 6.28 Ω | 62.8 Ω | 628 Ω | 6.28 kΩ | 62.8 kΩ | 628 kΩ |
| 100 MHz | 62.8 Ω | 628 Ω | 6.28 kΩ | 62.8 kΩ | 628 kΩ | 6.28 MΩ |
Apparent inductance near the self-resonant frequency
With Cp across a lossless L, the inductance seen at f is L / (1 − (f/SRF)²). The same factor applies to every inductor, so this table works with any part.
| f / SRF | Apparent L / L | Error versus XL = 2πfL |
|---|---|---|
| 0.05 | 1.0025 | +0.3 % |
| 0.1 | 1.0101 | +1.0 % |
| 0.2 | 1.0417 | +4.2 % |
| 0.3 | 1.0989 | +9.9 % |
| 0.5 | 1.3333 | +33.3 % |
| 0.7 | 1.9608 | +96.1 % |
| 0.9 | 5.2632 | +426.3 % |
What the formula leaves out
Inductance is not fixed. In a cored inductor it falls with DC bias as the core approaches saturation, so XL at full load current can be well below the value computed from the label. The resistance that sets Q is not the DCR either: skin effect in the wire and loss in the core add to it as frequency rises, which is why Q curves rise, peak and fall back to zero at the SRF. Datasheets usually list the SRF as a minimum, and the measured value depends on the fixture and the board, so leave margin. Near the SRF, the real impedance peak is limited by core loss and is much lower than a model with only the DCR predicts.
Glossary
- Inductive reactance (XL)
- Also called inductor reactance: the opposition of an inductor to alternating current, 2πfL, in ohms.
- DCR
- DC resistance of the winding, usually given on datasheets as a maximum.
- Q (quality factor)
- Reactance divided by effective series resistance at a stated frequency. Higher Q means lower loss.
- Self-resonant frequency (SRF)
- Where the winding’s distributed capacitance resonates with the inductance. Above it the part is capacitive.
- Distributed capacitance (Cp)
- The turn-to-turn capacitance of the winding, modeled as one capacitor across the inductor.
- Saturation current
- The DC current at which the inductance has fallen by a specified amount, commonly 10 % or 20 %.
Related guides
- Capacitive reactance calculator: Xc = 1/(2πfC), with ESR and ESL.
- Resonant frequency calculator: where XL and Xc are equal.
Frequently asked questions
What is the impedance of an inductor?
For an ideal inductor the impedance magnitude equals its reactance, XL = 2πfL, and the voltage leads the current by 90°. With winding resistance R in series, the inductor impedance formula is |Z| = √(R² + XL²), at a phase of arctan(XL / R).
What is the reactance of a 10 µH inductor?
6.283 Ω at 100 kHz and 62.83 Ω at 1 MHz. At 60 Hz it is only 3.77 mΩ, so at mains frequency a 10 µH part is close to a short circuit.
What is the difference between inductive and capacitive reactance?
Inductive reactance rises with frequency (XL = 2πfL) and the voltage leads the current by 90°; capacitive reactance falls with frequency (Xc = 1/(2πfC)) and the current leads. They are equal at the resonant frequency f = 1/(2π√(LC)).
How do you calculate the Q of an inductor?
Q = XL / R, where R is the effective series resistance at that frequency. Using the DCR gives an upper bound: a 10 µH inductor with 40 mΩ DCR at 500 kHz works out to Q = 785, but skin effect and core loss raise the real resistance, so datasheet Q curves are much lower and peak below the SRF.
What happens above an inductor’s self-resonant frequency?
The capacitance between the turns resonates with the inductance at the SRF, where the impedance peaks and Q falls to zero. Above it the capacitance dominates and the part behaves as a capacitor, so XL = 2πfL no longer applies.
Does DC current change the inductive reactance?
Yes, through saturation. DC bias lowers the inductance of a cored inductor, and datasheets define the saturation current as the point where L has dropped by a stated amount, commonly 10 % or 20 %. XL falls in the same proportion.
What is the phase angle of an inductor?
An ideal inductor’s voltage leads its current by 90°. With winding resistance R the phase is arctan(XL / R): it is 45° where XL = R (637 Hz for 10 µH and 40 mΩ) and approaches 90° well above that.
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Sources
- OpenStax, University Physics Volume 2, 15.2 Simple AC Circuits (inductive reactance, Example 15.1)
- Vishay, Inductor and Magnetic Product Terminology (document 34053): impedance, Q, DCR, SRF, saturation current
- OMICRON Lab, Bode 100 application note: Power Inductor Modelling (Rs, L and Cp from the SRF)
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