Impedance to Inductance Calculator

How to Use the Impedance to Inductance Converter

Determining inductance from alternating current (AC) circuit characteristics is simple. Follow these steps:

1. 1
   Enter Impedance (Z): Input the impedance in Ohms and select your scaling unit.
2. 2
   Enter Frequency (f): Input the operating line frequency and select unit.
3. 3
   Click Calculate: Click 'Calculate Inductance' to view equivalent inductance in Henries.

How to Calculate Impedance to Inductance (Step-by-Step Guide)

Inductors oppose changes in current by producing a back-EMF voltage. This opposition is defined as inductive reactance (XL), which dictates the AC impedance of the component. The formulas and mathematical workflow are presented below.

Inductive Reactance Formula

Assuming a purely reactive, lossless coil where total impedance (Z) equals XL, we rearrange to isolate physical inductance (L):

Where:

• L: Inductance in Henries (H)
• Z: Purely inductive impedance in Ohms (Ω)
• f: Alternating current frequency in Hertz (Hz)
• π (pi): Mathematical constant approximately equal to 3.14159

Real-Life Scenario: Sizing an AC Line choke (50 Ohms at 60 Hz)

An electrical technician wants to verify the winding inductance needed for an input choke. The choke must present 50 Ohms of impedance on a 60 Hz utility line. Sizing is calculated as:

1. 1
   Set Parameters:
   Z = 50 Ω, f = 60 Hz.
2. 2
   Multiply Constants:
   2 × π × f = 2 × 3.14159 × 60 = 376.9911
3. 3
   Divide Impedance:
   L = 50 ÷ 376.9911 ≈ 0.1326 H
4. 4
   Convert Units:
   L = 0.1326 H = 132.63 mH

Final Output: The required choke must provide exactly 0.1326 Henries (132.63 mH) of inductance.

Impedance to Inductance Reference Conversion Chart

The table below displays pre-calculated inductance values (H) for common AC impedances at a standard line frequency of 60 Hz:

Inductor Impedance Formula

Under alternating current, the mathematical inductor impedance formula is expressed as: Z_L = jωL = j(2πfL), where 'j' represents the imaginary unit indicating a 90-degree phase shift.

Inductor vs Impedance

Comparing an inductor vs impedance reveals that the inductor is a physical component, whereas impedance represents the total vector opposition (combining reactance and DCR resistance) to AC flow.

Impedance of Capacitor

Unlike coils, the impedance of capacitor components drops as line frequency increases, defined by the inverse relationship: Z_C = 1 ÷ (j2πfC).

Impedance of Inductor and Capacitor

Combining the impedance of inductor and capacitor in series yields a net reactance of X = XL - XC, which dictates overall current phase angles.

Capacitor Impedance Calculation

A standard capacitor impedance calculation relies on frequency and capacitance to match tuning networks in RF power amplifiers.

Impedance of Inductor Derivation

The mathematical impedance of inductor derivation relies on Faraday's law of induction: v(t) = L × (di/dt), which translates to the frequency domain as V = jωLI.