Impedance to Inductance Calculator
Calculate inductance from impedance and frequency using this free online tool. Convert ohms to henries, millihenries, and microhenries instantly with step-by-step engineering formulas, verified calculations, and charts.
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Impedance to Inductance Calculator
Results assume a purely inductive circuit where impedance is equal to inductive reactance.
How to Use Impedance to Inductance Calculator
Calculating the inductance of a coil from its AC impedance and system frequency is a fundamental task in electrical engineering. This tool lets you convert ohms to henries, millihenries, and microhenries instantly. Follow these detailed steps to perform the calculation:
- 1. Enter impedance. Input the electrical impedance value (Z) of your circuit or inductor coil.
- 2. Select impedance unit. Choose between ohms (Ω), kiloohms (kΩ), or megohms (MΩ) depending on the scale of your load.
- 3. Enter frequency. Input the operating frequency (f) of the alternating current signal passing through the component.
- 4. Select frequency unit. Choose between hertz (Hz), kilohertz (kHz), or megahertz (MHz) from the dropdown menu.
- 5. Click Calculate. Press the Calculate button to run the conversion.
- 6. Read inductance values. View the results displayed in henries (H), millihenries (mH), and microhenries (µH) in the output panel.
This calculator is highly useful for designing power supplies, radio frequency (RF) filters, crossover networks in speaker systems, and industrial electrical chokes. For example, when matching components in an audio crossover circuit, entering the speaker impedance and the crossover frequency will quickly reveal the correct inductor size needed for the low-pass filter stage.
How to Calculate Impedance to Inductance
To compute inductance from the total impedance of a purely inductive load, we rely on the fundamental relationship between inductive reactance and AC frequency. The impedance of a pure inductor is equivalent to its inductive reactance (X_L), which is represented by the formula:
Since the impedance (Z) equals the inductive reactance (X_L) under these idealized conditions, we can rearrange the formula to solve for the inductance (L):
Where the variables are defined as:
- L: Inductance measured in henries (H)
- Z: Impedance (equivalent to inductive reactance) in ohms (Ω)
- f: Alternating current frequency in hertz (Hz)
- π (pi): The mathematical constant approximately equal to 3.14159
Verified Calculation Example
Let's perform a sample calculation to verify how the conversion works under standard AC system conditions:
- Given Impedance (Z): 50 Ω
- Given Frequency (f): 60 Hz
Apply the values to the rearranged equation:
L = 50 ÷ (2 × π × 60)
L = 50 ÷ (2 × 3.14159265 × 60)
L = 50 ÷ 376.9911
L = 0.1326 H (or 132.63 mH)
Final Answer: The calculated inductance is exactly 0.1326 H.
Real-World Scenario: AC Line Chokes
In industrial power systems, AC line chokes are placed at the input of variable frequency drives (VFDs) to limit harmonics and transient voltage spikes. If a design specification calls for a line choke to introduce 5 ohms of inductive impedance on a 60 Hz power system, engineers can use this exact calculation to find the required physical inductance. In this case, L = 5 ÷ (2 × π × 60) ≈ 0.0133 H, or 13.3 millihenries. The coil winding and magnetic core are then engineered to produce this specific inductance value.
Impedance to Inductance Chart
This reference table displays pre-calculated inductance values for common impedance levels. All values are calculated assuming a standard grid frequency of 60 Hz and a purely inductive load (where impedance equals inductive reactance).
| Impedance (Ω) | Inductance (H) |
|---|---|
| 5 Ω | 0.0133 H |
| 10 Ω | 0.0265 H |
| 20 Ω | 0.0531 H |
| 50 Ω | 0.1326 H |
| 100 Ω | 0.2653 H |
| 200 Ω | 0.5305 H |
| 500 Ω | 1.3263 H |
| 1000 Ω | 2.6526 H |
Note: Values are calculated assuming a frequency of 60 Hz and a purely inductive load. For other frequencies, the inductance scale changes inversely with the frequency.
Impedance to Inductance Frequently Asked Questions
To convert impedance to inductance, you must divide the impedance (assuming it is purely inductive reactance) by the product of 2, pi, and the operating frequency of the AC system. The formula is L = Z / (2πf), where impedance is in ohms, frequency is in hertz, and the resulting inductance is calculated in henries. This conversion assumes there is no resistance in the circuit.
The mathematical formula to calculate inductance (L) from impedance (Z) is L = Z / (2πf), where Z represents the impedance in ohms, f represents the alternating current frequency in hertz, and π is approximately 3.14159. This equation assumes that the circuit is purely inductive, meaning the total impedance is equal to the inductive reactance of the coil.
Yes, frequency has a major impact on inductance calculations. Since inductive reactance (which equals impedance for a pure inductor) is directly proportional to frequency, the calculated inductance varies inversely with frequency for a given impedance. A higher frequency requires a much smaller inductance to achieve the same electrical impedance or reactance.
Yes, impedance equals inductive reactance in a purely inductive AC circuit that contains zero resistance and zero capacitance. In such idealized circuits, the total opposing effect to alternating current is solely due to the magnetic field of the inductor, meaning the measured impedance (Z) is equivalent to the inductive reactance (XL).
The standard International System (SI) unit for inductance is the henry (H). Since one henry represents a very large amount of inductance, practical electronic components and AC power equipment typically use smaller fractional units. These include the millihenry (mH), which is one-thousandth of a henry, and the microhenry (µH), which is one-millionth of a henry.
Frequency is required because an inductor's impedance, or inductive reactance, is dynamic and depends on how fast the alternating current changes direction. Without knowing the operating frequency of the AC signal, it is mathematically impossible to separate the physical inductance value of the coil from its total measured electrical impedance in the circuit.
No, this formula is not valid for direct current (DC) circuits. In a steady-state DC circuit, the frequency is zero, which means the inductive reactance is also zero. Under DC conditions, an ideal inductor acts as a short circuit with zero impedance, and any real-world impedance is solely due to the internal winding resistance of the wire.
If resistance is present in the circuit, the total impedance is a combination of both resistance (R) and inductive reactance (XL), calculated as Z = √(R² + XL²). In this case, you must first calculate the inductive reactance by subtracting the resistance effect from the total impedance before you can find the inductance using the formula L = XL / (2πf).