Please enter all required numeric values.
Input Parameters Specification
Select ConverterChoose Series to Parallel or Parallel to Series equivalent impedance conversion.
ResistanceEnter series resistance Rs or parallel resistance Rp depending on selected mode.
Component TypeSelect direct reactance, capacitance or inductance for impedance conversion.
Reactive ValueEnter X, C or L value with the selected multiplier unit.
FrequencyRequired for capacitance and inductance conversion because reactance depends on frequency.
ResultsCalculator returns equivalent series and parallel resistance, reactance and component values.
Formulas & Mathematical Logic
Series to Parallel: Rp = Rs × (1 + Xs² / Rs²). This converts a series resistance into an equivalent parallel resistance at the same frequency.
Series to Parallel: Xp = Xs × (1 + Rs² / Xs²). This finds the equivalent parallel reactance.
Parallel to Series: Rs = (Rp × Xp²) / (Rp² + Xp²). This converts a parallel resistance into a matching series resistance.
Parallel to Series: Xs = (Xp × Rp²) / (Rp² + Xp²). This finds the equivalent series reactance.
Capacitance reactance: Xc = -1 / (2 × π × f × C). Capacitors show negative reactance that changes with frequency.
Inductance reactance: XL = 2 × π × f × L. Inductors show positive reactance that increases with frequency.
Step-by-Step Example
Example mode: Series to Parallel.
Given values: Rs = 10 Ω, Xs = 50 Ω, frequency = 1 MHz.
Rp = 10 × (1 + 50² / 10²) = 10 × (1 + 25) = 260 Ω.
Xp = 50 × (1 + 10² / 50²) = 50 × (1 + 0.04) = 52 Ω.
Practical meaning: at 1 MHz, a 10 Ω + j50 Ω series model behaves like about 260 Ω in parallel with j52 Ω.
About This Calculator
Convert series and parallel impedance without getting lost in complex-number math.
This CalcBoy calculator helps you move between equivalent series and parallel circuit models for resistance, reactance, capacitance and inductance at a selected frequency.
In AC circuits, the same real-world component can often be described in two useful ways: as a series impedance model or as a parallel impedance model. A capacitor with loss, an inductor with winding resistance, or a resonant RF network may look different on paper, but at one operating frequency these models can represent the same electrical behavior.
Best UseRF matching networks, tuned circuits, filters, audio crossovers and impedance transformation.
Supported InputsResistance, reactance, capacitance, inductance and frequency with practical engineering units.
Helpful ForComparing ESR models, inductor losses, simulation values and measured impedance data.
Design ReminderEquivalent conversion is frequency-specific, so always use the real operating frequency.
The calculator is especially useful when a datasheet, simulation tool, LCR meter or RF design method gives a value in one form, but your circuit calculation needs the other form. For example, an impedance analyzer may report a parallel model while your matching network uses a series model, or a filter equation may require a parallel resistance even though the component loss is measured as series resistance.
Quick idea: series impedance is often easier to understand as resistance plus reactance in the signal path, while parallel impedance is useful when leakage, damping or shunt loss must be modeled across a circuit node.
For practical circuit design, treat the result as an equivalent value at the selected frequency, not as a universal value for every frequency. Real components also include parasitic capacitance, winding resistance, lead inductance, dielectric loss, temperature drift and tolerance. These effects matter more at high frequency, so RF impedance conversion and filter design should always be checked with actual component data or measurement.
Frequently Asked Questions
What is series to parallel impedance conversion?
It converts a series resistance and reactance model into an equivalent parallel resistance and reactance model at the same frequency.
Why does frequency matter?
Capacitive reactance and inductive reactance change with frequency, so capacitance and inductance conversion needs the operating frequency.
Can I use this calculator for RF matching?
Yes. It is useful for RF matching networks, resonant circuits and filter analysis, but final RF design should also consider PCB layout and parasitics.
Does this work for capacitors and inductors?
Yes. Select capacitance or inductance, enter the value and frequency, and the calculator converts the reactive part into equivalent series and parallel forms.
Is this the same as resistor series-parallel conversion?
No. This calculator works with impedance, so it includes both resistance and reactance, not only pure resistance.
Why are some reactance values negative?
Capacitive reactance is shown as negative because capacitors have negative imaginary impedance in AC circuit analysis.