Calculator
Positive reactance is inductive. Negative net reactance is capacitive.
Formula Used
Series from R and X: Z = R + jX
Series magnitude: |Z| = √(R² + X²)
Series phase angle: θ = tan-1(X / R)
Series from R, XL, and XC: Z = R + j(XL - XC)
Parallel from R branch and X branch: Y = 1/R - j(1/X), then Z = 1/Y
Parallel from R, XL, and XC branches: Y = 1/R + j(1/XC - 1/XL), then Z = 1/Y
Power factor: PF = cos θ
Current when voltage is known: I = V / |Z|
How to Use This Calculator
- Select the circuit model that matches your problem.
- Choose the same unit for all resistance and reactance inputs.
- Enter resistance and either net reactance or separate XL and XC values.
- Add source voltage if you also want current and power values.
- Press the calculate button.
- Read the result table above the form.
- Download CSV for spreadsheet work or PDF for reporting.
Example Data Table
| Case | Type | R (Ω) | XL (Ω) | XC (Ω) | Net X (Ω) | |Z| (Ω) | Angle |
|---|---|---|---|---|---|---|---|
| 1 | Series R and X | 10 | - | - | 8 | 12.806 | 38.66° |
| 2 | Series R, XL, XC | 15 | 24 | 9 | 15 | 21.213 | 45° |
| 3 | Parallel R and X | 20 | - | - | -30 | 16.641 | -33.69° |
| 4 | Parallel R, XL, XC | 50 | 100 | 40 | -27.586 | 24.910 | -56.06° |
Understanding Impedance Without Frequency
This calculator helps when frequency is unknown, omitted, or already absorbed into given reactance values. In many worksheets, lab notes, and repair sheets, reactance is provided directly in ohms. That means you can still solve impedance. You do not need to recompute reactance from inductance, capacitance, and frequency first.
Impedance combines resistance and reactance into one opposition value. Resistance stays on the real axis. Reactance stays on the imaginary axis. Together they form a complex quantity. The calculator returns rectangular form, polar form, phase angle, admittance, and power factor. It also estimates current and power when supply voltage is entered.
Why This Method Works
If inductive reactance and capacitive reactance are already known, frequency is no longer required for the final impedance step. You only combine the values correctly. For series circuits, reactances subtract. For parallel circuits, susceptances combine through admittance. This is why the tool offers direct series and parallel modes.
Useful Inputs
Use resistance for the real part. Use net reactance if the circuit is already simplified. Use separate inductive and capacitive reactance values when both branches matter. The optional voltage field adds practical output values. These include current, apparent power, real power, and reactive power. That helps students, technicians, and reviewers check complete circuit behavior from one screen.
Best Practice
Keep units consistent before calculation. Enter ohms, kilo-ohms, or mega-ohms carefully. Positive reactance is inductive. Negative net reactance is capacitive. A positive phase angle shows lagging behavior. A negative angle shows leading behavior. When the angle is near zero, the circuit behaves almost resistively.
This page is useful for quick checking, homework support, maintenance notes, and design review. It is also helpful when a problem statement gives reactance directly and skips source frequency. The example table below shows common cases. Use it to compare series and parallel responses before entering your own values.
Reading the Output
Magnitude tells the total opposition. Rectangular form shows the real and imaginary parts clearly. Polar form shows size and angle together. Admittance is useful for parallel analysis. Power factor indicates how effectively supplied power becomes useful work. These outputs make the calculator suitable for study, checking, and documentation. It also helps verify sign conventions before final submission.
FAQs
1. Can impedance be calculated without frequency?
Yes. If reactance values are already given in ohms, frequency is no longer needed for the final impedance step.
2. What does positive reactance mean here?
Positive reactance means the circuit behaves inductively. The phase angle becomes positive and current lags voltage.
3. What does negative reactance mean?
Negative reactance means the circuit behaves capacitively. The phase angle becomes negative and current leads voltage.
4. Why does the calculator show admittance too?
Admittance is very useful for parallel networks. It makes branch combination easier and helps verify the impedance result.
5. Can I use kilo-ohms or mega-ohms?
Yes. Choose the correct input unit first. Keep all resistance and reactance values in the same selected unit.
6. What is the difference between series and parallel modes?
Series mode combines resistance and reactance directly. Parallel mode combines conductance and susceptance through admittance first.
7. Is source voltage required?
No. Voltage is optional. Add it only when you also want current, apparent power, real power, and reactive power.
8. Does this tool replace full AC circuit analysis?
No. It solves impedance from entered resistance and reactance values. It does not derive reactance from component values and frequency.