Enter Polar Impedance
Formula used
Z = |Z|∠θ = R + jX
R = |Z| cos(θ)
X = |Z| sin(θ)
θ radians = θ degrees × π / 180
Y = 1 / Z = (R - jX) / (R² + X²)
The calculator converts the magnitude into ohms first. It then converts the angle when degrees are selected. Finally, it computes the real and imaginary parts.
How to use this calculator
- Enter the impedance magnitude from your phasor, datasheet, or test result.
- Enter the phase angle and choose degrees or radians.
- Select input and output units for clear engineering notation.
- Add frequency only when you need an equivalent L or C estimate.
- Press the convert button to see rectangular impedance above the form.
- Use copy, CSV, or PDF buttons to save the result.
Example data table
| Polar input | Angle unit | Rectangular output | Meaning |
|---|---|---|---|
| 10 Ω ∠ 30° | Degrees | 8.6603 + j5 Ω | Inductive load |
| 25 Ω ∠ -45° | Degrees | 17.6777 - j17.6777 Ω | Capacitive load |
| 5 kΩ ∠ 0.7854 rad | Radians | 3.5355 + j3.5355 kΩ | Positive reactance |
Understanding Polar Impedance
Impedance often appears in polar form during alternating current analysis. The magnitude shows the opposition size. The angle shows how voltage and current are shifted. This form is useful for phasors, filters, motors, coils, capacitors, and transmission studies. Yet many design tasks need rectangular form. Rectangular form separates resistance and reactance. That split makes circuit behavior easier to inspect.
Why Rectangular Form Matters
A rectangular impedance is written as R plus jX. The real part is resistance. It turns electrical energy into heat. The imaginary part is reactance. It stores and returns energy each cycle. Positive reactance usually points to inductive behavior. Negative reactance usually points to capacitive behavior. This calculator exposes both parts from one polar entry.
Advanced Conversion Details
The tool accepts angles in degrees or radians. It also supports common impedance units. The calculation first converts the entered magnitude into ohms. Then it converts the angle into radians when needed. The cosine of the angle gives the resistive ratio. The sine of the angle gives the reactive ratio. Multiplying those ratios by magnitude gives the final rectangular values.
Reading the Result
A result such as 6 plus j8 ohms means two things. The circuit has 6 ohms of resistance. It also has 8 ohms of inductive reactance. A result such as 10 minus j4 ohms points to capacitive reactance. The sign of X is important. It changes the phase and stored energy type. It can also affect resonance and matching decisions.
Using Frequency Options
Frequency is optional because rectangular conversion does not need it. However, frequency helps interpret reactance. If X is positive, the tool estimates an equivalent series inductance. If X is negative, it estimates an equivalent series capacitance. These estimates are helpful for quick checks. They should not replace full component modeling at high frequencies.
Accuracy and Rounding
Use enough decimal places for engineering work. Too little rounding can hide small reactance values. Too much rounding can create noisy reports. The angle should also match the sign convention used in your course or design sheet. Most electrical phasor work uses counterclockwise positive angles. That convention is used here.
Practical Uses
This calculator helps with AC networks, impedance matching, audio crossovers, RF design, and power studies. It is also useful when datasheets list impedance magnitude and phase. Converting to rectangular form makes series combinations easier. It also helps when comparing measured data with circuit models. Use the export buttons when you need clean records for reports.
Checking Complex Work
Rectangular values also make addition simple. Series impedances add by combining all R parts and all X parts. Parallel work is often easier after converting impedance into admittance. The calculator includes an admittance check for that reason. It helps spot impossible values, unusual angles, and unit mistakes before they move into a larger design file. This saves time during repeated laboratory calculation checks too.
FAQs
What is polar impedance?
Polar impedance gives impedance as a magnitude and angle. The magnitude shows total opposition. The angle shows phase shift between voltage and current.
What is rectangular impedance?
Rectangular impedance gives the same value as R plus jX. R is resistance. X is reactance. This form is useful for direct circuit addition.
Which formula converts polar form to rectangular form?
Use R equals magnitude times cosine theta. Use X equals magnitude times sine theta. The final answer is R plus jX.
Can I enter angles in radians?
Yes. Choose radians from the angle unit field. The tool will use the entered angle directly in the trigonometric calculation.
Why is reactance sometimes negative?
Negative reactance usually indicates capacitive behavior. Positive reactance usually indicates inductive behavior. The sign depends on the impedance angle.
Does the conversion require frequency?
No. Frequency is not required for rectangular conversion. It is only used to estimate an equivalent series inductor or capacitor from reactance.
What does a zero angle mean?
A zero angle means the impedance is purely resistive. The reactance part becomes zero, so the rectangular form is only R.
Can I convert kilo-ohms and mega-ohms?
Yes. Select the input unit and output unit. The calculator converts internally through ohms before showing the final answer.
What is admittance in the result?
Admittance is the reciprocal of impedance. It is shown in siemens. It can help with parallel network calculations and quick checks.
Is angle normalization required?
No. It is optional. Normalization keeps the angle in a principal range. The rectangular result remains equivalent for repeated full rotations.
Can this help with RF matching?
Yes. It can convert measured magnitude and phase into R and X. Use full RF models when parasitic effects are important.