Calculator Inputs
Enter polar impedance details. Optional component fields help compare reactance.
Formula Used
Polar impedance is usually written as Z = |Z|∠θ. Rectangular impedance is written as Z = R + jX.
The calculator uses these formulas:
- R = |Z| × cos(θ)
- X = |Z| × sin(θ)
- Z = R + jX
- Power factor = cos(θ)
- |Y| = 1 / |Z|
Here, R is resistance. X is reactance. Positive X suggests inductive behavior. Negative X suggests capacitive behavior.
How to Use This Calculator
- Enter the impedance magnitude in ohms.
- Enter the phase angle value.
- Select degrees or radians for the angle unit.
- Choose the reactance sign mode when needed.
- Select the rounding level for displayed answers.
- Add frequency, inductance, or capacitance for extra checks.
- Press the convert button to view rectangular impedance.
Example Data Table
| |Z| Ω | Angle | Type | Rectangular Form |
|---|---|---|---|
| 50 | 36.87° | Inductive | 40 + j30 Ω |
| 25 | -53.13° | Capacitive | 15 - j20 Ω |
| 100 | 0° | Pure resistance | 100 + j0 Ω |
| 75 | 90° | Pure reactance | 0 + j75 Ω |
Understanding Impedance Conversion
Impedance describes how a circuit opposes alternating current. It combines resistance and reactance in one value. Resistance turns electrical energy into heat. Reactance stores and returns energy. Inductors and capacitors create reactance. The rectangular form shows these parts separately.
Many instruments show impedance in polar form. That form gives magnitude and phase angle. Magnitude tells the total opposition. Phase angle shows the timing shift between voltage and current. Engineers often need rectangular form for circuit equations. It is easier to add series impedances in rectangular form.
Why Rectangular Form Matters
Rectangular impedance is written as R + jX. The R part is the real component. The X part is the imaginary component. The letter j is used in electrical work. It prevents confusion with current, often shown as i. A positive imaginary part means inductive reactance. A negative imaginary part means capacitive reactance.
This calculator helps when checking filters, motors, coils, speakers, antennas, and power networks. It also helps students study phasors. You can compare the result with manual work. You can also change the angle unit. That is useful because some textbooks use radians. Most circuit examples use degrees.
Input Choices
The sign mode adds control for practical cases. Use the entered angle when your source already has the correct sign. Force inductive mode when the branch is known to be inductive. Force capacitive mode when the branch is known to be capacitive. This reduces mistakes during quick analysis.
The optional frequency field supports extra reactance checks. Inductive reactance grows as frequency rises. Capacitive reactance falls as frequency rises. These checks do not change the main conversion. They simply help you compare expected component behavior.
Good Calculation Practice
Use consistent units before entering values. Keep impedance magnitude in ohms. Enter inductance in henry. Enter capacitance in farad. Use hertz for frequency. Round final answers according to your project needs. More decimals may help during design work. Fewer decimals may help reports.
Always review the angle sign. A small sign error can change a circuit meaning. For example, 40 + j30 Ω is inductive. The value 40 - j30 Ω is capacitive. Both have the same magnitude. They behave differently in alternating current circuits. Verify source data before making final decisions.
Rectangular conversion is simple, but it is powerful. It turns a compact phasor into useful circuit parts. The result can support network reduction, load matching, resonance checks, and power factor review. Clear impedance values make circuit decisions faster and safer.
Frequently Asked Questions
What is rectangular impedance?
Rectangular impedance writes impedance as R + jX. R is resistance. X is reactance. The form separates real and imaginary circuit opposition.
What is polar impedance?
Polar impedance writes impedance as magnitude and angle. It often appears as |Z|∠θ. The angle shows phase shift between voltage and current.
How do I convert impedance to rectangular form?
Multiply magnitude by cosine of the angle for resistance. Multiply magnitude by sine of the angle for reactance. Then write R + jX.
What does positive reactance mean?
Positive reactance usually means inductive behavior. Current lags voltage in that case. Coils and motors often have positive reactance.
What does negative reactance mean?
Negative reactance usually means capacitive behavior. Current leads voltage in that case. Capacitors create negative reactance in common circuit notation.
Can I use radians instead of degrees?
Yes. Select radians from the phase unit field. The calculator converts correctly based on your selected unit.
Why is j used instead of i?
Electrical engineering uses j for the imaginary unit. The letter i is often used for current, so j avoids confusion.
Does frequency affect this conversion?
Frequency does not affect the polar to rectangular conversion directly. It affects component reactance, so optional checks use frequency.
What happens when the angle is zero?
The impedance is purely resistive. Reactance becomes zero, and rectangular form equals the magnitude plus j0.
What happens when the angle is ninety degrees?
The resistance becomes nearly zero. The impedance is mainly reactive. A positive angle means positive imaginary reactance.
Can this calculator help with circuit homework?
Yes. It shows formulas, steps, and key values. Still, check your teacher’s rounding rules before submitting work.