Formula Used
A phasor in polar form is written as:
M∠θ = M(cos θ + j sin θ)
The rectangular form is:
a + jb
The real component is:
a = M cos θ
The imaginary component is:
b = M sin θ
The calculator returns the imaginary part as jb.
How to Use This Calculator
- Enter the phasor magnitude.
- Enter the phase angle.
- Select degrees or radians.
- Choose decimal places for rounding.
- Press Calculate to view the result.
- Use CSV or PDF buttons to save the output.
Example Data Table
| Magnitude |
Angle |
Unit |
Formula |
Imaginary Component |
| 10 |
30 |
Degrees |
10 × sin(30°) |
j5 |
| 25 |
-45 |
Degrees |
25 × sin(-45°) |
-j17.6777 |
| 8 |
1.5708 |
Radians |
8 × sin(1.5708) |
j8 |
| 12 |
210 |
Degrees |
12 × sin(210°) |
-j6 |
Phasor Imaginary Component Guide
What This Tool Does
A phasor stores magnitude and phase in one compact value.
Engineers use phasors for AC circuits, signals, waves, and controls.
The value is often given as magnitude and angle.
That form is useful, but rectangular form is also needed.
Rectangular form separates the horizontal and vertical components.
The vertical part is the imaginary component.
Why the Imaginary Part Matters
The imaginary component shows the quadrature part of a phasor.
It is tied to sine of the phase angle.
A positive value means the phasor points above the real axis.
A negative value means it points below the real axis.
This sign is important in impedance, current, voltage, and signal work.
Wrong signs can change circuit interpretation.
How Conversion Works
Polar phasor form uses magnitude and angle.
Rectangular form uses real and imaginary values.
The calculator first checks the angle unit.
Degree values are converted to radians internally.
Radian values are used directly.
Then the tool multiplies the magnitude by sine of the angle.
That gives the imaginary coordinate.
It also calculates the real coordinate for reference.
Useful Practical Notes
Use the same magnitude type throughout your work.
Do not mix RMS and peak values in one calculation.
Enter negative angles when the phasor lags.
Enter positive angles when it leads.
Select more decimals when checking homework or lab data.
Select fewer decimals for reports and quick estimates.
CSV export helps with spreadsheets.
PDF export is useful for saving a single result.
Common Applications
This calculator helps with AC circuit analysis.
It is useful for impedance conversion.
It also supports signal phase calculations.
Students can use it to verify manual answers.
Technicians can use it for quick checks.
Designers can compare several phasor cases.
The formula is simple, but errors are easy.
This tool reduces angle unit mistakes and rounding confusion.
FAQs
1. What is a phasor imaginary component?
It is the vertical rectangular coordinate of a phasor. In rectangular form, it appears as the value after j. It equals magnitude multiplied by sine of the phase angle.
2. What formula does this calculator use?
It uses b = M sin θ. Here, M is the phasor magnitude. The angle θ is the phase angle. The rectangular form becomes a + jb.
3. Can I use degrees and radians?
Yes. Select degrees when your angle is measured in degrees. Select radians when your angle is already in radian form. The tool handles the required conversion.
4. Why is my imaginary component negative?
A negative imaginary value means the phasor lies below the real axis. This usually happens with negative angles or angles in the third and fourth quadrants.
5. Does this tool also find the real component?
Yes. The main focus is the imaginary part. The result also shows the real component and full rectangular form for easier checking.
6. What does j mean in rectangular form?
The symbol j represents the imaginary unit in engineering. It is used instead of i because i often represents electric current.
7. Can I download my result?
Yes. Use the CSV button for spreadsheet data. Use the PDF button to save a clean report of the current calculation.
8. Is this useful for AC circuit analysis?
Yes. Phasor conversion is common in AC voltage, current, impedance, admittance, and signal phase work. It helps compare polar and rectangular forms.