Imaginary Part from Magnitude and Phase (Degrees) Reference Values

Calculate the imaginary component of a complex number from magnitude and phase angle in degrees.

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Last updatedFebruary 22, 2026

PublishedFebruary 22, 2026

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Reference Table

Imaginary Part from Magnitude and Phase (Degrees) reference values
Scenario	Imaginary Part
0 Magnitude Magnitude; -180 deg Phase Angle (Degrees)	-0 Imaginary Part
0 Magnitude Magnitude; -150 deg Phase Angle (Degrees)	-0 Imaginary Part
0 Magnitude Magnitude; -120 deg Phase Angle (Degrees)	-0 Imaginary Part
0 Magnitude Magnitude; -90 deg Phase Angle (Degrees)	-0 Imaginary Part
0 Magnitude Magnitude; -60 deg Phase Angle (Degrees)	-0 Imaginary Part
0 Magnitude Magnitude; -45 deg Phase Angle (Degrees)	-0 Imaginary Part
0 Magnitude Magnitude; -30 deg Phase Angle (Degrees)	-0 Imaginary Part
0 Magnitude Magnitude; 0 deg Phase Angle (Degrees)	0 Imaginary Part
0 Magnitude Magnitude; 30 deg Phase Angle (Degrees)	0 Imaginary Part
0 Magnitude Magnitude; 45 deg Phase Angle (Degrees)	0 Imaginary Part
0 Magnitude Magnitude; 60 deg Phase Angle (Degrees)	0 Imaginary Part
0 Magnitude Magnitude; 90 deg Phase Angle (Degrees)	0 Imaginary Part
0 Magnitude Magnitude; 120 deg Phase Angle (Degrees)	0 Imaginary Part
0 Magnitude Magnitude; 150 deg Phase Angle (Degrees)	0 Imaginary Part
0 Magnitude Magnitude; 180 deg Phase Angle (Degrees)	0 Imaginary Part
1 Magnitude Magnitude; -180 deg Phase Angle (Degrees)	-0 Imaginary Part
1 Magnitude Magnitude; -150 deg Phase Angle (Degrees)	-0.5 Imaginary Part
1 Magnitude Magnitude; -120 deg Phase Angle (Degrees)	-0.866025 Imaginary Part
1 Magnitude Magnitude; -90 deg Phase Angle (Degrees)	-1 Imaginary Part
1 Magnitude Magnitude; -60 deg Phase Angle (Degrees)	-0.866025 Imaginary Part
1 Magnitude Magnitude; -45 deg Phase Angle (Degrees)	-0.707107 Imaginary Part
1 Magnitude Magnitude; -30 deg Phase Angle (Degrees)	-0.5 Imaginary Part
1 Magnitude Magnitude; 0 deg Phase Angle (Degrees)	0 Imaginary Part
1 Magnitude Magnitude; 30 deg Phase Angle (Degrees)	0.5 Imaginary Part
1 Magnitude Magnitude; 45 deg Phase Angle (Degrees)	0.707107 Imaginary Part
1 Magnitude Magnitude; 60 deg Phase Angle (Degrees)	0.866025 Imaginary Part
1 Magnitude Magnitude; 90 deg Phase Angle (Degrees)	1 Imaginary Part
1 Magnitude Magnitude; 120 deg Phase Angle (Degrees)	0.866025 Imaginary Part
1 Magnitude Magnitude; 150 deg Phase Angle (Degrees)	0.5 Imaginary Part
1 Magnitude Magnitude; 180 deg Phase Angle (Degrees)	0 Imaginary Part
2 Magnitude Magnitude; -180 deg Phase Angle (Degrees)	-0 Imaginary Part
2 Magnitude Magnitude; -150 deg Phase Angle (Degrees)	-1 Imaginary Part
2 Magnitude Magnitude; -120 deg Phase Angle (Degrees)	-1.732051 Imaginary Part
2 Magnitude Magnitude; -90 deg Phase Angle (Degrees)	-2 Imaginary Part
2 Magnitude Magnitude; -60 deg Phase Angle (Degrees)	-1.732051 Imaginary Part
2 Magnitude Magnitude; -45 deg Phase Angle (Degrees)	-1.414214 Imaginary Part
2 Magnitude Magnitude; -30 deg Phase Angle (Degrees)	-1 Imaginary Part
2 Magnitude Magnitude; 0 deg Phase Angle (Degrees)	0 Imaginary Part
2 Magnitude Magnitude; 30 deg Phase Angle (Degrees)	1 Imaginary Part
2 Magnitude Magnitude; 45 deg Phase Angle (Degrees)	1.414214 Imaginary Part
2 Magnitude Magnitude; 60 deg Phase Angle (Degrees)	1.732051 Imaginary Part
2 Magnitude Magnitude; 90 deg Phase Angle (Degrees)	2 Imaginary Part
2 Magnitude Magnitude; 120 deg Phase Angle (Degrees)	1.732051 Imaginary Part
2 Magnitude Magnitude; 150 deg Phase Angle (Degrees)	1 Imaginary Part
2 Magnitude Magnitude; 180 deg Phase Angle (Degrees)	0 Imaginary Part
5 Magnitude Magnitude; -180 deg Phase Angle (Degrees)	-0 Imaginary Part
5 Magnitude Magnitude; -150 deg Phase Angle (Degrees)	-2.5 Imaginary Part
5 Magnitude Magnitude; -120 deg Phase Angle (Degrees)	-4.330127 Imaginary Part
5 Magnitude Magnitude; -90 deg Phase Angle (Degrees)	-5 Imaginary Part
5 Magnitude Magnitude; -60 deg Phase Angle (Degrees)	-4.330127 Imaginary Part
5 Magnitude Magnitude; -45 deg Phase Angle (Degrees)	-3.535534 Imaginary Part
5 Magnitude Magnitude; -30 deg Phase Angle (Degrees)	-2.5 Imaginary Part
5 Magnitude Magnitude; 0 deg Phase Angle (Degrees)	0 Imaginary Part
5 Magnitude Magnitude; 30 deg Phase Angle (Degrees)	2.5 Imaginary Part
5 Magnitude Magnitude; 45 deg Phase Angle (Degrees)	3.535534 Imaginary Part
5 Magnitude Magnitude; 60 deg Phase Angle (Degrees)	4.330127 Imaginary Part
5 Magnitude Magnitude; 90 deg Phase Angle (Degrees)	5 Imaginary Part
5 Magnitude Magnitude; 120 deg Phase Angle (Degrees)	4.330127 Imaginary Part
5 Magnitude Magnitude; 150 deg Phase Angle (Degrees)	2.5 Imaginary Part
5 Magnitude Magnitude; 180 deg Phase Angle (Degrees)	0 Imaginary Part
10 Magnitude Magnitude; -180 deg Phase Angle (Degrees)	-0 Imaginary Part
10 Magnitude Magnitude; -150 deg Phase Angle (Degrees)	-5 Imaginary Part
10 Magnitude Magnitude; -120 deg Phase Angle (Degrees)	-8.660254 Imaginary Part
10 Magnitude Magnitude; -90 deg Phase Angle (Degrees)	-10 Imaginary Part
10 Magnitude Magnitude; -60 deg Phase Angle (Degrees)	-8.660254 Imaginary Part
10 Magnitude Magnitude; -45 deg Phase Angle (Degrees)	-7.071068 Imaginary Part
10 Magnitude Magnitude; -30 deg Phase Angle (Degrees)	-5 Imaginary Part
10 Magnitude Magnitude; 0 deg Phase Angle (Degrees)	0 Imaginary Part
10 Magnitude Magnitude; 30 deg Phase Angle (Degrees)	5 Imaginary Part
10 Magnitude Magnitude; 45 deg Phase Angle (Degrees)	7.071068 Imaginary Part
10 Magnitude Magnitude; 60 deg Phase Angle (Degrees)	8.660254 Imaginary Part
10 Magnitude Magnitude; 90 deg Phase Angle (Degrees)	10 Imaginary Part
10 Magnitude Magnitude; 120 deg Phase Angle (Degrees)	8.660254 Imaginary Part
10 Magnitude Magnitude; 150 deg Phase Angle (Degrees)	5 Imaginary Part
10 Magnitude Magnitude; 180 deg Phase Angle (Degrees)	0 Imaginary Part
20 Magnitude Magnitude; -180 deg Phase Angle (Degrees)	-0 Imaginary Part
20 Magnitude Magnitude; -150 deg Phase Angle (Degrees)	-10 Imaginary Part
20 Magnitude Magnitude; -120 deg Phase Angle (Degrees)	-17.320508 Imaginary Part
20 Magnitude Magnitude; -90 deg Phase Angle (Degrees)	-20 Imaginary Part
20 Magnitude Magnitude; -60 deg Phase Angle (Degrees)	-17.320508 Imaginary Part
20 Magnitude Magnitude; -45 deg Phase Angle (Degrees)	-14.142136 Imaginary Part
20 Magnitude Magnitude; -30 deg Phase Angle (Degrees)	-10 Imaginary Part
20 Magnitude Magnitude; 0 deg Phase Angle (Degrees)	0 Imaginary Part
20 Magnitude Magnitude; 30 deg Phase Angle (Degrees)	10 Imaginary Part
20 Magnitude Magnitude; 45 deg Phase Angle (Degrees)	14.142136 Imaginary Part
20 Magnitude Magnitude; 60 deg Phase Angle (Degrees)	17.320508 Imaginary Part
20 Magnitude Magnitude; 90 deg Phase Angle (Degrees)	20 Imaginary Part
20 Magnitude Magnitude; 120 deg Phase Angle (Degrees)	17.320508 Imaginary Part
20 Magnitude Magnitude; 150 deg Phase Angle (Degrees)	10 Imaginary Part
20 Magnitude Magnitude; 180 deg Phase Angle (Degrees)	0 Imaginary Part
50 Magnitude Magnitude; -180 deg Phase Angle (Degrees)	-0 Imaginary Part
50 Magnitude Magnitude; -150 deg Phase Angle (Degrees)	-25 Imaginary Part
50 Magnitude Magnitude; -120 deg Phase Angle (Degrees)	-43.30127 Imaginary Part
50 Magnitude Magnitude; -90 deg Phase Angle (Degrees)	-50 Imaginary Part
50 Magnitude Magnitude; -60 deg Phase Angle (Degrees)	-43.30127 Imaginary Part
50 Magnitude Magnitude; -45 deg Phase Angle (Degrees)	-35.355339 Imaginary Part
50 Magnitude Magnitude; -30 deg Phase Angle (Degrees)	-25 Imaginary Part
50 Magnitude Magnitude; 0 deg Phase Angle (Degrees)	0 Imaginary Part
50 Magnitude Magnitude; 30 deg Phase Angle (Degrees)	25 Imaginary Part
50 Magnitude Magnitude; 45 deg Phase Angle (Degrees)	35.355339 Imaginary Part
50 Magnitude Magnitude; 60 deg Phase Angle (Degrees)	43.30127 Imaginary Part
50 Magnitude Magnitude; 90 deg Phase Angle (Degrees)	50 Imaginary Part
50 Magnitude Magnitude; 120 deg Phase Angle (Degrees)	43.30127 Imaginary Part
50 Magnitude Magnitude; 150 deg Phase Angle (Degrees)	25 Imaginary Part
50 Magnitude Magnitude; 180 deg Phase Angle (Degrees)	0 Imaginary Part

Frequently Asked Questions

Frequently asked questions for Imaginary Part from Magnitude and Phase (Degrees) and its reference values.

What does the Imaginary Part from Magnitude and Phase (Degrees) calculator do?

It helps with converting polar complex form into rectangular imaginary component.

What formula does the Imaginary Part from Magnitude and Phase (Degrees) calculator use?

Imaginary part = magnitude × sin(phase angle in degrees).

What inputs are valid?

Magnitude must be non-negative; phase angle can be any finite degree value.

When would I use this?

converting polar complex form into rectangular imaginary component

Methodology and Review

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