HesapHanem

Phasor Addition Calculator

Enter the magnitude and angle (degrees) of each phasor.

How it is calculated

Each phasor A∠θ is split into rectangular parts with the angle in degrees: x = A cos θ, y = A sin θ. The parts are added, x = x1 + x2, y = y1 + y2, and converted back: magnitude = √(x² + y²), phase = atan2(y, x). The phase is reported between −180° and +180° with two decimals, and the magnitude and rectangular form with four decimals; a negative imaginary part is written with a minus sign, for example 10.0000 − 6.0000j. If the two phasors cancel exactly (equal magnitudes 180° apart) the result is reported as magnitude 0 and phase 0° rather than a meaningless angle from rounding noise. Both phasors must have the same frequency; the tool does no unit conversion, so use the same unit (V, A) for both. Negative magnitudes are accepted and act like a 180° shift. Only two phasors can be added at a time.

Worked example

Add 10∠20° and 6∠75°. First phasor: x = 10 cos 20° = 9.397, y = 10 sin 20° = 3.420. Second: x = 6 cos 75° = 1.553, y = 6 sin 75° = 5.796. Sum: x = 10.9498 and y = 9.2158, shown as 10.9498 + 9.2158j. Magnitude = √(10.9498² + 9.2158²) = 14.3119. Phase = atan2(9.2158, 10.9498) = 40.09°. Note the result is well below the plain sum 16 because the phasors are 55° apart.

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Common mistakes

  • Entering angles in radians; the tool expects degrees, so 1.57 means 1.57° and not 90°.
  • Adding the magnitudes directly (10 + 6 = 16); that is correct only when both phasors have the same angle.
  • Mixing RMS values for one phasor and peak values for the other; the result is only meaningful if both use the same convention.
  • Subtracting a phasor by adding it as is; to subtract, add 180° to its angle or enter a negative magnitude. For example 10∠0° and −6∠0° give 4∠0°.
  • Mixing sine and cosine references, so one angle is 90° off; convert both signals to the same reference before adding.

About this calculator

A phasor represents a sinusoidal AC quantity — like a voltage or current — as a rotating vector with a magnitude and a phase angle, written in polar form as A∠θ. Because two AC signals of the same frequency don't simply add their magnitudes when they're out of phase with each other, this calculator converts each phasor to rectangular (real + imaginary) form, adds the components, and converts the sum back to polar form to give the resultant magnitude and phase angle.

Phasor addition is fundamental to AC circuit analysis in electrical engineering, used whenever multiple AC sources or branch currents/voltages combine — analyzing power in three-phase systems, combining currents at a node under Kirchhoff's current law, or working out the net voltage in an AC network with components at different phase angles. Electrical engineering students learn it as the standard technique for handling AC math without resorting to time-domain trigonometric addition.

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Comments (1)

  • Editorial team

    A quick check on the answer is the triangle rule: the resultant magnitude always lies between the difference and the sum of the two magnitudes, so for 3 and 4 it must fall between 1 and 7. For three phasors, add two, then type the magnitude and phase you get back in as one input of a second run. How many phasors do you usually need to add?

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