Rectangular Equation To Polar Calculator

Scheme

The two sine waves A and B (B leads A by φ = 20°) are represented past a phasor diagram, in which sine wave A has a larger amplitude than sine wave B as indicated by the length of their phasors.

This Cartesian-polar (rectangular–polar) phasor conversion computer tin catechumen complex numbers in the rectangular form to their equivalent value in polar class and vice versa.

Example 1: Convert an impedance in rectangular (complex) form Z = 5 + j2 Ω to polar grade.

Example 2: Convert a voltage in polar form U = 206 ∠120° V to rectangular (complex) form.

Polar to Rectangular

Radius

Bending

∠φ

To calculate, select degrees or radians, enter the radius and angle and click or tap the Convert button.

Rectangular to Polar

Complex number

To calculate, enter the real and imaginary parts and click or tap the Catechumen button.

Definitions and Formulas

In electric applied science and electronics, when dealing with frequency-dependent sinusoidal sources and reactive loads, we need non simply real numbers, but also circuitous numbers to be able to solve complex equations. Complex numbers allow mathematical operators with phasors and are very useful in the analysis of AC circuits with sinusoidal currents and voltages. Using complex numbers, we tin can practice iv arithmetic operations with quantities that have both magnitude and angle, and sinusoidal voltages and other Air conditioning circuit quantities are precisely characterized past aamplitude and angle. See our Electrical, RF and Electronics calculators and Electrical Applied science Converters.

A circuitous number z tin be expressed in the form z = ten + jy where ten and y are real numbers and j is the imaginary unit commonly known in electrical engineering as the j-operator that is defined by the equation j² = –1. In a complex number x + jy, ten is chosen the real part and y is called the imaginary function. We use the alphabetic character j in electrical engineering considering the letter i is reserved for instantaneous electric current. In math, the alphabetic character i is used instead of j.

A complex number z = x + jy = r ∠φ is represented as a point and a vector in the complex plane

Circuitous numbers tin be visually represented as a vector on the complex plane, which is a modified Cartesian plane, where the horizontal centrality is chosen the real axis Re and displays the existent office and the vertical axis is called the imaginary centrality Im and displays the imaginary part. Any complex number can exist represented by a displacement along the horizontal centrality (existent role) and a displacement along the vertical centrality (imaginary function).

A complex number can also be represented on the complex airplane in the polar coordinate system. The polar representation consists of the vector magnitude r and its angular position φ relative to the reference centrality 0° expressed in the following form:

Formula

In electrical engineering and electronics, a phasor (from phase vector) is a complex number in the form of a vector in the polar coordinate arrangement representing a sinusoidal part that varies with time. The length of the phasor vector represents the magnitude of a function and the angle φ represents the angular position of the vector. Positive angles are measured counterclockwise from the reference axis 0° and negative angles are measured clockwise from the reference axis.

As the polar representation of a complex number is based on a right-angled triangle, we can employ the Pythagorean theorem to find both the magnitude and the bending of a complex number, which is described below.

To convert from Cartesian coordinates x, y to polar coordinates r, φ, utilize the following formulas:

Formula

If these formulas are used in electrical engineering calculations (see our AC Power Calculator and Three-Phase Ac Power Calculator), then x is always positive and y is positive for an inductive load (lagging current) and negative for a capacitive load (leading electric current). In this case, for capacitive loads, the angles should be negative in the range of –ninety° ≤ φ ≤ 0 and should non be corrected equally described in the in a higher place formulas (that is, 360° is not added).

To convert from polar coordinates r, φ to Cartesian coordinates x, y, do the following:

Formula