Rectangular To Polar Equation Calculator

Scheme

The two sine waves A and B (B leads A by φ = twenty°) are represented by 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 calculator can convert circuitous numbers in the rectangular class to their equivalent value in polar form and vice versa.

Example one: Convert an impedance in rectangular (circuitous) grade Z = five + j2 Ω to polar form.

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

Polar to Rectangular

Radius

Angle

∠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 summate, enter the real and imaginary parts and click or tap the Convert push.

Definitions and Formulas

In electrical engineering and electronics, when dealing with frequency-dependent sinusoidal sources and reactive loads, nosotros need not only 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 assay of AC circuits with sinusoidal currents and voltages. Using complex numbers, nosotros can do iv arithmetic operations with quantities that take both magnitude and angle, and sinusoidal voltages and other AC excursion quantities are precisely characterized by amplitude and angle. See our Electrical, RF and Electronics calculators and Electric Engineering Converters.

A complex number z can be expressed in the form z = x + jy where x and y are real numbers and j is the imaginary unit commonly known in electric engineering equally the j-operator that is defined by the equation j² = –1. In a complex number x + jy, 10 is chosen the real role and y is called the imaginary office. Nosotros apply the letter j in electrical engineering because the letter i is reserved for instantaneous current. In math, the letter i is used instead of j.

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

Complex numbers tin be visually represented every bit a vector on the complex plane, which is a modified Cartesian aeroplane, where the horizontal axis is called the real axis Re and displays the existent role and the vertical axis is called the imaginary centrality Im and displays the imaginary part. Whatever complex number can be represented by a displacement along the horizontal centrality (real part) and a deportation along the vertical axis (imaginary office).

A complex number tin too be represented on the circuitous plane in the polar coordinate system. The polar representation consists of the vector magnitude r and its angular position φ relative to the reference axis 0° expressed in the following form:

Formula

In electrical applied science and electronics, a phasor (from phase vector) is a complex number in the form of a vector in the polar coordinate system representing a sinusoidal function that varies with fourth dimension. 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 centrality 0° and negative angles are measured clockwise from the reference centrality.

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

To convert from Cartesian coordinates ten, y to polar coordinates r, φ, use the following formulas:

Formula

If these formulas are used in electric engineering calculations (come across our AC Power Figurer and Three-Stage Air-conditioning Ability Reckoner), and so ten is always positive and y is positive for an inductive load (lagging current) and negative for a capacitive load (leading current). In this instance, for capacitive loads, the angles should be negative in the range of –xc° ≤ φ ≤ 0 and should not be corrected every bit described in the above formulas (that is, 360° is not added).

To convert from polar coordinates r, φ to Cartesian coordinates 10, y, exercise the following:

Formula