However, by using the drop-down menu, the option can changed to radians, so that theĮxample With Rectangular (Cartesian) CoordinatesĬonvert the rectangular coordinates (2, 3, 8) into its equivalent spherical coordinates. If desired toĬonvert a 3D rectangular coordinate, then the user enters values into all 3 form fields, X, Y, and Z.īy default, the calculator will compute the result in degrees. To convert a 2D rectangular coordinate, then the user just enters values into the X and Y form fields and leaves the 3rd field, the Z field, blank. This calculator can be used to convert 2-dimensional (2D) or 3-dimensional rectangular coordinates to its equivalent spherical coordinates. To use this calculator, a user just enters in the (X, Y, Z) values of the rectangular coordinates and then clicks the 'Calculate' button,Ĭoordinates will be automatically computed and shown below. Contributed by: Jeff Bryant (March 2011) Open content licensed under CC BY-NC-SA. Move the sliders to compare spherical and Cartesian coordinates. When converted into spherical coordinates, the new values will be depicted as Spherical coordinates are an alternative to the more common Cartesian coordinate system. Rectangular coordinates are depicted by 3 values, (X, Y, Z). When necessary to define a unique set of spherical coordinates for each point, the user must restrict the range, aka interval, of each coordinate.This spherical coordinates converter/calculator converts the rectangular (or cartesian) coordinates of a unit to its equivalent value in sphericalĬoordinates, according to the formulas shown above. Using Fig.1 below, the trigonometric ratios and Pythagorean theorem, it can be shown that the relationships between spherical coordinates (,) (, , ) and cylindrical coordinates (r,z) ( r,, z) are as follows: r sin r sin, , z. This article will use the ISO convention frequently encountered in physics, where the naming tuple gives the order as: radial distance, polar angle, azimuthal angle, or ( r, θ, φ ). Convert spherical to cylindrical coordinates using a calculator. (See graphic re the "physics convention"-not "mathematics convention".)īoth the use of symbols and the naming order of tuple coordinates differ among the several sources and disciplines. The depression angle is the negative of the elevation angle. The user may choose to ignore the inclination angle and use the elevation angle instead, which is measured upward between the reference plane and the radial line-i.e., from the reference plane upward (towards to the positive z-axis) to the radial line. The polar angle may be called inclination angle, zenith angle, normal angle, or the colatitude. The radial distance from the fixed point of origin is also called the radius, or radial line, or radial coordinate. To Covert: xrhosin (phi)cos (theta) yrhosin (phi)sin (theta) zrhosin (phi) Get the free 'Spherical Integral Calculator' widget for your website, blog, Wordpress, Blogger, or iGoogle. If you have Cartesian coordinates, convert them and multiply by rho2sin (phi). Nota bene: the physics convention is followed in this article (See both graphics re "physics convention" and re "mathematics convention"). This widget will evaluate a spherical integral. Once the radius is fixed, the three coordinates (r, θ, φ), known as a 3- tuple, provide a coordinate system on a sphere, typically called the spherical polar coordinates. (See graphic re the "physics convention".) The azimuthal angle φ is measured between the orthogonal projection of the radial line r onto the reference x-y-plane-which is orthogonal to the z-axis and passes through the fixed point of origin- and either of the fixed x-axis or y-axis, both of which are orthogonal to the z-axis and to each other. The polar angle θ is measured between the z-axis and the radial line r. In mathematics, a spherical coordinate system is a coordinate system for three-dimensional space where the position of a given point in space is specified by three numbers, ( r, θ, φ): the radial distance of the radial line r connecting the point to the fixed point of origin (which is located on a fixed polar axis, or zenith direction axis, or z-axis) the polar angle θ of the radial line r and the azimuthal angle φ of the radial line r. This is the convention followed in this article. Spherical coordinates ( r, θ, φ) as commonly used: ( ISO 80000-2:2019): radial distance r ( slant distance to origin), polar angle θ ( theta) (angle with respect to positive polar axis), and azimuthal angle φ ( phi) (angle of rotation from the initial meridian plane). 3-dimensional coordinate system The physics convention.
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