Cylindrical to Spherical Coordinates Converter

Convert cylindrical coordinates (r, θ, z) to spherical coordinates (ρ, φ, θ) with this calculator.

Input Parameters

Calculation Results

Calculation Formula

ρ = √(r² + z²), φ = atan2(r, z), θ = θ

Where:
ρ = radial distance
φ = polar angle
θ = azimuthal angle

Cylindrical to Spherical Coordinates Converter Calculator Usage Guide

Learn how to use the Cylindrical to Spherical Coordinates Converter calculator and its working principles

Overview

This calculator converts cylindrical coordinates (r, θ, z) to spherical coordinates (ρ, φ, θ). Cylindrical coordinates are used in three-dimensional space, where 'r' is the radial distance from the origin to the point in the xy-plane, 'θ' is the azimuthal angle in the xy-plane from the positive x-axis, and 'z' is the axial distance from the xy-plane.

How to Use

  1. Enter the radial distance (r), azimuthal angle (θ) in radians, and axial distance (z) in the input fields.
  2. Click the "Calculate" button to perform the conversion.
  3. The calculator will display the spherical coordinates (ρ, φ, θ) in the result fields.

Formula Explanation

The conversion from cylindrical to spherical coordinates is done using the following formulas:

  • ρ (radial distance) = √(r² + z²)
  • φ (polar angle) = atan2(r, z)
  • θ (azimuthal angle) = θ (remains the same)

Applications

Cylindrical to spherical coordinate conversion is useful in various fields such as physics, engineering, and mathematics, especially when dealing with problems that have cylindrical symmetry.