spherical coordinates: meaning, definition, pronunciation and examples
C1/C2Technical / Academic
Quick answer
What does “spherical coordinates” mean?
A system for locating points in three-dimensional space using distance from a central point (radius) and two angles (polar and azimuthal).
Audio
Pronunciation
Definition
Meaning and Definition
A system for locating points in three-dimensional space using distance from a central point (radius) and two angles (polar and azimuthal).
A coordinate system particularly useful for describing phenomena with spherical symmetry, commonly applied in mathematics, physics (e.g., quantum mechanics, electromagnetism), astronomy, and computer graphics.
Dialectal Variation
British vs American Usage
Differences
No significant lexical differences. The mathematical conventions (e.g., the order of angles, which angle is polar vs. azimuthal) are globally standardised; national curricula might differ in when the concept is introduced.
Connotations
Purely technical, with identical meaning and application in UK and US academic and scientific contexts.
Frequency
Equal frequency in relevant technical disciplines.
Grammar
How to Use “spherical coordinates” in a Sentence
[Subject] + [Verb] + in + spherical coordinatesConvert + [Object] + to/into + spherical coordinatesThe + [Point/Function] + is + expressed + in + spherical coordinatesVocabulary
Collocations
Examples
Examples of “spherical coordinates” in a Sentence
verb
British English
- We must spherical-coordinate-transform the wavefunction.
- The data were sphericalised for the analysis.
American English
- We need to spherical-coordinate-transform the potential.
- The model was sphericalized for computation.
adverb
British English
- The function was expressed spherical-coordinately.
American English
- The problem is formulated spherical-coordinate-wise.
adjective
British English
- The spherical-coordinate approach simplified the integral.
- A spherical-coordinate representation is preferable here.
American English
- The spherical-coordinate method is more elegant.
- This is a spherical-coordinate formulation of the law.
Usage
Meaning in Context
Business
Virtually never used.
Academic
Core terminology in advanced mathematics, physics, and engineering courses.
Everyday
Not used.
Technical
Essential in fields like geodesy, computer graphics (for environment mapping), antenna theory, and orbital mechanics.
Vocabulary
Synonyms of “spherical coordinates”
Strong
Neutral
Weak
Vocabulary
Antonyms of “spherical coordinates”
Watch out
Common Mistakes When Using “spherical coordinates”
- Using 'spherical coordinates' to refer to 2D polar coordinates.
- Confusing the order or naming of the angles (θ and φ).
- Treating it as an uncountable noun (e.g., 'many spherical coordinate').
FAQ
Frequently Asked Questions
The radial distance (r), the polar/inclination angle (θ), and the azimuthal angle (φ).
Polar coordinates are for two dimensions (r, θ). Spherical coordinates extend this to three dimensions (r, θ, φ).
Astronomy, physics (especially electromagnetism and quantum mechanics), computer graphics (for lighting and environment maps), and geolocation.
Conventions vary between disciplines (physics vs. mathematics). In physics, θ is often the polar angle from the z-axis, and φ is the azimuthal angle in the x-y plane. Always check the local definition.
A system for locating points in three-dimensional space using distance from a central point (radius) and two angles (polar and azimuthal).
Spherical coordinates is usually technical / academic in register.
Spherical coordinates: in British English it is pronounced /ˈsfɛrɪkəl kəʊˈɔːdɪnəts/, and in American English it is pronounced /ˈsfɪrɪkəl koʊˈɔːrdənəts/. Tap the audio buttons above to hear it.
Phrases
Idioms & Phrases
- “in spherical polar form”
Learning
Memory Aids
Mnemonic
Think of a globe: 'Latitude' and 'Longitude' are like the two angular spherical coordinates (but on a fixed radius).
Conceptual Metaphor
A cosmic address: giving directions not by streets (grid) but by distance and angles from a central star.
Practice
Quiz
What is a key advantage of using spherical coordinates?