Coordinate System Converter
Convert Cartesian, polar, cylindrical and spherical coordinates. Choose degree/radian angles, length units and an explicit inclination or elevation convention.
YOUR CALCULATION
Result
—
Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Use sine and cosine for angular inputs. For Cartesian inputs, recover radial distances with hypot and select the azimuth quadrant usingatan2. Spherical inclination is measured from+z; elevation is its complement, measured from thexy-plane.
x=r cosθ; y=r sinθ; spherical r=ρsinφ andz=ρcosφ for inclinationφ
Worked example
Cartesian(3,4,0)m corresponds to cylindrical(5m,53.130102°,0m), spherical radius5m and inclination90°. Cartesian(0,0,5)m has inclination0° but no unique azimuth.
Assumptions and input details
All entered coordinates/radii share the input length unit and are converted together. Base coordinates and input radii are limited to magnitude1e12m; radii cannot be negative. Azimuth input magnitude≤1e6 in the selected angle unit. Output azimuth is normalized to[0,360°) or[0,2π). On thez-axis azimuth is undefined; at the origin both spherical vertical angles are undefined. Inclination/elevation limits apply even at zero radius. The diagram shows only theXY projection, withz reported separately. Cylindrical and spherical options extend high-school polar/trigonometric work for design and computing.
References: OpenStax cylindrical and spherical coordinates
Unit definitions
Unit selection is independent of language. Each selector contains only units for its physical quantity. Calculations use defined base units internally.
Choose from 23 length definitions, including explicitly labelled regional measures. Area conversions square the length factor; geometric volumes cube it.
Regional measures are not interchangeable merely because their names look similar. This is a documented selection, not a claim to include every historical unit.
NIST measurement tables · Japanese traditional units · Mainland China and Hong Kong unit distinctions
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
Reflect, rotate or translate a point in the coordinate plane. Keep exact fractional coordinates and compare the original point with its image on equal-scale axes.
Enter two three-component vectors to calculate their sum, difference, dot product, cross product, magnitudes and angle, with an XY-projection diagram.
Add, subtract, multiply or divide two complex numbers. Enter real and imaginary parts separately, then inspect magnitude, argument and an equal-scale complex-plane diagram.
Reserved advertising space.