Calculator Input
Enter chemistry coordinates below. The page stays single column, while fields use a responsive 3, 2, and 1 column grid.
Recent Conversion History
The latest 25 calculations are stored in the session for review and CSV export.
| Time | Label | r | θ | φ | Convention | x | y | z | ρ |
|---|---|---|---|---|---|---|---|---|---|
| No saved conversions yet. | |||||||||
Example Data Table
| Label | r | θ | φ | Angle Unit | x | y | z |
|---|---|---|---|---|---|---|---|
| Atom A | 5 | 60 | 45 | Degrees | 3.062 | 3.062 | 2.500 |
| Atom B | 8 | 90 | 30 | Degrees | 6.928 | 4.000 | 0.000 |
| Atom C | 6 | 35 | 120 | Degrees | -1.721 | 2.981 | 4.915 |
Formula Used
1) Polar Convention
Meaning: θ is the polar angle from the positive z-axis. φ is the azimuth angle in the xy-plane from the positive x-axis.
Equations:
x = r sin(θ) cos(φ)
y = r sin(θ) sin(φ)
z = r cos(θ)
2) Elevation Convention
Meaning: θ is the azimuth angle in the xy-plane. φ is the elevation angle measured above the xy-plane.
Equations:
x = r cos(φ) cos(θ)
y = r cos(φ) sin(θ)
z = r sin(φ)
Chemistry Interpretation
These conversions help map atom positions, electron distributions, and molecular vectors into x, y, and z coordinates for modeling, visualization, and geometry checks.
How to Use This Calculator
Step 1
Enter a point label for the atom, orbital point, or molecular vector.
Step 2
Provide the radial distance r and both spherical angles.
Step 3
Choose degrees or radians based on your chemistry source, simulation, or textbook.
Step 4
Select the convention that matches your coordinate definition.
Step 5
Click Convert Coordinates to calculate x, y, z, planar radius, and the distance check.
Step 6
Review the 3D chart, then export the result as CSV or PDF when needed.
FAQs
1) What does this calculator convert?
It converts spherical coordinates into Cartesian x, y, and z values. This is useful for chemistry problems involving molecular geometry, directional vectors, and spatial modeling.
2) Why are there two spherical conventions?
Different books and software define theta and phi differently. The calculator includes both common conventions, so you can match your class notes, simulation package, or reference text.
3) Should I use degrees or radians?
Use whichever unit your source provides. Laboratory exercises often use degrees, while programming, modeling, and mathematical functions frequently use radians.
4) What does the planar radius ρ mean?
ρ is the distance from the z-axis to the point’s projection in the xy-plane. It helps interpret lateral spread before considering vertical position.
5) Why does the distance check matter?
The distance check verifies that the converted x, y, and z coordinates still reproduce the original radial distance r. It confirms numerical consistency.
6) Can I use negative r values?
This calculator restricts r to zero or positive values. That matches standard spherical coordinate definitions used in chemistry and geometry.
7) What does the Plotly graph show?
The chart shows a 3D point and a vector from the origin to that point. It helps visualize molecular direction and position in Cartesian space.
8) Can I save multiple calculations?
Yes. Each new conversion is added to the recent session history table. You can export that history as CSV or clear it anytime.
Notes for Chemistry Use
Always confirm how your course or software defines theta and phi before interpreting atomic or molecular coordinates.