Polar Function Plotter Form
Enter a polar equation for r(θ). Use explicit multiplication such as 2*sin(3*theta).
Supported terms include sin, cos, tan, sqrt, abs,
log, ln, log10, exp, pow, pi, and e.
Example Data Table
Sample equation: r(θ) = 2 + cos(θ) using degree display.
| θ (deg) | θ (rad) | r | x = r cosθ | y = r sinθ |
|---|---|---|---|---|
| 0 | 0.0000 | 3.0000 | 3.0000 | 0.0000 |
| 30 | 0.5236 | 2.8660 | 2.4821 | 1.4330 |
| 60 | 1.0472 | 2.5000 | 1.2500 | 2.1651 |
| 90 | 1.5708 | 2.0000 | 0.0000 | 2.0000 |
| 120 | 2.0944 | 1.5000 | -0.7500 | 1.2990 |
| 150 | 2.6180 | 1.1340 | -0.9821 | 0.5670 |
| 180 | 3.1416 | 1.0000 | -1.0000 | 0.0000 |
Formula Used
- Polar equation: r = f(θ)
- Cartesian conversion: x = r cos(θ), y = r sin(θ)
- Approximate enclosed area: A ≈ ½ ∫ r² dθ, evaluated numerically with trapezoidal sampling
- Approximate arc length: computed from successive Cartesian distances between sampled points
- Angle handling: when degree input is selected, values are converted to radians for evaluation and plotting calculations
How to Use This Calculator
- Enter your polar equation in terms of theta.
- Select degree or radian input for the angle range.
- Set the start angle, end angle, and number of sample points.
- Choose line mode, fill mode, line width, marker size, and color.
- Tick the close-curve option when plotting loops or filled regions.
- Press Plot Function to generate the metrics, graphs, and sampled coordinate table.
- Use the export buttons to download the plotted coordinates as CSV or save a PDF report.
Frequently Asked Questions
1. What expressions can this plotter evaluate?
You can use theta, numbers, parentheses, powers, and common functions like sin, cos, tan, sqrt, abs, log, ln, exp, min, max, pi, and e.
2. Does the calculator support degree input?
Yes. Choose degrees in the form, then enter start and end angles in degrees. The calculator converts them internally for trigonometric evaluation.
3. Why do some curves cross the origin several times?
Many polar equations naturally produce repeated origin crossings, especially roses and sinusoidal forms. Negative radius values can also reflect points through the origin.
4. What does the enclosed area value represent?
It is a numerical estimate based on sampled points over your chosen interval. For open intervals, the value reflects the traced polar integral across that range.
5. Why should I increase the sample point count?
Higher sample counts usually produce smoother plots and better numerical estimates for area, arc length, and coordinate detail, especially for rapidly changing equations.
6. When should I use the close-curve option?
Use it for loops, petals, and enclosed shapes when you want the graph to visually reconnect the final point to the starting point.
7. What is the Cartesian preview for?
It shows the same polar data transformed into x and y coordinates. This helps compare symmetry, width, height, and plotting behavior on standard axes.
8. What is included in the CSV and PDF downloads?
The CSV contains sampled point data. The PDF includes equation details, summary metrics, a graph snapshot, and a sample coordinate table.