Parametric Plotter
Plot parametric curves x(t), y(t)
About this calculator
The Parametric Plotter traces a curve (x(t), y(t)) over a parameter range, sampling 600 points to draw the path and report its start and end coordinates, bounding box, and approximate arc length from the summed polyline segments. It detects closed curves — where the endpoints coincide relative to the curve's size — and treats out-of-domain samples as pen breaks rather than false connections. Type any expressions in t, from circles and spirals to Lissajous figures.
How to use the Parametric Plotter calculator
- Enter the values for your problem into the input fields.
- Read the result — it updates instantly as you type.
- Check the formula and the visual explanation to follow how the answer was found.
- Copy the page URL to share the exact calculation.
Common examples
- x = cos(t), y = sin(t), t ∈ [0, 2π] → the unit circle, closed, arc length ≈ 6.2832
- Archimedean spiral x = t·cos(t), y = t·sin(t), t ∈ [0, 4π] → arc length ≈ 80.818
- x = t, y = t², t ∈ [−2, 2] → a parabola from (−2, 4) to (2, 4), arc length ≈ 9.2936
- Lissajous x = cos(3t), y = sin(2t) over [0, 2π] → a closed figure, arc length ≈ 15.289
Frequently asked questions
How does the Parametric Plotter calculator work?
Enter your values and the calculator applies the exact mathematical method for this problem, showing the result together with the formula it used. Everything is computed with high-precision arithmetic, so the answer you see is not limited by ordinary floating-point rounding.
When would I use the Parametric Plotter calculator?
It is useful for homework and exam preparation, for checking work done by hand, and whenever a step in a larger problem needs this calculation done quickly and reliably.
How accurate are the results?
Calculations run at 30 significant digits of precision internally. Displayed values are rounded for readability, but the underlying result is far more precise than a typical hand or pocket-calculator computation.
Can I share a specific calculation with someone else?
Yes. Every value you enter updates the URL, so copying the address bar and sharing the link reopens the exact same calculation for whoever clicks it.