Plot parametric curves, inspect derivatives, and export computed tables. Explore motion, geometry, and curve behavior with clear visuals.
| x(t) | y(t) | t Start | t End | Steps | Highlighted t | Use Case |
|---|---|---|---|---|---|---|
| 3*cos(t) | 2*sin(t) | 0 | 6.283185 | 120 | 1.570796 | Ellipse tracing |
| t*cos(t) | t*sin(t) | 0 | 12.56637 | 200 | 6.283185 | Spiral analysis |
| sin(3*t) | sin(4*t) | 0 | 6.283185 | 240 | 0.785398 | Lissajous curve |
For a parametric curve, coordinates are defined by two functions of the same variable:
x = x(t) and y = y(t)
The instantaneous slope of the curve is:
dy/dx = (dy/dt) / (dx/dt), when dx/dt ≠ 0.
The tangent speed magnitude at a selected value is:
Speed = √[(dx/dt)² + (dy/dt)²]
The curve length over the interval is estimated numerically by summing segment distances:
Arc Length ≈ Σ √[(xᵢ - xᵢ₋₁)² + (yᵢ - yᵢ₋₁)²]
The calculator also estimates derivatives numerically using a central difference method around each sampled t value.
Enter an expression for x(t) and another for y(t). Use the variable t and supported functions like sin, cos, sqrt, and log.
Choose radians or degrees, then enter the starting and ending t values. Select the number of steps to control sampling detail.
Add a highlighted t value to inspect one specific point on the curve. The calculator then shows x(t), y(t), derivatives, slope, speed, arc length, and a plotted graph.
Use the export buttons to download a CSV table or a PDF report of the current results.
It evaluates parametric equations, samples points across a t interval, estimates derivatives, finds slope and speed at a chosen point, approximates arc length, and plots the curve.
You can use t, arithmetic operators, powers, parentheses, and common functions such as sin, cos, tan, sqrt, abs, log, log10, exp, asin, acos, and atan.
It marks one specific parameter value for detailed evaluation. The result summary shows the exact coordinates, derivatives, slope, and speed at that chosen point.
When dx/dt equals zero, the tangent slope formula divides by zero. That usually indicates a vertical tangent or a point where the slope is not finite.
It is a numerical approximation based on sampled points. Increasing the number of steps generally improves accuracy, especially for highly curved or rapidly changing paths.
Use radians for most mathematical and calculus work. Use degrees when your expressions are naturally defined that way, especially in classroom exercises or geometry problems.
Yes. The calculator handles both closed curves, such as circles and ellipses, and open curves, such as spirals and wave-based trajectories.
They are used in geometry, kinematics, trajectory modeling, curve design, computer graphics, and calculus problems involving motion, tangent lines, and path length.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.