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Parametric curve grapher

Plot a curve defined by x(t) and y(t) as the parameter t sweeps an interval — the natural way to draw circles, Lissajous figures, spirals and roses that no single y=f(x) can. Pick a preset or type your own expressions; it samples the pair, auto-scales, and draws the curve in your browser.

Related tools

All Geometry tools →
Null Space Calculator (basis of Nul(A), nullity, parametric solution)Solve Ax = 0 for any matrix up to 8×8: a basis of the kernel in exact fractions and in cleared integers, the free variables, the parametric solution, the rank–nullity check and A·v = 0 verified exactly.Function GrapherPlot up to three functions f, g and h over a custom x- and y-range on an interactive canvas.System of Inequalities GrapherGraph a system of linear inequalities in x and y: shade the feasible region, draw each boundary (dashed for strict), list the region's vertices and tell you whether it is bounded, unbounded or empty.Trigonometric Function GrapherPlot A·f(Bx − C) + D for sin, cos, tan, cot, sec and csc with the asymptotes drawn, plus amplitude, period, phase shift, midline, domain, range and key points.3D Distance CalculatorCompute the distance between two points in space, with an isometric view, the Δx / Δy / Δz components and the midpoint.Angle Bisector Calculator (triangle)Enter the three sides or the three vertices and get the length of each internal angle bisector, the incenter, the inradius, and the exact point where every bisector cuts the opposite side. The angle bisector theorem is the heart of it: the bisector splits the opposite side in the ratio of the two adjacent sides. The triangle inequality is checked before anything is computed, and the triangle is drawn with its three bisectors.Annulus (ring) area calculatorCompute the area of a ring from its outer and inner radius.Aquarium volume calculatorCompute the water volume of a rectangular aquarium in litres and gallons.

Parametric curve grapher is free to use as often as you like, directly from this page. Its place is under Geometry; Null Space Calculator (basis of Nul(A), nullity, parametric solution) and Function Grapher answer the questions closest to this one.

How to use it

  1. Open the tool — no signup or install needed.
  2. Enter your input or adjust the available options.
  3. Get your result instantly, then copy or download it.

Frequently asked questions

What is Parametric curve grapher?

Plot a curve defined by x(t) and y(t) as the parameter t sweeps an interval — the natural way to draw circles, Lissajous figures, spirals and roses that no single y=f(x) can. Pick a preset or type your own expressions; it samples the pair, auto-scales, and draws the curve in your browser.

What does a concrete case look like?

x = cos t, y = sin t, t ∈ [0, 2π] — the tool shows every step in between, not just the final figure.

When would I actually use this?

Homework and site work alike: how much paint a wall takes, how much water a tank holds, whether a corner is square — and, on the coordinate side, the slope between two points, the distance across a plan, the midpoint of a span.

What is the most common mistake?

Mixing units inside one shape. Entering a length in centimetres and a width in metres gives an area wrong by a factor of a hundred, and the result looks perfectly plausible.

How is Parametric curve grapher different from Null Space Calculator (basis of Nul(A), nullity, parametric solution)?

They sit next to each other but answer different questions: Null Space Calculator (basis of Nul(A), nullity, parametric solution) is the one to open when you need it to solve Ax = 0 for any matrix up to 8×8: a basis of the kernel in exact fractions and in cleared integers, the free variables, the parametric solution, the rank–nullity check and A·v = 0 verified exactly. Pick whichever matches what you're starting from — both are free.

Is there a tool for the next step?

Function Grapher is the closest one after this: Plot up to three functions f, g and h over a custom x- and y-range on an interactive canvas.

What else is worth having open alongside it?

System of Inequalities Grapher and Trigonometric Function Grapher — they come up in the same task often enough to be worth a second tab.

Where do the figures come from?

The formulas are the classical ones and the results are exact to the precision shown — geometry does not change with the year or the country, so nothing here needs updating.

Further reading

All guides →
How-toHow Much Substrate Does an Aquarium Need? Depth, Weight and Grain SizeThe depth follows the job: a bare display, a planted tank whose roots need room, an under-gravel plate. Then comes the number people are unprepared for — substrate is what puts a filled tank past what a piece of furniture can hold. Plus why fine sand compacts and coarse gravel traps waste.ExplainerHow Many Fish Can a Tank Hold? The Inch-per-Gallon Rule Is WrongEvery stocking calculator implements a length-per-volume rule, and waste output scales with body mass, not length. A fish twice as long makes nearly five times the ammonia. Run through the tool's five methods, the same tank comes back holding anywhere from 6 to 12 fish.How-toWhat Wattage of Heater Does an Aquarium Need? Volume Is Only Half the AnswerThe same tank needs a 100 W heater in a warm flat and 300 W in an unheated room. The variable is the gap between the water and the room, which most rules of thumb drop entirely. Plus why two smaller heaters beat one big one, and where this calculator's recommendation stops being trustworthy.ExplainerThe Flat Pattern of a Cone Is a Sector, Not a CircleRoll a 50 mm cone 80 mm tall and its pattern is a 190.8° slice of a 94 mm circle. Flatten a nearly cylindrical lampshade and the pattern radius runs to 839 mm — the shallower the taper, the further away the apex.How-toHow to Find the Distance Between Two PointsUse the distance formula d = √((x₂−x₁)² + (y₂−y₁)²) to measure the straight-line distance between two points on a plane, with a worked example and the midpoint too.How-toHow to Calculate the Slope of a Line: Rise Over RunFind the slope of a line from two points with m = (y₂ − y₁) / (x₂ − x₁), and read what a positive, negative, zero, or undefined slope tells you.