usefulweb.site Graphing Calculator

Math & science

Graphing Calculator

Plot up to 6 functions or parametric curves with roots, extrema, intersections and SVG/PNG export.

Functions: "y = x^2 - 2" or just "x^2 - 2". Parametric: "cos(t), sin(t)" per line. Up to 6 lines.

Optional; automatic (asymptotes are clipped) when empty.

Optional.

Default 2π.

Optional step for the table of values (default: a tenth of the range; at most 41 rows).

Try an example: Sine and a parabola · Cubic with roots and extrema · Parametric circle and Lissajous curve · Rational function with asymptotes

How it works

Graphs y = f(x) for up to six functions (or parametric curves x(t), y(t)) over the range you choose, lists the roots, local minima and maxima and the intersection points numerically, prints a table of values and offers the graph as SVG and PNG downloads.

  • Each function is parsed by the shared CAS core and evaluated in double precision at 600 points; jumps across vertical asymptotes are broken instead of joined, and extreme values are clipped unless you set y min/max.
  • Roots: sign changes on a 4,000-point grid refined by bisection, plus touching roots (local minima of |f| that reach zero). Poles are excluded because |f| must be tiny at a root.
  • Extrema: the derivative is computed symbolically and its roots are found the same way; each critical point is classified by comparing neighbouring values (inflection points are skipped).
  • Intersections: roots of f_i − f_j for every pair of functions. All of these are numeric approximations (about 10 significant digits) and only cover the plotted range.
  • The graph is an accessible SVG (title, description, data table); the PNG is rasterised from the same SVG with ImageMagick.

For scripts and AI agents

  • JSON API: POST https://graphingcalculator.usefulweb.site/api/v1/calculate (same calculation as this page)
  • Interface description: OpenAPI 3.1 · AI guide: llms.txt
  • MCP server (Streamable HTTP): https://graphingcalculator.usefulweb.site/mcp · tool name graphing_calculator
Example request
curl -s -X POST https://graphingcalculator.usefulweb.site/api/v1/calculate \
  -H 'content-type: application/json' \
  -d '{"functions":"y = sin(x)\ny = x^2/4 - 1","xMin":-5,"xMax":5}'

Related tools

  • Math Workbench – Simplify, factor, differentiate, integrate, solve, take limits, series and plots in one box.
  • Step-by-Step Equation Solver – Solve linear, quadratic, rational and radical equations or linear systems with every step shown.
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