Enter any mathematical expression using ‘x’ as the variable, such as x^2 – 4, sin(x), or 2*x + 1. Set your x-range (domain) and y-range, then click Plot to render the graph on the canvas. You can plot trigonometric, logarithmic, exponential, and polynomial functions in standard mathematical notation. The calculator will automatically detect and mark roots, turning points, and y-intercepts on the graph.

The calculator supports all standard mathematical functions: sin(x), cos(x), tan(x), asin, acos, atan, log(x) for base-10 logarithm, ln(x) for natural logarithm, sqrt(x), abs(x), exp(x), and powers using the ^ operator (e.g. x^2 or x^3). Standard arithmetic operators +, -, *, / and parentheses () are fully supported. You can also use implicit multiplication like 2x or 3(x+1).

The roots of an equation f(x) = 0 are the points where the graph crosses the x-axis (y = 0). When you plot a function, the calculator automatically detects all roots within your x-range using a numerical sign-change method with bisection refinement, and marks them with red dots on the graph, listing the exact x-values below. This is equivalent to solving the equation algebraically, and works for polynomials of any degree as well as transcendental functions like sin(x) − 0.5.

Use the ‘Compare Functions’ tab to plot two equations on the same axes. The calculator finds all intersection points by detecting where f(x) = g(x) within the specified x-range — it evaluates h(x) = f(x) − g(x) and finds all zeros of that function. Intersection points are marked with purple dots on the graph and their (x, y) coordinates are listed below. This is the standard way to solve systems of equations graphically.

Yes. Trig functions use radians by default, which is the standard in all higher-level mathematics. For example, plot sin(x) from x = -2π to 2π (enter x-min as -6.28 and x-max as 6.28) to see a full sine wave with two complete cycles. You can also plot combinations like 2*sin(3*x) + cos(x) or sin(x)/x. The calculator understands ‘pi’ as a constant (approximately 3.14159), so you can write expressions like sin(2*pi*x).

When you plot a function, the calculator numerically locates all local minima and maxima (turning points) within your x-range and lists their coordinates. This is done by numerically differentiating the function and detecting where the derivative changes sign, then refining with bisection. For polynomials and smooth functions this is highly accurate. For example, a cubic like x³ − 3x will show both the local maximum at (−1, 2) and local minimum at (1, −2).

Yes — all calculations and plotting happen entirely in your web browser using JavaScript. No functions, inputs, or results are ever sent to our servers or any third-party service. You can use the graphing calculator offline once the page has loaded, making it ideal for students doing homework, teachers preparing lessons, or engineers needing a quick function sketch. Nothing is logged or stored.

In this calculator, ln(x) is the natural logarithm (base e, where e ≈ 2.71828), which is the standard in calculus, physics, and engineering. log(x) is the common logarithm (base 10), commonly used in chemistry (pH scale), acoustics (decibels), and older scientific notation. To compute a log in any other base, use the change-of-base formula: log_b(x) = ln(x) / ln(b), so log₂(x) would be written as ln(x)/ln(2).

Adjust the X min, X max, Y min, and Y max values to zoom in on any region of interest. For example, if you want to examine the behaviour near a root you found at x = 2.34, set the x-range from 2 to 3 and a narrower y-range around zero. You can disable auto-scale to manually control the y-axis. Each re-plot gives you finer resolution — the calculator always samples 800+ points across the x-range for a smooth curve.