Maths New Zealand
Graphing Calculator NZ
Type a function in terms of x and it draws. Nothing is uploaded, nothing is stored, and there is no sign-in — the plotting happens entirely in your browser.
Free, no signup Runs in your browser
Use ^ for powers, * for multiply. Available: sin cos tan sqrt abs ln log exp, and the constants pi and e.
f(x) at a glance
—Roots in range
—
y-intercept
—
Minimum in range
—
Maximum in range
—
How do you graph a function online?
Enter the function in terms of x — something like x^2 - 3*x + 2 — set the range of x and y you want to see, and the curve is drawn point by point across that range. Roots, where the curve crosses the x-axis, are marked automatically along with the y-intercept.
Writing the expression
Multiplication has to be explicit. Write 3*x rather than 3x, and 2*sin(x) rather than 2sin(x) — the parser will not guess where an implied multiplication belongs, because guessing wrong silently is worse than saying so.
Powers use the caret: x^2, x^3, 2^x. The caret is right-associative, matching normal mathematical convention, so 2^3^2 evaluates as 2^(3^2) = 512 rather than (2^3)^2 = 64.
Available functions are sin, cos, tan, sqrt, abs, ln, log and exp, plus the constants pi and e. Trigonometric functions work in radians, which is what NCEA calculus uses.
If a function does not draw, check the brackets first. An unclosed bracket is the most common reason an expression is rejected.
Reading the axes
The four range fields set the window, and choosing it well is most of the skill in reading a graph.
A range that is too wide flattens interesting behaviour into a straight line; too narrow and you miss where the curve goes. If a plot looks empty, the curve is almost certainly outside the y range — widen it before assuming the function is wrong.
Asymptotes need care. A function like 1/x runs to infinity near zero, and the plot deliberately breaks the line there rather than drawing a vertical stroke that does not exist. That gap is information, not a rendering fault.
How this is calculated
The expression is parsed once into a form the machine can evaluate, then evaluated at every pixel column across the range.
1. tokenise — split the text into numbers, names, operators and brackets2. shunting-yard — convert infix to postfix, respecting precedence^ binds tighter than * and /, which bind tighter than + and −^ is right-associative, so 2^3^2 is 2^(3^2) = 512, not 643. evaluate the postfix form at each x across the plotted range4. a sign change between consecutive points brackets a root, refined by bisection
No expression library is loaded to do this. A parser of this size is about eighty lines, and pulling in a general-purpose maths library would cost more in download than the whole rest of the page — on a site whose entire premise is that nothing external is requested.
The root finder looks for sign changes between adjacent sample points and then bisects to narrow each one down. That finds any root the curve actually crosses, and misses roots where the curve only touches the axis without passing through it — a repeated root like x² has no sign change either side, so nothing flags it.
A worked example: a quadratic
Plotting f(x) = x² − 3x + 2 across x from −6 to 6.
- Factorised(x − 1)(x − 2)
- Roots where y = 0x = 1 and x = 2
- y-intercept, f(0)2
- Vertex at x = −b ÷ 2ax = 1.5
- Minimum value f(1.5)−0.25
- Shapeupward parabola
A parabola crossing the axis at 1 and 2, with its lowest point at (1.5, −0.25).
The calculator finds those roots numerically rather than by factorising, which is why it works just as well on expressions that do not factorise neatly.
What this does not replace
NCEA examinations specify what technology may be used, and a web page on a phone is not it. This is for homework, checking work and understanding what a function looks like before an exam, not during one.
It also does not do algebra. It will not factorise, differentiate, integrate or solve symbolically — it evaluates numerically and draws the result. For the roots of a quadratic it gives you the numbers; it will not show the working, and the working is usually what is being marked.
The most useful way to use it is to sketch by hand first and then check. Doing it the other way round teaches you what the tool knows rather than what you know.
What this calculator does not do
- Finds roots by sign change, so it misses repeated roots that touch without crossing
- Radians only for trigonometric functions
- Multiplication must be written explicitly — 3x is not accepted, 3*x is
- Plots functions of x only; implicit relations and parametric curves are out of scope
- Not permitted technology for an examination
Common questions
How do I graph a function online for free?
Type it in terms of x, set the x and y ranges you want to see, and it draws. No account, no download, and nothing leaves your browser.
Why does 3x not work?
Multiplication has to be explicit — write 3*x. The parser does not infer implied multiplication, because inferring it wrongly and saying nothing would be worse than rejecting it.
Are the trig functions in degrees or radians?
Radians, which is what NCEA calculus uses. To work in degrees, convert inside the expression — sin(x*pi/180).
Why is there a gap in my curve?
The function is undefined or runs to infinity there — 1/x at zero, or tan(x) at its asymptotes. The line is broken deliberately rather than drawing a vertical stroke that is not part of the curve.
Can I use this in an exam?
No. NCEA specifies what technology is permitted and a web page is not it. This is for homework and for checking your own work.
Where these numbers come from
- Wolfram MathWorld — function graphing Fixed mathematics, nothing to go out of date
- NZQA — NCEA assessment conditions The authority on what technology is permitted in an examination
Method last reviewed 2026-10-28 This calculator uses fixed rules rather than rates that change, and its method is re-checked against the sources above at least once a year. Out of date? Tell us and we will fix it.
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