About Graphing Calculator
This graphing calculator is free, needs no sign-up and runs in your browser, so your expressions are never uploaded. Type y = x^2 - 4 and it is drawn at once. Add more lines to the list, each with its own colour and a show or hide switch, the way Desmos does it.
Any letter other than x becomes a parameter with its own slider. Write y = a*x^2 + b*x + c and three sliders appear, so you can watch how each coefficient bends the parabola. Roots, y-intercepts and the points where curves cross are marked on the graph and listed in a table.
You can also plot vertical lines (x = 2) and points ((1, 3)), trace along a curve, read a table of values, fit a line or a parabola to your own data points, download the graph as a PNG and share it with a link that keeps the whole graph in the address.
How to use Graphing Calculator
- Type an expression in the first row, such as y = sin(x), or just sin(x). The graph updates as you type.
- Press Add expression for more rows. Use the coloured dot to change the colour and the eye to hide a row.
- Use a letter such as a, b or m in an expression and a slider for it appears under the list. Open Range to change its minimum, maximum and step.
- Drag the graph to move it, pinch or scroll to zoom, and use Fit or Square to reset the window. Hover or tap the graph to trace it.
- Read the Roots and intersections table, or the Table of values for any function.
- Press the share link button to copy a link to the graph, or use the download button under the graph for a PNG image.
Features
- A list of expressions: functions y = f(x), vertical lines x = c and points (a, b).
- A colour and a show or hide switch for every expression, with a typeset preview of what was understood.
- Automatic sliders for every free parameter, with editable minimum, maximum and step.
- Roots, y-intercepts and intersections between curves, found numerically, marked and listed.
- Trace by hovering or tapping, and a trace slider that reads every function at one x.
- Fit, Square, zoom in, zoom out and reset, with drag, pinch and wheel on the graph.
- A table of values for any function, with your own start and step.
- Linear and quadratic regression on a table of data points, with the equation and R².
- PNG export, and a share link that stores the graph in the URL hash so nothing is sent to a server.
- Presets that open real example graphs: sine and cosine, a parabola with sliders, a system of equations and two regressions.
How roots and intersections are found
To find where f and g cross, the calculator looks for zeros of f(x) − g(x) across the visible window. It samples the difference, spots each sign change and narrows it down by bisection, halving the interval 80 times. A candidate is rejected if the value there is not close to zero, which filters out jumps such as the asymptotes of tan(x).
Curves that only touch, like (x − 1)² against the x-axis, are found by a minimum search. A crossing outside the window is not listed, so zoom out to look further.
crossings of f and g = zeros of h(x) = f(x) − g(x)
roots of f = zeros of f(x)
bisection: keep the half of [a, b] where the sign changesWorked examples
y = x^2 - 4 and y = x + 2 gives (-2, 0) and (3, 5)
Solving x² − 4 = x + 2 gives x² − x − 6 = 0, so x = −2 or x = 3.
y = a*x^2 + b*x + c with a = 1, b = −2, c = −3 gives Roots −1 and 3
The vertex is at x = −b ÷ 2a = 1, where y = −4.
Fit a line to eight measurements gives y = 1.99762x + 0.0357143, R² = 0.998839
The slope is close to 2 because every step of x adds about 2 to y.
What you can type
| Kind | Example | Result |
|---|---|---|
| Function | y = x^2 - 4 | A curve |
| Function without y | sin(x)/x | A curve |
| Vertical line | x = 2 | A line through x = 2 |
| Point | (1, -3) | A labelled dot |
| Several points | (1,2), (3,4) | Two dots |
| Parameter | y = m*x + b | A curve and sliders for m and b |
Functions and constants that work
| Name | Meaning |
|---|---|
| sin cos tan | Trigonometry in radians |
| asin acos atan | Inverse trigonometry |
| sinh cosh tanh | Hyperbolic functions |
| sec csc cot | Reciprocal trigonometry |
| ln | Natural logarithm |
| log | Base-10 logarithm, or log(x, b) for base b |
| exp, sqrt, cbrt, abs | e to a power, roots, absolute value |
| pi, e | The constants π and e |
Good to know
What it does not do
It graphs functions of x, vertical lines and points. It does not plot implicit curves such as x² + y² = 1, polar graphs or inequality shading, and it says so when you type one. Trigonometric functions use radians, so sin(90) is the sine of 90 radians, not 90 degrees.
Floor, ceiling and modulo are not available in graphs. Write multiplication of letters either way: ax^2 is read as a*x^2.
Numerical answers
Roots and intersections are numerical results to about six significant digits, not exact symbolic answers. For an exact solution of an equation use the equation solver on this site.
Privacy: how it works
- The graph is computed and drawn in your browser. The share link keeps the expressions after the # sign of the address, which browsers never send to a server, so the people you share it with receive the graph from the link itself and Ulkaa never sees it.
Tips
- Press Fit after typing a function to bring the curve into view, and Square to give both axes the same scale so circles look round and slopes look true.
- To see how a parameter acts, put one curve on screen and drag its slider slowly. Open Range to widen the slider if the value you want is out of reach.
- On a phone the graph is at the top and the list scrolls below it, so you can edit and watch at the same time.
- Hide a row with the eye instead of deleting it to compare graphs quickly.
- The share link only contains the graph. Anyone with the link sees it exactly as you left it, with the same sliders and window.
Frequently asked questions
Is it really free?
Yes. There is no price, no trial and no credit card. Ulkaa Tool does the work with your own device, so there is no server bill to pass on to you.
Do I need an account?
No. There is no sign-up and no login. Open the page and use it. An Ulkaa account is not needed for anything on this tool.
Does it run in my browser?
Yes. Your expressions are processed by code running in your browser tab, on your own device.
Is my data uploaded?
No. Your expressions are never sent to Ulkaa or to anyone else. You can check this yourself by watching the Network tab in your browser developer tools while you use the tool.
How do I graph a function?
Type it in the first row, for example y = x^2 or sin(x). Use ^ for powers and * for multiplication where it helps, such as 2*x.
How do sliders work?
Any letter other than x, e and pi is treated as a parameter. A slider for it appears with a default range of −10 to 10. Open Range under the slider to change the minimum, maximum and step.
How do I find where two graphs intersect?
Add both functions. The crossings are marked on the graph and listed in the Roots and intersections table. Zoom out if a crossing is outside the window.
How do I plot a vertical line or a point?
Type x = 2 for a vertical line and (1, 3) for a point. You can list several points: (1,2), (3,4).
How do I fit a line to data?
Open Data points and regression, enter x and y pairs and choose Line or Parabola. The fitted curve is drawn, its equation and R² are shown, and one button adds the equation to your list.
Can I save or share my graph?
Yes. Copy the share link to send the graph, or download the PNG under the graph. The link holds the graph in the address after the # sign, so nothing is stored on a server.
Does it do polar graphs or inequalities?
No. It plots y = f(x), vertical lines and points. If you type a polar equation or an inequality it tells you that it is not supported.
Are angles in degrees or radians?
Radians. To graph sine in degrees, write sin(x*pi/180).
Popular Graphing Calculator pages
- Graph of Sine and CosineBoth waves on one set of axes, with their crossing points marked.
- Parabola GrapherDrag a, b and c and watch the parabola, its roots and its vertex change.
- Linear Equation GrapherDrag the slope m and the intercept b and watch the line move.
- Cubic Function GrapherA cubic with its three roots, two turning points and a horizontal line cutting it.
- Tangent Function GrapherSee tan(x) shoot to infinity at each asymptote and cross zero at every multiple of π.
- Absolute Value Graph CalculatorThe V-shaped graph of abs(x − 2) + 1 and the horizontal line y = 4.
- Exponential Function GrapherCompare 2^x and e^x: both pass through (0, 1) and then grow at different speeds.
- Logarithm Graph CalculatorThe natural log ln(x) and the base-10 log(x) on the same axes.
- System of Equations GrapherGraph two equations and read the solution where the lines cross.
- Linear Regression GrapherEnter x and y pairs, see them as points and fit the best straight line.
- Quadratic Regression GrapherFit y = ax² + bx + c to seven points and see how well a parabola describes them.