What Desmos does and where to find it
Desmos is a free online graphing tool that plots equations, shows you the shape of the graph, and lets you change numbers to see how the graph changes in real time. You do not need to read anything — you open it in a web browser at desmos.com, or use the free app on a phone or tablet.
Unlike a physical graphing calculator, Desmos shows your work as you type. If you enter an equation like y = 2x + 3, the line appears on the screen when ready. If you change the 2 to a 3, the line rotates and updates while you watch. This makes it useful for learning why equations produce the shapes they do, not just getting an answer.
Desmos works on any device with a web browser — Windows, Mac, Chromebook, iPad, or Android phone. The web version and the app versions are free. You can save your graphs if you create a free account, but you do not need one to use the calculator.
Key Takeaways
- Open desmos.com in any web browser to start graphing without downloading or signing up.
- Type an equation in the left sidebar and the graph appears on the right side of the screen when ready.
- Use the plus button to add more equations, and Desmos will color each one differently so you can see them all at once.
- Drag the graph to move around it, scroll to zoom in and out, and click on points to see their exact coordinates.
- Create a free account to save your work, but you can use Desmos without one.
Entering your first equation
When you open desmos.com, you see a blank graph in the center with a sidebar on the left. The sidebar is where you type equations. Click in the first empty box and type your equation using standard math notation. For example, type y = x^2 to graph a parabola, or y = sin(x) to graph a sine wave.
Desmos understands common math symbols. Use ^ for exponents (x^2 means x squared), / for division, * for multiplication, and sqrt() for square root. You can also type Greek letters by typing their names — type pi and Desmos converts it to π. Press Enter or click elsewhere and the graph appears when ready.
If you make a mistake, Desmos shows a red error message below the equation. Common errors are forgetting parentheses (type y = 1/(x-2) not y = 1/x-2) or using the wrong symbol (use ^ not ** for powers). Fix the equation and the graph updates right away.
Adding more equations and comparing them
To graph a second equation on the same axes, click the plus button below your first equation in the sidebar. A new empty box appears. Type your second equation — for example, y = x^2 + 1. Desmos colors it differently (usually blue if the first was red) so you can tell them apart.
You can add as many equations as you want. This is useful for comparing how changing one number changes the shape. For instance, graph y = x^2, then y = 2x^2, then y = 0.5x^2 to see how the coefficient makes the parabola narrower or wider. All three appear on the same graph in different colors.
To delete an equation, click the trash icon next to it in the sidebar. To hide an equation without deleting it, click the eye icon — the graph disappears but the equation stays in the sidebar so you can show it again later.
Moving around the graph and finding coordinates
The graph shows a default window (usually from about -10 to 10 on both axes). To see a different part of the graph, click and drag the graph itself. To zoom in, scroll up with your mouse wheel or trackpad. To zoom out, scroll down. On a phone or tablet, pinch to zoom and drag with your finger.
To find the exact coordinates of a point on the graph, click on the curve. A dot appears and Desmos shows the x and y values below the graph. This is useful for finding where two lines cross (the intersection point) or where a parabola reaches its lowest point. Click different spots on the curve to see different coordinates.
If you want to see the graph on a specific range, look for the wrench icon in the top right corner. Click it to open settings where you can type the exact x and y ranges you want to see. For example, set x from 0 to 10 and y from 0 to 100 to zoom into a specific region.
Using sliders to change equations and see the effect
One of Desmos's most useful features is the slider. Instead of typing a fixed number in an equation, type a letter (like m or a). Desmos automatically creates a slider you can drag to change that number. For example, type y = mx + 2. A slider labeled m appears in the sidebar. Drag it left and right to watch the line rotate around the point (0, 2).
Sliders help you understand how each part of an equation affects the graph. Type y = a*sin(bx) and you get two sliders — one for a (which controls the height of the wave) and one for b (which controls how many waves fit on the screen). Drag them and watch the sine curve change shape in real time.
You can set the range of a slider by clicking on it. By default, sliders go from -10 to 10, but you can change that to any range you want. This is useful if you only want to see positive values, or if you want finer control (like 0 to 1 in steps of 0.01).
Graphing points and tables
You can plot individual points by typing them in the sidebar. Click the plus button and select "table" from the menu. A spreadsheet appears where you can type x and y values. Each row becomes a point on the graph. This is useful if you have data from an experiment or a list of coordinates you want to visualize.
You can also type a single point by entering it as a coordinate pair. For example, type (3, 5) in an equation box and Desmos plots that point. Type multiple points separated by commas: (1, 2), (2, 4), (3, 6) and all three appear on the graph.
If you have a table of points, Desmos can fit a line or curve through them. Click on the table, then click the regression button (it looks like a curve with a line through it). Choose the type of fit you want — linear, quadratic, exponential, or others — and Desmos shows the equation that best matches your data.
Saving your work and sharing graphs
To save a graph, create a free account by clicking the sign-in button in the top right. You can sign in with Google, Apple, or an email address. Once you are signed in, your graphs save automatically. You can give each graph a title and organize them into folders.
To share a graph with someone else, click the share button (it looks like a link icon) in the top right. Desmos creates a link you can copy and send to anyone. They can open it in a browser and see your graph, and they can even modify it (though their changes do not affect your original unless they save their own copy).
If you do not want to create an account, you can still use Desmos — your graphs just disappear when you close the browser. You can take a screenshot to save an image of the graph, or use your browser's print function to save it as a PDF.
Frequently Asked Questions
Can I graph inequalities like y > x^2?
Yes. Type the inequality using >, <, ≥, or ≤ symbols. Desmos shades the region that satisfies the inequality. For example, y > x^2 shades everything above the parabola. You can graph multiple inequalities at once to see where regions overlap.
How do I graph a circle or other shapes?
Type the equation in standard form. For a circle centered at (0, 0) with radius 5, type x^2 + y^2 = 25. For a circle centered at (2, 3), type (x-2)^2 + (y-3)^2 = 25. You can also graph parametric equations by clicking the plus button and selecting "parametric" from the menu.
What if my equation does not show up on the graph?
The equation might be outside the current viewing window. Use the zoom controls to see a wider range, or click the wrench icon to set specific x and y ranges. Check for error messages in red text below the equation. If the equation is correct but still does not appear, try clicking on the curve icon next to the equation to toggle it on.
Can I use Desmos on my phone without the app?
Yes. Open desmos.com in your phone's web browser and it works the same way as on a computer. The app version is optional and offers the same features. Both are free.
How do I find where two graphs intersect?
Graph both equations on the same axes. Click on the point where the curves cross and Desmos shows the coordinates. If you want to find all intersection points, you can also type an equation that sets them equal — for example, if you graphed y = x^2 and y = 2x, type x^2 = 2x to see where they meet.