Writing Inequalities From A Graph Worksheet

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Do you need to print out some graph paper for an assignment, a project, or just for fun? Are you curious about the different types and what they're used for? Then you've come to the right place to browse and print out whatever graph paper you need!

What Is Graph Paper?

In the most basic sense, graph paper is paper that comes pre-printed with faint lines that make up a grid. There are all different ways to accomplish this, but the most common is a grid made of squares composed of parallel horizontal and vertical lines.

You're probably already familiar with ruled paper—paper that comes pre-printed with horizontal lines that you can use to write on neatly. Graph paper provides assistance in a similar way, but with a grid that anchors your work to two dimensions rather than just one.

You'll most likely need graph paper for math and math-based work. For example, as a beginning student, you can use it for visual representations of numbers when learning multiplication or addition. Later in school, you'll find it's much easier to use grid paper to graph geometric figures on a XY-plane than blank or ruled paper. Finally, of course, any schematic, drawing, or design that needs to be to-scale and precise is easier to do on grid paper.

However, you can also use graph paper for fun. It's perfect for creating complex designs for interior design, quilting, beading, embroidery, and knitting. It's also an excellent tool for games that feature maps or strategic divisions of space: for instance, most role-playing games use graph paper to show where characters are in relation to terrain, each other, and enemies.

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This complex textile design uses graph paper to figure out how to create a repeating pattern.

Download Free Graph Paper

Depending on your project, you'll need a different kind of grid on your graph paper. I've created 10 printable graph paper PDFs (with alternate JPG versions) to meet your needs.

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Quad-Ruled Graph Paper

Here are several versions of the most standard kind of graph paper—the kind that is made up of squares.

Use this paper for math projects like graphing lines or functions, for science projects like creating charts of experiment results, or for developing creative symmetrical or repeating designs.

⅛ inch squares: JPG Version | PDF Version
¼ inch squares (most common size): JPG version | PDF version
½ inch squares: JPG version | PDF version

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Quad-Ruled Graph Paper with XY-Coordinates

If you're doing a lot of coordinate geometry, save yourself some time with graph paper that already has an XY-axis on it!

Full-page coordinate grid: JPG version | PDF version
Half-page coordinate grids: JPG version | PDF version

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Multi-Line Graph Paper

This graph paper features a standard ¼ inch quad grid overlaid with slightly heavier lines in intervals of 4 or 5 squares.

Use it to learn skip-counting when first discovering numbers, or use it to easily create bar graphs and other kinds of visual data representation

¼ inch minor lines, with major lines every 4 squares: JPG version | PDF version
¼ inch minor lines, with major lines every 5 squares: JPG version | PDF version

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Dot Paper

Dot paper is graph paper that only marks the corners of the grid squares and leaves out their sides.

Use it for charts and designs, particularly if you'd like a less visually cluttered result. Because the paper only has dots, any lines you draw won't have to compete with the pre-printed lines that standard quad paper has.

¼ inch spaced dots: JPG version | PDF version
½ inch spaced dots: JPG version | PDF version

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Isometric (Triangle Grid) Paper

In this kind of graph paper, instead of squares, the grid is made up out of equilateral triangles.

Use it to create 3-dimensional drawings for designs like woodworking plans, interior space planning, or graphing on an XYZ-axis. Draw your vertical lines normally, and then draw any horizontal lines using the sides of the triangles. Because the grid creates angled cubes, your drawings are instantly in 3D.

¼ inch isometric graph paper: JPG version | PDF version

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Here's a cool example of what you can do with isometric paper.
(Image: tygerbaer2013 via Deviant Art)

Expert Tips for Using Graph Paper in Math

If you're using graph paper to learn math, let me share a few ideas for how to get the most productive use out of this tool.

For Beginner Students

For younger students, you can use graph paper to help with concepts like:

The number line. Drawing a number line on graph paper automatically correctly spaces each segment. You can use the cross-lines to represent units, fives, tens, or hundreds.

Addition and subtraction. Use different color pencils to add or remove squares from a whole. Alternatively, you can use a number line to show that addition and subtraction are ways or moving up or down on it.

Multiplication and division. Use rectangular shapes to demonstrate how 3x8 yields the same result as 4x6 by graphing 3 rows of 8, then graphing 4 rows of six, and then counting the resulting squares.

Fractions. Divide a rectangle into a variety of equal parts with colored pencils to show how many equal parts can make up a whole.

Mapping an environment. Connect our 3D world to 2D space by making a map of the room you're in, or of your street.

For More Advanced Learning

As you continue in school, graph paper should become one of the many tools in your problem-solving arsenal.

Automatically use graph paper. Remember that you may find it easier to solve problems with graph paper even if they don't explicitly say to use it. For example, many geometry problems are easier to figure out when you see them represented visually.

Graph paper makes the best scratch paper. Use grid paper as your math scratch paper—it will force you to be neater and more precise when organizing proofs, reducing formulas, and so on.

What's Next?

Learning coordinate geometry and struggling with some of the concepts? Use our guides to the four graph quadrants and completing the square to help fill in some of the gaps.

What graph-related math do you need to know for the SAT/ACT? Find out with our articles about coordinate geometry in the SAT and ACT.

Have friends who also need help with test prep? Share this article!

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About the Author

Anna scored in the 99th percentile on her SATs in high school, and went on to major in English at Princeton and to get her doctorate in English Literature at Columbia. She is passionate about improving student access to higher education.