Coordinate Plane
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Coordinate plane
Numbered x and y axes, in all four quadrants or just the first.
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Save this to Pinterest1 cm coordinate plane
Or take one that is already made
Ruled sheets at the standard sizes, each one a single page. The measurement is printed at the foot, so a reprint can be checked against a ruler.
1 cm coordinate plane graph paper, −10 to 1010 mm squares, every unit numberedDownload PDF ↓
1 cm coordinate plane graph paper, four quadrants10 mm squares, numbered both ways from zeroDownload PDF ↓
1 cm coordinate plane graph paper, first quadrant10 mm squares, positive numbers onlyDownload PDF ↓
1/4 inch coordinate plane graph paper, four quadrants6.35 mm squares, numbered both ways from zeroDownload PDF ↓
1/4 inch coordinate plane graph paper, first quadrant6.35 mm squares, positive numbers onlyDownload PDF ↓
5 mm coordinate plane graph paper, four quadrants5 mm squares, numbered both ways from zeroDownload PDF ↓
5 mm coordinate plane graph paper, first quadrant5 mm squares, positive numbers onlyDownload PDF ↓Every sheet here is free to print as often as you like. If one saved you time, the tip jar is on Ko-fi.
A coordinate plane is graph paper with the two axes drawn on it and numbered, and it is the sheet every plotting exercise assumes you already have. Ordered pairs, straight-line graphs, translations and reflections all need one, and a lesson stalls while somebody rules axes onto blank squares and numbers them by hand.
The four-quadrant sheets number outward from zero in both directions, which is what you want once negative coordinates have been introduced. The first-quadrant sheets keep the same number of squares but move the origin down to the bottom left, one square in from the corner, and print no negative numbers. They come as ready-made sheets of their own as well as a quadrants setting in the maker, because a plane full of negative numbers is a distraction for a class that has not met them yet.
One centimeter is the size to print if you are unsure: on US Letter it runs nine units either side of the origin across and twelve up and down, which covers most textbook questions and leaves room to number every unit. The quarter inch and five millimeter sheets give up some of that room in exchange for range, for graphs that need to run further out.
For a plane that runs the same distance both ways, one more 1 cm sheet, the one shown first, is numbered from −10 to 10 on both axes, every unit, in a square 20 cm on a side. Twenty 1 cm squares come to 200 mm, wider than the 182 mm the other sheets leave between their margins, so this grid comes to about 8 mm from each side edge of US Letter. It is a ready-made sheet only: the maker on this page always runs its plane as far as the squares fit.
The squares print in a light gray hairline and the two axes in a much darker, heavier rule, so a plotted point or a ruled graph sits on top of the paper rather than competing with it. The axis numbers are set in small six point type, a shade lighter than the axes, and apart from them and the square size printed at the foot, the page carries nothing but the plane.
What range of x and y values each coordinate plane sheet covers
The 1 cm four-quadrant coordinate plane covers x from −9 to 9 and y from −12 to 12, and the finer sheets cover more: −14 to 14 across by −19 to 19 up on the quarter inch, and −18 to 18 by −24 to 24 on the 5 mm. The y range is always the longer one because the page is portrait. The first-quadrant sheets run from 0 to 17 across and 0 to 23 up at 1 cm, 0 to 27 and 0 to 37 at quarter inch, and 0 to 35 and 0 to 47 at 5 mm. The other sheet, the one shown first, is a 1 cm plane that stops at −10 to 10 on both axes, twenty squares each way. All seven use one square per unit on both axes, and because the numbers are printed, that scale is fixed.
The fixed scale decides which graphs fit. A straight line such as y = 2x + 1 stays on the 1 cm four-quadrant sheet for whole-number x from −6 to 5, since x = 6 would need y = 13. A curve that climbs faster runs out sooner: y = x² fits only from x = −3 to 3 on the 1 cm sheet, because 4² is 16, and from −4 to 4 on the quarter inch and 5 mm sheets, because 25 is past the top of both. For a curve that needs a different scale on each axis, plain squared paper with axes you number yourself is the better sheet to print.
Why the 5 mm and quarter inch coordinate planes number every second unit
The 5 mm and quarter inch coordinate planes number every second unit, which keeps the small axis numbers far enough apart to read at a glance; only the 1 cm sheets have the room to number every unit. On the finer sheets the axes read 2, 4, 6 and so on, so a point such as (3, 5) is found by counting one line on from 2 across and from 4 up. The numbers sit below the x axis and to the left of the y axis, outside the first quadrant, with a single 0 in the corner where the axes meet, so a point plotted at whole-number coordinates never lands on a label.
Which sheet a lesson needs follows from the topic. Plotting a picture from a list of points, a common first exercise, needs only positive numbers, so the 1 cm first-quadrant sheet with every unit numbered is the easiest to read, and "along the hallway and up the stairs" is the familiar reminder that x comes first. Reflections in the x or y axis, and translations that carry a shape across zero, need all four quadrants. So do straight-line graphs with a negative slope or a negative intercept, while a reflection in the line y = x can be done on either sheet.
Common questions
Four quadrants or just the first?
Four once negative coordinates have been introduced, and the first quadrant before that. The first-quadrant sheet does more than hide the negatives: with the origin near the corner, the same page gives nearly twice the positive range, 0 to 17 across and 0 to 23 up at 1 cm against 0 to 9 and 0 to 12 on the four-quadrant sheet, which suits plotting a picture from a long list of points.
How far do the axes go?
On every sheet but one, as far as the squares reach on US Letter, which on the 1 cm four-quadrant sheet is −9 to 9 across and −12 to 12 up, with every unit numbered. The exception is the 1 cm sheet numbered −10 to 10, which stops at 10 in all four directions so that both axes run the same distance. On the quarter inch and 5 mm sheets only even units carry a number, so the last number can stop one square short of the grid: the quarter inch four-quadrant sheet is numbered to 18 up and down although its squares reach 19, and the first-quadrant sheets are numbered to 26 and 36 at quarter inch and 34 and 46 at 5 mm, one short of their last line.
Where is the origin on the first-quadrant coordinate plane?
One square in from the bottom-left corner of the grid, not on the corner itself. Placed on the very edge, the axes would look like the border of the grid and their numbers would fall into the page margin, so the sheet gives up one row and one column to keep both readable. That strip carries no numbers, so no negative values appear on the sheet.
Want to know when new printables go up?
New printables when they go up, mostly seasonal, a few times a year.