Carpet with holes inside holes9 by 9 squares, repeat. Shade the middle 3 by 3 block, then the centre cell of each of the 8 blocks round it.
WOW: a word that is its own reflection15 by 5 squares, mirror. W, O and W each have a mirror line and the word reads the same backwards. Try MUM and TOOT.
Wall of shifted dark and light tiles24 by 12 squares, repeat. Tiles 4 wide, 2 tall, each row shifted 1 square. Rule the row lines grey. Do they look level?
Calculator digits 0 to 9 in seven bars29 by 4 squares, count. Each digit is two stacked 2 by 2 boxes. Ink only the edges that light: 8 uses all 7, 1 uses 2.
Castle wall with square battlements24 by 14 squares, count. Battlements go 1 up, 2 along, 1 down, 2 along. Two towers stand 4 squares above the wall.
Chessboard with a light square at your right16 by 16 squares, count. 64 cells of 2 by 2, every other one shaded. Players sit with a light corner at their right.
City skyline built only from rectangles30 by 12 squares, count. Ten towers of different widths and heights. Windows are single squares. Leave some unlit.
Dice-roll skyline12 by 6 squares, count. Roll a die for each of the 12 columns and colour that many squares. A bar chart in disguise.
Floor plan of your bedroom to scale20 by 16 squares, count. Let 1 square be 25 cm. Measure the bed and desk, then draw each as a rectangle from above.
Maze with one true path and three dead ends15 by 15 squares, count. Pencil the true path first and wall it in. Branch the dead ends off it, 1 square wide.
Mystery grid puzzle for a friend24 by 12 squares, scale. Draw on 6 by 6 lettered cells. On a second sheet copy the cells out of order, with labels.
Piano keyboard, one octave wide14 by 8 squares, count. Seven white keys, each 2 wide. Five black keys sit on the joins: a group of two, then three.
Robot built from squares and rectangles12 by 18 squares, count. Square head, rectangle body, arms 2 wide. Rivets sit on the crossings, buttons fill one square.
Skyline reflected in a lake24 by 16 squares, mirror. The mirror line lies flat. Every tower hangs below it at the same height, in broken dashes.
Snakes and ladders board numbered to 10020 by 20 squares, count. Cells are 2 by 2. Number from the bottom left, snaking back along each row. Add 5 of each.
Treasure island with a lettered map grid12 by 10 squares, count. Letter the columns A to L and number the rows. Hide the treasure and write its square, like G7.
Your name in block capitals five squares tall23 by 5 squares, count. Letters are 3 wide and 5 tall with a 1-square gap, so six fit. E is a spine plus three bars.
Mirror and turn 17
Butterfly mirrored across a centre line16 by 12 squares, mirror. Rule the line first. Draw the left wings corner to corner, then count each corner across.
Crossword grid with half-turn symmetry15 by 15 squares, turn. Shade black squares in pairs, the same distance from opposite corners, as American grids do.
Dragon curve from a folded paper strip12 by 8 squares, turn. Fold a strip in half 4 times the same way. Open each crease to a right angle. Copy its 16 steps.
Eight-point compass star16 by 16 squares, turn. Four long points run 8 squares along grid lines, four short ones 4 along diagonals.
Four-way mirrored tile12 by 12 squares, mirror. Fill one 6 by 6 quarter with shapes. Mirror it to the right, then mirror both halves downward.
Half a face from a photo, the other half drawn16 by 20 squares, mirror. Glue half a printed face against the centre line. Build the missing half cell by cell.
Half a monster for a friend to finish14 by 16 squares, mirror. Draw the left half up to the centre line. A friend mirrors it by counting squares. Then swap.
Nested squares, each half the last16 by 16 squares, turn. Join the middles of the sides into a tilted square, and again inside it. Each has half the area.
Pattern mirrored across a diagonal12 by 12 squares, mirror. Rule corner to corner. A point 5 across and 2 up reflects to 2 across, 5 up: the counts swap.
Pinwheel of four triangles8 by 8 squares, turn. Split a 4 by 4 quarter corner to corner and shade half. Quarter-turn the page and repeat, 4 times.
Snowflake with four mirror lines16 by 16 squares, mirror. Real flakes have six arms; squared paper gives four or eight. Draw one eighth and reflect it.
Spirolateral from 1 to 510 by 10 squares, turn. Lines of 1 to 5 squares, a right turn after each. Four rounds bring you home. 1 to 4 never does.
Spirolateral from the rule 1, 2, 38 by 8 squares, turn. Draw 2 squares, turn right, 4, turn right, 6, turn right. Repeat. It closes after 4 rounds.
Two faces that make a vase between them14 by 14 squares, mirror. Draw a face in profile on the left, nose 2 squares from centre. Mirror it. The gap is a vase.
WOW: a word that is its own reflection15 by 5 squares, mirror. W, O and W each have a mirror line and the word reads the same backwards. Try MUM and TOOT.
Your initial turned four times into a badge14 by 14 squares, turn. Letter in one quarter. In a quarter turn, a point 3 across and 1 up moves to 1 across, 3 down.
Your name mirrored into a strange creature23 by 12 squares, mirror. Block capitals stand on the line and hang upside down below it. Turn the page and add eyes.
Repeat and tessellate 14
All twelve pentominoes20 by 12 squares, count. Every shape made by joining 5 squares edge to edge. There are 12, and they fill a 6 by 10 box.
Arc tiles laid by coin flip16 by 16 squares, repeat. Each 2 by 2 tile gets two quarter circles joining the middles of adjacent sides. Flip a coin.
Basket weave of paired bricks16 by 16 squares, repeat. Two 4 by 2 bricks lying flat make a square. Stand the next pair up. Swap like a chessboard.
Brick wall in stretcher bond24 by 12 squares, repeat. Bricks are 4 by 2. Shift every other row along by 2 squares so no upright joints line up.
Carpet with holes inside holes9 by 9 squares, repeat. Shade the middle 3 by 3 block, then the centre cell of each of the 8 blocks round it.
Cat heads whose ears fit the chin above16 by 16 squares, repeat. A 4 by 4 head with two triangle ears on top. Cut the same two triangles out of the chin.
Gingham-style check in one pencil16 by 16 squares, repeat. Shade every other column lightly, then every other row. Crossing squares get shaded twice.
Greek key border along the page edge30 by 5 squares, repeat. One unbroken line winds into a squared spiral, out again and on to the next. It never crosses.
Herringbone floor of 3 by 1 blocks18 by 18 squares, repeat. Lay a block flat, stand the next at its end to make an L, and keep stepping. The Ls nest.
Plus signs that lock with no gaps15 by 15 squares, repeat. Each plus is 5 squares. Put the next one 2 across and 1 up, and the next. No gaps are left.
Tartan of your own design24 by 24 squares, repeat. Pick a stripe order, say 4, 1, 2, 1 squares. Use that order across and down, as weavers do.
Tessellating fish cut from a square18 by 12 squares, repeat. Each fish is 6 by 6. Notch the left side as a mouth. Add that shape to the right as a tail.
Wall of shifted dark and light tiles24 by 12 squares, repeat. Tiles 4 wide, 2 tall, each row shifted 1 square. Rule the row lines grey. Do they look level?
Woven ribbons going over and under20 by 20 squares, repeat. Ribbons 2 wide cross with 2-square gaps. Rub out the hidden edges, swapping over and under.
Cubes, stairs and 3D 13
Checkerboard floor running to a dot24 by 12 squares, 3D. Mark every 2 squares along the bottom and rule each to the dot. One diagonal finds the rows.
Cube from 2-across, 1-up lines12 by 12 squares, 3D. Uprights follow grid lines. Other edges slope 2 across for 1 up. Top light, left mid, right dark.
Cube from two squares and four slanted lines8 by 8 squares, 3D. Draw a 4 by 4 square and the same square 2 across and 2 up. Join matching corners. Dot hidden edges.
Impossible fork: three prongs into two bars20 by 8 squares, 3D. Six long parallel lines. Cap one end as three round prongs and the other as two square bars.
Net of a cube to cut out and fold12 by 9 squares, count. Six 3 by 3 squares: four in a row, one above and one below the second. A cube has 11 such nets.
Pyramid of cubes seen from one corner16 by 16 squares, 3D. Stack 3, 2, 1 with 2-across, 1-up slopes. Draw the front cube first so it hides those behind.
Road to the horizon with shrinking poles24 by 16 squares, 3D. Road edges meet at a dot. A line from the first pole top to the dot sets every other height.
Room in one-point perspective24 by 18 squares, 3D. Dot on the centre crossing, a back wall 8 by 6 round it. Rule from the dot through each corner.
See-through cube that flips as you stare8 by 8 squares, 3D. Draw all 12 edges as solid lines with nothing hidden. Stare: front and back faces swap places.
Square tunnel of shrinking frames16 by 16 squares, 3D. Nested squares 2 apart, both diagonals ruled through. Shade the floor and one wall darker.
Staircase climbing toward the corner16 by 14 squares, 3D. Steps go 2 along and 2 up. Slide every corner 2 across and 2 up for depth, then join the pairs.
Tiny room seen from one corner20 by 16 squares, 3D. Floor edges slope 2 across for 1 up, left and right. Add a bed, rug and plant on the same slopes.
Your initials as solid block letters16 by 10 squares, 3D. Letters 5 tall. Copy each corner 1 across and 1 up, join the pairs and shade the new faces.
Maths class 11
3, 4, 5 triangle with a square on each side10 by 11 squares, count. Squares of 9, 16 and 25 cells. Tilted one: go 3 along, 4 up from each end of the long side.
Cartoon face stretched to twice its width16 by 8 squares, scale. Draw a face on 8 by 8. Copy it cell by cell into cells 2 wide, 1 tall. Then try twice as tall.
Curve made of nothing but straight lines10 by 10 squares, count. Number both axes 1 to 10. Rule 1 to 10, 2 to 9, 3 to 8 and on. The lines wrap a parabola.
Doodle enlarged from 4 by 4 to 16 by 1616 by 16 squares, scale. Every small square becomes a 4 by 4 block. Copy a cell at a time. Note where lines cross edges.
Fibonacci squares with a spiral through them21 by 13 squares, count. Squares of side 1, 1, 2, 3, 5, 8 and 13 fill it exactly. Arc a quarter circle across each.
Monster with an area of exactly 30 squares12 by 12 squares, count. Whole squares count 1. A square cut corner to corner counts a half. Keep a running total.
Number spiral with the primes shaded11 by 11 squares, turn. Write 1 in the centre cell and spiral out to 121. Shade the primes, then look along diagonals.
Picture written as coordinates for a friend20 by 20 squares, count. Rule axes through the middle. Draw a shape corner to corner, then list each corner as (x, y).
Tangram square cut into seven pieces8 by 8 squares, count. Five triangles, a square and a parallelogram. On 8 by 8, every corner falls on a crossing.
Times-table square coloured by last digit10 by 10 squares, count. Write every answer up to 10 times 10. Colour cells by last digit. A diagonal mirror appears.
Your hand outline at half size16 by 20 squares, scale. Trace your hand on the squares. Every 2 by 2 block of the tracing becomes 1 square of the copy.
Copy and enlarge 7
Bicycle from a side-on photo24 by 16 squares, scale. Hard freehand, fair with a grid. Wheels span equal numbers of cells. The frame is 2 triangles.
Leaf traced on the squares, then made huge24 by 30 squares, scale. Trace a real leaf on the squares and it comes with a grid. Redraw it, 3 squares for every 1.
One eye from a magazine, four times bigger24 by 16 squares, scale. Rule 6 by 4 small cells over the eye. Each becomes a 4 by 4 block. Count to place the shine.
Outline of your country from an atlas20 by 24 squares, scale. Rule cells over a photocopied map. Coastlines cross each cell edge at a point you can measure.
Paperclip, five times life size30 by 10 squares, scale. Trace the clip on the squares. Each traced square becomes a 5 by 5 block. Keep the wire even.
Photo of a pet, copied cell by cell16 by 20 squares, scale. Rule 8 by 10 cells over a printed photo. Each is a 2 by 2 block on your sheet. Outlines first.
Upside-down copy of your own cartoon12 by 12 squares, scale. Turn the original and your sheet upside down. Cell by cell you copy shapes, not things.
How it works
Count, mirror, turn, repeat, 3D or scale: each of these 76 grid drawing ideas is built by one rule and sized in squares, so it fits any squared pad. Six groups sort them, from block-capital names and mazes to tessellating fish, see-through cubes and a pet photo enlarged cell by cell.
Read the full guide
Designs that use the lines
The best graph paper drawing ideas would fall apart on plain paper. The lines do the measuring, so a butterfly's second wing is counted, not guessed, and a brick wall stays level for 24 squares. Two slopes come free. One across and one up is 45 degrees. Two across and one up is the gentler slope that turns a flat square into the top of a cube.
Tessellations start with a square
A tessellation covers the page with one shape, with no gaps or overlaps. Only three regular shapes manage it alone: the equilateral triangle, the square and the hexagon. Your paper is already the square one. For tessellation art ideas of your own, cut a bite out of one side of a square and stick it on the opposite side. That is how the fish are made.
Count from the mirror line, not from the edge of the page.
Squares differ by country: 5 mm is usual in Europe, and US and Canadian pads often have 4 or 5 to the inch. Sizes here are in squares, so any pad works.
For graph drawing ideas that double as maths homework, try the Dice-roll skyline: a bar chart of your own rolls.
Questions and answers
What are easy things to draw on graph paper?
Press Count the squares. The easiest designs follow the lines and never leave them: your name in block capitals five squares tall, a skyline of rectangles, a castle wall with square battlements. For freehand subjects, see easy drawing ideas.
Are there coordinate plane drawing ideas with the points listed?
No. A point list has to be plotted and checked before it can be trusted, so this page prints none. The ideas here run the other way: draw a shape corner to corner, write each corner as an (x, y) pair and hand the list to a friend to plot.
What is the grid method of drawing?
It copies or enlarges a picture one cell at a time. Rule a grid over the original and a grid with the same number of cells on your sheet, bigger for an enlargement. Copy what is inside each cell, watching where lines cross the cell edges. The Copy and enlarge group has 12 to try.