Random Shape Generator

Press Generate Shape and you get one geometric shape picked at random from a list of 61: 32 flat 2D figures and 29 solids. The card shows a drawing of the shape, its name, whether it is 2D or 3D, and the formula for its area (or surface area, for solids). It's built for quick drawing warm-ups, geometry practice and classroom quizzes rather than for producing vector graphics.

What the random shape generator does

There are no settings. Each press shuffles the full list and shows one shape, so you can land on a circle one moment and a Klein bottle the next. The same shape can come up twice in a row occasionally, which is normal for a true random pick from a short list. Press again as many times as you like.

Every result card carries the same four things:

• a line drawing of the shape, served from our own image set;
• the shape name, for example "Hexagonal prism";
• the dimension label, 2D or 3D;
• the area formula for flat shapes, or the surface-area formula for solids, using the usual letters (r for radius, s for side, h for height, l for slant height, B for base area, P for base perimeter).

Which shapes are in the list

The 2D set covers the basics you'd expect in a school geometry unit plus a few extras: circle, square, rectangle, triangle (general, right and scalene), rhombus, kite, parallelogram, trapezoid and trapezium, ellipse and oval, and the regular polygons from pentagon through hexagon, heptagon, octagon, nonagon, decagon and dodecagon. Parts of circles are in there too: semicircle, sector, segment, annulus and ring. And there are a handful of everyday outline shapes, such as star, heart, arrow, cross and crescent, which have no standard area formula and so show none.

The 3D set starts with cube, cuboid, rectangular prism, cylinder, sphere, hemisphere and cone, then adds the pyramids (triangular, square, pentagonal, hexagonal), the prisms (triangular, pentagonal, hexagonal), the Platonic solids (tetrahedron, octahedron, dodecahedron, icosahedron), and several curved surfaces: torus, ellipsoid, paraboloid, hyperboloid, spherical cap, spherical sector and frustum. Two non-orientable surfaces, the Mobius strip and the Klein bottle, round out the list. If you only ever need flat shapes, roughly half your presses will be 2D, since the split is 32 to 29.

Ways people use it

• Geometry drills. A teacher presses the button, students name the shape and write its area formula before the card is revealed. The formulas on the card use standard notation, so answers are easy to check.
• Sketchbook warm-ups. Draw whatever comes up in 60 seconds, then press again. A random 3D shape generator is handy for practising perspective on solids like the frustum or hexagonal prism that you would rarely choose on your own. For a broader subject list, try Random Things to Draw or the Random Art Prompt Generator.
• Logo and pattern starting points. Designers use a random 2D shape as a constraint: build a mark from a crescent, a kite or a dodecagon and see where it leads. Pair it with the Random Color Palette Generator for a full set of constraints.
• Vocabulary practice. Learners of English pick up shape names that don't come up often in conversation (annulus, rhombus, torus), with a picture next to each word.
• Craft and classroom decorations. Random shapes for paper cutting, felt boards or tangram-style puzzles.

Reading the formulas on the cards

Flat shapes show an area formula: A = πr² for a circle, A = (1/2)bh for a triangle, A = (1/2)(a+b)h for a trapezoid. Regular polygons use the side length s; the hexagon's A = (3√3/2)s² is the one most people remember, and the heptagon, nonagon, decagon and dodecagon use the general form (n/4)s²cot(π/n).

Solids show surface area, labelled A(Surface Area) on the card. A cube is 6s², a sphere is 4πr², a closed cylinder is 2πrh + 2πr². Prisms use 2B + Ph (two base areas plus base perimeter times height), and pyramids use B + (1/2)Pl (base area plus half the base perimeter times the slant height). The ellipsoid card shows the Knud Thomsen approximation, which is why it carries an ≈ sign rather than an equals sign; there is no exact closed-form surface area for a general ellipsoid. Volume formulas are not included.

The tool draws shapes, not colors or textures. If you want a hue to go with your shape, the Random Color Generator gives you one with its hex code, and the Random Aesthetic Generator suggests an overall style. You can browse all fun, party and decision tools for more randomizers of this kind.