Which shapes are included?

Rectangle or square, regular polygons from 3 to 12 sides, trapezoid or parallelogram, ellipse, and right triangle.

What units does Shape Lab use?

Abstract units. Treat them as metres, feet, inches, or centimetres as long as every input uses the same unit.

How is ellipse perimeter calculated?

There is no simple exact closed form for a general ellipse perimeter. Shape Lab uses Ramanujan's approximation, which is accurate enough for design and study work.

What do the area tiles mean?

Each tile represents a 1×1 unit square clipped to the shape. The animated count is a rounded whole-number view of area as you drag.

Is the Pythagorean overlay a formal proof?

It is a visual check: squares on legs a and b and on hypotenuse c update live so you can see a² + b² match c². It is meant for intuition, not a written exam proof.

Can I use this offline?

Once the page is loaded, the calculator runs in your browser without uploading measurements. A network connection is still needed to open the page the first time.

Shape Lab

Choose a shape, then drag the handles on the diagram. Dimension labels, stats, and unit area tiles stay locked to the morphing outline so formulas feel physical, not abstract.

Use it for rectangles and squares, regular polygons, trapezoids or parallelograms, ellipses with foci, and right triangles with an optional Pythagorean square proof. Everything runs in your browser.

Geometry & Math

Shape Lab

Pick a shape, drag the handles, and watch area tiles count up. Numbers stay in sync with the diagram, so you can feel the formulas instead of only reading them.

Area tiles

0unit tiles ≈ area 40

WidthHeightLock square

Area

Perimeter

Diagonal

9.43

Shape

Rectangle

Tip: drag handles to grow or shrink the shape. While it fits, the grid stays at a fixed scale; when the outline would leave the stage, the view zooms out so it stays on the tiled background. Area tiles are 1×1 units.

About Shape Lab

What this tool does

Shape Lab is a visual geometry calculator for rectangles, regular polygons, trapezoids or parallelograms, ellipses, and right triangles. You pick a shape, then drag handles on a live diagram while area, perimeter, and related metrics update instantly.

Unit area tiles fill the outline so area is something you can count, not only a formula result. For right triangles, optional Pythagorean squares grow on each side so a² + b² = c² is visible.

Static calculators and chat answers can print the same numbers. This tool is built for interaction: morph the outline, watch dimension callouts move, and compare overlays like polygon apothems or ellipse foci strings.

Everything runs in your browser. Use abstract units for homework and design sketches, or treat the numbers as metres, feet, or centimetres as long as you stay consistent.

How to use it

1Choose a shape from the picker (rectangle, polygon, trapezoid, ellipse, or right triangle).
2Drag the bright handles on the diagram, or type values in the number fields.
3Read the living dimension labels on the edges and the stats row under the stage.
4Toggle Area tiles to see roughly how many 1×1 unit squares fit inside the shape.
5For a right triangle, turn on Pythagorean squares to compare a², b², and c² on the diagram.
6For polygons, change the side count to watch the outline and interior angle update together.
7For ellipses, note eccentricity and the foci string overlay (PF₁ + PF₂ = 2a).

Practical tips

Lock Square when you need equal sides on the rectangle tool.
Switch Trapezoid mode to Parallelogram when the top and bottom bases should stay equal.
If tiles look sparse or dense, that is expected: tile size tracks one world unit at the current zoom.
Prefer reduced-motion settings in your OS if you want the tile count to jump without the count-up animation.

Frequently asked questions

Which shapes are included?: Rectangle or square, regular polygons from 3 to 12 sides, trapezoid or parallelogram, ellipse, and right triangle.
What units does Shape Lab use?: Abstract units. Treat them as metres, feet, inches, or centimetres as long as every input uses the same unit.
How is ellipse perimeter calculated?: There is no simple exact closed form for a general ellipse perimeter. Shape Lab uses Ramanujan's approximation, which is accurate enough for design and study work.
What do the area tiles mean?: Each tile represents a 1×1 unit square clipped to the shape. The animated count is a rounded whole-number view of area as you drag.
Is the Pythagorean overlay a formal proof?: It is a visual check: squares on legs a and b and on hypotenuse c update live so you can see a² + b² match c². It is meant for intuition, not a written exam proof.
Can I use this offline?: Once the page is loaded, the calculator runs in your browser without uploading measurements. A network connection is still needed to open the page the first time.

Shape Lab

Shape Lab

About Shape Lab

What this tool does

How to use it

Practical tips

Frequently asked questions

More reading

Shape Lab

Shape Lab

About Shape Lab

What this tool does

How to use it

Practical tips

Frequently asked questions

More reading