Guide · Geometry
What Is a Superellipse (Squircle)? The Shape Between an Ellipse and a Rectangle
Look at an iOS app icon, a modern sofa tabletop, or Sergels torg — the famous roundabout in Stockholm — and you are looking at superellipses. A superellipse (often called a squircle) is the closed curve that sits smoothly between an ellipse and a rectangle: fuller than an ellipse, softer than a box.
This guide explains the formula in plain language, shows what the exponent n really controls, lists where squircles are actually used, and walks you through generating production-ready outlines with the free superellipse generator on this site.
The formula, in plain words
Here a is the half-width and b is the half-height of the shape — so the full drawing size is 2a × 2b. The exponent n decides the character of the curve:
| Exponent n | Shape | Typical use |
|---|---|---|
| n = 2 | Perfect ellipse | Wheels, rings, round windows |
| 2 < n < 3 | Soft “pillow” oval | Watch faces, posters, UI cards |
| n ≈ 3–4 | Classic squircle | App icons, tiles, tabletops |
| n = 5 | Nearly a rounded rectangle | Phone icons, panels, furniture |
| n → ∞ | Pure rectangle | Theoretical limit |
Unlike a rectangle with rounded corners — where the straight edge meets the arc with a visible kink — the superellipse’s curvature changes continuously. That is why designers say a squircle “has no corners you can point at”, and why the eye reads it as calmer and more expensive-looking.
Where superellipses show up in the real world
- App icons & UI: iOS and many Android launchers mask icons with a squircle mask rather than a plain rounded rectangle.
- Furniture & products: tabletops, trays, watch bezels and appliance panels often follow Lamé curves (the superellipse family) for a soft but spacious look.
- Urban planning: Sergels torg in Stockholm is a drivable superellipse; the shape gives more usable area than an ellipse while keeping traffic flow smooth.
- Laser cutting & CNC: plates, gaskets, boxes and inlays cut as squircles avoid the “dead zones” of sharp corners while keeping more material than an ellipse.
How to generate one (and export SVG / DXF)
- Open the superellipse generator. You will see a live preview on a gridded canvas.
- Set width a and height b in millimetres — these are the full dimensions of the shape (the tool draws 2a × 2b around the center). Sizes from 1 mm to 10 m are supported.
- Drag the exponent n slider between 2 and 5. n = 2 gives a pure ellipse; n = 5 is close to a rounded rectangle. Watch the preview update as you drag.
- Choose sample points (36–1440). More points mean a smoother exported curve — use 720+ for parts that will be cut or machined.
- Download SVG for design, print and the web — the file carries millimetre units and a proper viewBox, so it scales cleanly.
- Download DXF for CAD and CAM: a closed POLYLINE on layer SUPERELLIPSE that opens directly in AutoCAD, LibreCAD, LightBurn, LaserGRBL and most CNC software.
Production tips
- DXF coordinates are real millimetres, centered on the origin (0,0) — handy for fixtures and repeat jobs.
- The exported path is a centerline with zero thickness; set your laser/CAM kerf compensation on top of it.
- Match n to the physical process: for parts made on a rounded-corner jig, n = 5 approximates typical corner radii; for organic, pillow-like surfaces stay near n = 3.
- Scaling is safe: because the outline is a polyline, DXF consumers never need the formula — scale it in your CAM software freely.
Frequently asked questions
Is a squircle just a rounded rectangle?
No. A rounded rectangle stitches straight lines to circular arcs, so curvature jumps at the seams. A superellipse has continuously varying curvature — that is the whole aesthetic point.
Which n should I pick?
n = 2 is a true ellipse; n = 3–4 reads as a friendly “squircle”; n = 5 is close to a rounded rectangle. For icon-like shapes most designers settle between 4 and 5. The generator lets you slide across the whole 2–5 range live.
Are the exported files free to use commercially?
Yes. The geometry you generate is yours — use the SVG and DXF output in any project.
Why DXF instead of SVG for cutting?
Laser cutters, plasma tables and CNC mills speak DXF natively and expect real-world units (millimetres). SVG is ideal for screens and print; DXF is the exchange format for machines.
Can I make a non-square squircle?
Yes — set width and height independently (e.g. 1800 × 900 mm) and the curve adapts. That lamé-style oval-squircle is common for tables and trays.
Open the Superellipse Generator →
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