How this calculator works
A Möbius strip is made from a long rectangle joined end to end with a half twist. The twist gives the surface only one side and one edge. This calculator models the common construction in which the rectangle is bent into a circular loop: the centreline runs once around a circle of the given radius, so its length is the circumference. Because the strip keeps its width, its area is that length times the width. The edge is a single closed curve that travels around the loop twice, which is why its length is twice the centreline length. The inner and outer radii are the centreline radius plus or minus half the width.
Formula
Length = 2πR; surface area = 2πRw; edge length = 4πR; inner radius = R - w/2; outer radius = R + w/2, where R is the radius to the centreline and w is the width.
Worked example
A strip of width 2 m bent around a centreline radius of 5 m has length 10π ≈ 31.4159 m, surface area 20π ≈ 62.8319 m², edge length 20π ≈ 62.8319 m, inner radius 4 m and outer radius 6 m.
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Frequently asked questions
What makes a Möbius strip different from a ring?
A ring made from a rectangle without a twist has two sides and two edges. The half twist joins the ends with a flip, leaving one continuous side and one continuous edge.
Why is the edge twice as long as the strip?
The single edge traces the top boundary on one pass and the bottom boundary on the next. It must go around the loop twice before closing on itself.
Does the calculator include thickness?
No. The strip is treated as an ideal surface with no thickness. A real paper or metal strip has a small edge area and slightly different radii on its two faces.
Why does the width have a limit?
If the width reaches the diameter, the inner radius shrinks to zero and the strip would fold through itself. The calculator requires a width below the diameter.