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We study Kauffman's model of folded ribbon knots: knots made of a thin stripof paper folded flat in the plane. The ribbonlength is the length to widthratio of such a folded ribbon knot. We show for any knot or link type thatthere exist constants $c_1, c_2>0$ such that the ribbonlength is bounded aboveby $c_1\cdot Cr(K)^2$, and also by $c_2\cdot Cr(K)^{3/2}$. We use a differentmethod for each bound. The constant $c_1$ is quite small in comparison to$c_2$, and the first bound is lower than the second for knots and links with$Cr(K)\leq$ 12,748.

Ribbonlength and crossing number for folded ribbon knots