Metastatic cancer cells sense the complex and heterogeneous fibrous extracellular matrix (ECM) by formation of protrusions, and our knowledge of how cells physically recognize these fibers remains in its infancy. Here, using suspended ECM-mimicking isodiameter fibers ranging from 135 to 1,000 nm, we show that metastatic breast cancer cells sense fiber diameters differentially by coiling (wrapping-around) on them in a curvature-dependent manner, whereas non-tumorigenic cells exhibit diminished coiling. We report that coiling occurs at the tip of growing protrusions and the coil width and coiling rate increase in a curvature-dependent manner, but time to maximum coil width occurs biphasically. Interestingly, bundles of 135-nm diameter fibers recover coiling width and rate on 1,000-nm-diameter fibers. Coiling also coincides with curvature-dependent persistent and ballistic transport of endogenous granules inside the protrusions. Altogether, our results lay the groundwork to link biophysical sensing with biological signaling to quantitate pro- and anti-invasive fibrous environments. VIDEO ABSTRACT.