The anionic polysaccharides heparin and heparan sulphate play essential roles in the regulation of many physiological processes. Heparin is often used as an analogue for heparan sulphate. Despite knowledge of an NMR solution structure and 19 crystal structures of heparin-protein complexes for short heparin fragments, no structures for larger heparin fragments have been reported up to now. Here, we show that solution structures for six purified heparin fragments dp6-dp36 (where dp stands for degree of polymerisation) can be determined by a combination of analytical ultracentrifugation, synchrotron X-ray scattering, and constrained modelling. Analytical ultracentrifugation velocity data for dp6-dp36 showed sedimentation coefficients that increased linearly from 1.09 S to 1.84 S with size. X-ray scattering of dp6-dp36 gave radii of gyration R(G) that ranged from 1.33 nm to 3.12 nm and maximum lengths that ranged from 3.0 nm to 12.3 nm. The higher resolution of X-ray scattering revealed an increased bending of heparin with increased size. Constrained molecular modelling of 5000 randomised heparin conformers resulted in 9-15 best-fit structures for each of dp18, dp24, dp30, and dp36 that indicated flexibility and the presence of short linear segments in mildly bent structures. Comparisons of these solution structures with crystal structures of heparin-protein complexes revealed similar ranges of phi (phi) and psi (psi) angles between iduronate and glucosamine rings. We conclude that heparin in solution has a semi-rigid and extended conformation that is preformed for its optimal binding to protein targets without major conformational changes.