Collagen sequences frequently deviate from the most thermally stable (Gly-Pro-Hyp)(n) pattern, with many mutations causing osteogenesis imperfecta (or "brittle bone disease"). The effects of collagen mutations have been studied in short peptides. The analysis of this work is problematic, however, as triple-helices fray from their ends, making the coil/triple-helix equilibrium non-two-state. Here, I develop a statistical thermodynamic model to handle this equilibrium that is applicable to peptides that follow the (G-X-Y)(n) pattern, where Gly is present at every third position and where all three chains are identical. Parameters for substitutions at each position are included, as well as a penalty for initiating triple-helix formation. The model is applied to equilibrium experimental data at 37 degrees C to show that the extension of a triple-helix by a three residue unit stabilizes the triple-helix by 0.76 kcal/mol for Gly-Pro-Hyp and 0.33 kcal/mol for Gly-Pro-Pro. The replacement of Hyp by Arg, Asp, or Trp destabilizes the triple-helix by 1.5, 2.4, and 2.9 kcal/mol, respectively, where the substitution is present once in each chain. The model can thus be used to quantitatively interpret data on collagen peptides, giving free energies that can help rationalize mutations that affect collagen stability, and to design new collagen sequences.