In the physical chemistry study of polymers, the **end-to-end vector** is the vector that points from one end of a polymer to the other end.

If each monomer unit in a polymer is represented by a point in space, the translation vectors ${\vec {r}}_{i}$ connect between these points. The end-to-end vector ${\vec {R}}$ is the sum of these translation vectors:

- ${\vec {R}}=\sum _{i}{\vec {r}}_{i}$

The norm of the end-to-end vector is called the **end-to-end distance**.

The quadratic mean of the end-to-end distance $\left\langle r^{2}\right\rangle$ can be related to the quadratic mean of the radius of gyration $\left\langle s^{2}\right\rangle$ of a polymer by the relation:

- $\left\langle r^{2}\right\rangle =6\left\langle s^{2}\right\rangle$

- Freely Jointed Chain
- Worm-like chain

Text submitted to CC-BY-SA license. Source: End-to-end vector by Wikipedia (Historical)

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