  Since present Monte Carlo algorithms for lattice QCD may become trapped in a
fixed topological charge sector, it is important to understand the effect of
calculating at fixed topology. In this work, we show that although the
restriction to a fixed topological sector becomes irrelevant in the infinite
volume limit, it gives rise to characteristic finite size effects due to
contributions from all $\theta$-vacua. We calculate these effects and show how
to extract physical results from numerical data obtained at fixed topology.
