I characterize the efficiency of the Cournot equilibrium and provide bounds for the loss in consumer surplus, producer surplus and welfare when the number of firms in the market changes. I only assume that demand is decreasing in price and costs increasing in the quantity produced as long as equilibrium exists. I show how price, demand and average cost, before and after the number of firms in the market changes, can be used to compute these bounds. I apply these bounds to the Portuguese wireline market and conclude that welfare increased significantly when the monopolist was split in 2007.