Mosaic chromosomal alterations (mCAs) are common in cancers and can arise decades before diagnosis. A quantitative understanding of the rate at which these events occur, and their functional consequences, could improve cancer risk prediction and our understanding of somatic evolution. Using mCA clone size estimates from the blood of approximately 500,000 UK Biobank participants, we estimate mutation rates and fitness consequences of acquired gain, loss and copy-neutral loss of heterozygosity events. Most mCAs have moderate to high fitness effects but occur at a low rate, being more than tenfold less common than equivalently fit single-nucleotide variants. Notable exceptions are mosaic loss of X and Y, which we estimate have roughly 1,000-fold higher mutation rates than autosomal mCAs. Although the way in which most mCAs increase in prevalence with age is consistent with constant growth rates, some mCAs exhibit different behavior, suggesting that their fitness may depend on inherited variants, extrinsic factors or distributions of fitness effects.