All species are locked in a continual struggle to adapt to local ecological conditions. In cases where species fail to locally adapt, they face reduced population growth rates, or even local extinction. Traditional explanations for limited local adaptation focus on maladaptive gene flow or homogeneous environmental conditions. These classical explanations have, however, failed to explain variation in the magnitude of local adaptation observed across taxa. Here we show that variable levels of local adaptation are better explained by trait dimensionality. First, we develop and analyse mathematical models that predict levels of local adaptation will increase with the number of traits experiencing spatially variable selection. Next, we test this prediction by estimating the relationship between dimensionality and local adaptation using data from 35 published reciprocal transplant studies. This analysis reveals a strong correlation between dimensionality and degree of local adaptation, and thus provides empirical support for the predictions of our model.