Refractive error, one of the leading cause of visual impairment, can be corrected by simple interventions like prescribing eyeglasses. We trained a deep learning algorithm to predict refractive error from the fundus photographs from participants in the UK Biobank cohort, which were 45 degree field of view images and the AREDS clinical trial, which contained 30 degree field of view images. Our model use the "attention" method to identify features that are correlated with refractive error. Mean absolute error (MAE) of the algorithm's prediction compared to the refractive error obtained in the AREDS and UK Biobank. The resulting algorithm had a MAE of 0.56 diopters (95% CI: 0.55-0.56) for estimating spherical equivalent on the UK Biobank dataset and 0.91 diopters (95% CI: 0.89-0.92) for the AREDS dataset. The baseline expected MAE (obtained by simply predicting the mean of this population) was 1.81 diopters (95% CI: 1.79-1.84) for UK Biobank and 1.63 (95% CI: 1.60-1.67) for AREDS. Attention maps suggested that the foveal region was one of the most important areas used by the algorithm to make this prediction, though other regions also contribute to the prediction. The ability to estimate refractive error with high accuracy from retinal fundus photos has not been previously known and demonstrates that deep learning can be applied to make novel predictions from medical images. Given that several groups have recently shown that it is feasible to obtain retinal fundus photos using mobile phones and inexpensive attachments, this work may be particularly relevant in regions of the world where autorefractors may not be readily available.