Abstract Background Persistent symptoms are common after SARS-CoV-2 infection but correlation with objective measures is unclear. Methods We invited all 3098 adults who tested SARS-CoV-2 positive in Iceland before October 2020 to the deCODE Health Study. We compared multiple symptoms and physical measures between 1706 Icelanders with confirmed prior infection (cases) who participated, and 619 contemporary and 13,779 historical controls. Cases participated in the study 5–18 months after infection. Results Here we report that 41 of 88 symptoms are associated with prior infection, most significantly disturbed smell and taste, memory disturbance, and dyspnea. Measured objectively, cases had poorer smell and taste results, less grip strength, and poorer memory recall. Differences in grip strength and memory recall were small. No other objective measure associated with prior infection including heart rate, blood pressure, postural orthostatic tachycardia, oxygen saturation, exercise tolerance, hearing, and traditional inflammatory, cardiac, liver, and kidney blood biomarkers. There was no evidence of more anxiety or depression among cases. We estimate the prevalence of long Covid to be 7% at a median of 8 months after infection. Conclusions We confirm that diverse symptoms are common months after SARS-CoV-2 infection but find few differences between cases and controls in objective parameters measured. These discrepancies between symptoms and physical measures suggest a more complicated contribution to symptoms related to prior infection than is captured with conventional tests. Traditional clinical assessment is not expected to be particularly informative in relating symptoms to a past SARS-CoV-2 infection.