We analyse the impact of Covid-19 on productivity using data from an innovative monthly firm survey that asks for quantitative impacts of Covid-19 on inputs and outputs. We find total factor productivity (TFP) fell by up to 6% during 2020-21. The overall impact combined large reductions in ‘within-firm’ productivity, with offsetting positive ‘between-firm’ effects as less productive sectors, and less productive firms within them, contracted. Despite these large pandemic effects, firms' post-Covid forecasts imply surprisingly little lasting impact on aggregate TFP. We also see significant heterogeneity over firms and sectors, with the greatest impacts in those requiring extensive in-person activity.