Carbon accounting is important for quantifying the sources of greenhouse gas (GHG) emissions that are driving climate change, and is increasingly being used to guide policy, investment, business, and regulatory decisions. The current practice for accounting emissions from consumed electricity, guided by standards like the GHG Protocol, uses annual-average grid emission factors, although previous studies have shown that grid carbon intensity varies across seasons and hours of the day. Previous case studies have shown that annual-average carbon accounting can bias emission inventories, but none have shown that this bias is substantial or widespread. This study addresses this gap by calculating emission inventories for thousands of residential, commercial, industrial, and agricultural facilities across the U.S., and explores the magnitude and direction of this bias compared to hourly accounting of emissions. Our results show that annual-average accounting can over- or under-estimate carbon inventories as much as 35% in certain settings but result in effectively no bias in others. Bias will be greater in regions with high variation in carbon intensity, and for end-users with high variation in their electricity consumption across hours and seasons. As variation in carbon intensity continues to grow with growing shares of variable and intermittent renewable generation, these biases will only continue to worsen in the future. In most cases, using monthly-average emission factors does not substantially reduce bias compared to annual averages. Thus, the authors recommend that hourly accounting be adopted as the best practice for emissions inventories of consumed electricity.