Methane emissions contribute to global warming, damage public health and reduce the yield of agricultural and forest ecosystems. Quantifying these damages to the planetary commons by calculating the social cost of methane (SCM) facilitates more comprehensive cost-benefit analyses of methane emissions control measures and is the first step to potentially incorporating them into the marketplace. Use of a broad measure of social welfare is also an attractive alternative or supplement to emission metrics focused on a temperature target in a given year as it incentivizes action to provide benefits over a broader range of impacts and timescales. Calculating the SCM using consistent temporal treatment of physical and economic processes and incorporating climate- and air quality-related impacts, we find large SCM values, e.g. ~$2400 per ton and ~$3600 per ton with 5% and 3% discount rates respectively. These values are ~100 and 50 times greater than corresponding social costs for carbon dioxide. Our results suggest that ~110 of 140 Mt of identified methane abatement via scaling up existing technolgy and policy options provide societal benefits that outwiegh implementation costs. Within the energy sector, renewables compare far better against use of natural gas in electricity generation when incorporating these social costs for methane. In the agricultural sector, changes in livestock management practices, promoting healty diets including reduced beef and dairy consumption, and reductions in food waste have been promoted as ways to mitigate emissions, and these are shown here to indeed have the potential to provide large societal benefits (~$50-150 billion yr-1). Examining recent trends in methane and carbon dioxide, we find that increases in methane emissions may have offset much of the societal benefits from a slowdown in the growth rate of carbon dioxide emissions. The results indicate that efforts to reduce methane emissions via policies spanning a wide range of technical, regulatory and behavioural options provide benefits at little or negative net cost. Recognition of the full SCM, which has typically been undervalued, may help catalyze actions to reduce emissions and thereby provide a broad set of societal benefits.