Different greenhouse gas emissions are often reported as 'carbon dioxide (CO2) equivalent' quantities. But the typical way of deriving these by using simple per-emission weighting factors (most commonly, the 100-year global warming potential) does not reliably indicate the climate effects of short-lived gases such as methane, as they cannot represent their non-cumulative impacts. In this paper, we suggest a different approach, a "CO2-warming equivalent," which is not based on a like-for-like per emission weighting, but reports CO2 emissions that would result in a similar temperature response to a given emission scenario. We show how an alternative application of global warming potentials, GWP*, can provide a simple means of estimating CO2-warming equivalent emissions by reporting a change in short-lived gas emission rates as a large emission or removal of CO2, and sustained emissions of short-lived gases as equivalent to emitting a relatively small amount of CO2. This new approach could provide a useful new means of relating emissions from livestock to their contribution to global warming, as a significant amount of methane is emitted from animal manures and particularly enteric fermentation.