Emission metrics, a crucial tool in setting effective exchange rates between greenhouse gases, currently require an arbitrary choice of time horizon. Here, we propose a novel framework to calculate the time horizon that aligns with scenarios achieving a specific temperature goal. We analyze the Intergovernmental Panel on Climate Change Special Report on Global Warming of 1.5 °C Scenario Database to find that time horizons aligning with the 1.5 °C and 2 °C global warming goals of the Paris Agreement are 24 [90% prediction interval: 7, 41] and 58 [90% PI: 41, 74] years, respectively. We then use these time horizons to quantify time-dependent emission metrics for methane. We find that the Global Warming Potential (GWP) values that align with the 1.5 °C and 2 °C goals are GWP1.5 °C = 75 [90% PI: 54, 107] and GWP2 °C = 42 [90% PI: 35, 54]. For the Global Temperature change Potential (GTP) they are GTP1.5 °C = 41 [90% PI: 16, 102] and GTP2 °C = 9 [90% PI: 7, 16]. The most commonly used time horizon, 100 years, underestimates methane's GWP and GTP by 34% and 38%, respectively, relative to the values we calculate that align with the 2 °C goal and by 63% and 87%, respectively, relative to the 1.5 °C goal. To best align emission metrics with the Paris Agreement 1.5 °C goal, we recommend a 24 year time horizon, using 2045 as the endpoint time, with its associated GWP1.5 °C = 75 and GTP1.5 °C = 41.