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Emission metrics, a crucial tool in setting effective equivalences between greenhouse gases, currently require a subjective, arbitrary choice of time horizon. Here, we propose a novel framework that uses a specific temperature goal to calculate the time horizon that aligns with scenarios achieving that 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 that align with the 1.5 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 with methane as our main example. We find that the Global Warming Potential values that align with the 1.5 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 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 emission metrics by 34-38% relative to the values we calculate that align with the 2 C goal and 63-87% relative to the 1.5 C goal. To best align emission metrics with the 1.5 C goal of the Paris Agreement, 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.