Climate models are expensive to run and often underestimate how sensitive Arctic sea ice is to climate change. To address this, we developed a simple model that emulates the response of sea ice to global warming. We find that the remaining carbon dioxide (CO₂) emissions that will avoid a seasonally ice-free Arctic Ocean are lower than previous estimates of 821 Gt of CO₂. Our model also provides insights into the future of winter sea ice, examining a larger ensemble than previously possible.