State-of-the-art climate models simulate a large spread in the projected decline of Arctic sea-ice area (SIA) over the 21st century. Here we diagnose causes of this intermodel spread using a simple model that approximates future SIA based on present SIA and the sensitivity of SIA to Arctic temperatures. This model accounts for 70-95% of the intermodel variance, with the majority of the spread arising from present-day biases. The remaining spread arises from intermodel differences in Arctic warming, with some contribution from differences in the local sea-ice sensitivity. Using observations to constrain the projections moves the probability of an ice-free Arctic forward by 10-35 years when compared to unconstrained projections. Under a high-emissions scenario, an ice-free Arctic will likely (>66% probability) occur between 2036-2056 in September and 2050-2068 from July-October. Under a medium-emissions scenario, the ‘likely’ date occurs between 2040-2062 in September and much later in the 21st century from July-October.