When will China overtake the US to become the largest economy?
Lately we hear news about Chine more often, there is a good reason for that. China is becoming world leader, and the popular one. The main reason is China doesn't involve in armed conflicts and doesn't interfere in other country's policies. Military budget of China is 215.7 billion and it's 1.9% of it's GDP which is considerably smaller than USA (611.2 bn. which makes 3.3% US GDP).
Now about question, when Chinese Economy overtake USA? It depends what economic indicator you take to compare them. For example if you take GDP (Purchasing power parity) China is already bigger than USA. Latest IMF report shows Chinese GPD(PPP) is 23.122 billion which nearly 4 bn. larger than United States GDP (19.362 bn.).
Some economist argue we should compare countries by nominal GDP instead to see how much goods and services they can purchase globally not just domestic. Here Chine (11.2 bn.) is behind USA (18.6 bn.). So correct question might be: When will China overtake the US by nominal GDP. There is few projections, the most pessimistic scenario is that China will catch up USA in 2027. (If USA grows 2% and China 7%).
There is another indicator called contribution to Global Economy, for example in 2015 China had 15.6%, USA had 16.7% of global contribution. There is projection that China will overtake USA by 2018.
Why China has been growing so fast? I would say there is 3 main reasons: 1. High School Education - Chinese students perform much better than other advanced economies is universal tests like PISA test. 2. Hardworking culture - it's not secret than east asian people work more and more efficiently. 3. Infrastructure - just one example, China has the longest High Speed Railway lines in the world. China has 22000 km of high speed railway, where second largest lines are in Spain 3100km which is several times shorter. To compare USA has just 44km of lines.