Is there a way to go on the subway from Beijing Capital Airport to Tiannamen Square?

Yes, you can take the airport express to get to Dongzhimen first. The ticket fare is CNY 25 per person. And the duration is around half an hour. Then take subway line 2 to Jianguomen Station and line 1 to Tiananmen East Station, Exit A. It takes around 15 mins with the ticket fare of CNY 4 per person. After arriving, walk west along West Chang'an Street around 530 yards to find the destination.