Goulding was born Launceston, Tasmania. He attended West Launceston Primary School and spent a lot of time around Australian rules football thanks to his father Steve. He started playing basketball in Launceston, and upon moving to Queensland with his family as an 8-year-old, he began to play it competitively. In Brisbane, he continued primary school at Gumdale State School and then attended secondary school at Brisbane State High School. He graduated from Brisbane State High in 2005. As a junior, he played for the Southern Districts Spartans.

Goulding began his professional career as a development player with the Brisbane Bullets during the 2006–07 NBL season. He made his NBL debut and lone appearance of the season on 23 December 2006 against the Townsville Crocodiles, recording one assist in 5½ minutes. The Bullets went on to win the NBL championship in March 2007, earning Goulding his first title. He appeared in 15 games for the Bullets during the 2007–08 NBL season, but following the club’s collapse, he moved west for the 2008–09 NBL season to play for the Perth Wildcats.

Between 2006 and 2009, Goulding played with the Southern Districts Spartans in the QBL (2006) and SEABL (2007–09). In 2006, he was a member of the Spartans’ championship-winning team. As a member of the Spartans for three seasons in the SEABL, Goulding won East Youth Player of the Year two consecutive seasons in 2008 and 2009 while also making the All-Star Five in his last year. In 2008, he averaged 24.5 points per game to finish second in the competition and had a season-high 43 points during the season. In 2009, averaged 20.8 points to finish fifth, second in free throw percentage (83%), ninth in three-point percentage (39%) and seventh in assists (three). Between 2010 and 2012, he played three seasons for the Northside Wizards in the QBL, earning All-League Team honours in 2010. In 2013, he had a three-game stint with the QBL’s Gladstone Port City Power.

Goulding is the son of Steve and Christine. He is married to wife Molly. His father played and coached at North Launceston Football Club, and was inducted into the AFL Tasmania Hall of Fame in 2008.

For the 2012–13 NBL season, Goulding joined the Melbourne Tigers. In December 2012, he was named MVP of the NBL All-Star Game for his 24 points.

After a stint with the Cleveland Cavaliers during the 2013 NBA Summer League, Goulding continued on with the Tigers for the 2013–14 NBL season. On 9 March 2014, he scored a career-high 50 points in the Tigers’ 92–82 win over the Sydney Kings. It was the NBL’s first individual 50-point game in the 40-minute era. He was subsequently crowned the NBL scoring champion for the 2013–14 season with a league-best 23.0 points per game.

As a youth, Goulding represented Australia in under-18s, under-19s and under-20s, including playing at the 2007 FIBA Under-19 World Championship in Serbia. In 2014, he played for the Australian Boomers at the FIBA World Cup in Spain. He went on to play for the Boomers at the 2015 FIBA Oceania Championship and the 2016 Rio Olympics. In 2018, he won a gold medal with the Boomers at the Commonwealth Games, and in 2019, he competed at the FIBA World Cup in China.

In December 2019, Goulding played his 300th NBL game.

On 17 July 2020, Goulding re-signed with United on a three-year deal.