Goethe comes from a motorsport family. His father, Roald Goethe, is a gentleman driver who competed in the FIA World Endurance Championship and owns a celebrated collection of Gulf Oil race cars operating under the ROFGO name. His younger brother Oliver Goethe has raced in Formula 2. Benjamin was educated at Millfield School in Somerset.
Goethe began karting in 2015, competing in regional and national events in France before entering selected international competitions in his final karting year of 2017. His single-seater debut came in 2018 with Drivex School in the F4 Spanish Championship, where he finished 13th in the standings with a season-best result of fifth at Jerez.
Goethe switched to GT racing in 2019 with GPX Racing in four rounds of the Blancpain GT Series Endurance Cup, partnering Jordan Grogor and his former karting and F4 coach Stuart Hall. The team finished 20th in the Silver Cup standings, but Goethe earned the SRO Merit Award for the season. He also took his first car racing podium that year, finishing third overall in the 24 Hours of Barcelona in the 24H GT Series.
For 2020 Goethe joined ROFGO Racing with Team WRT after becoming a member of the Bullet Sports Management roster. The campaign produced mixed results: an eighth in class at Imola, a retirement at the Hockenheimring, and an incident at the 24 Hours of Spa — where he became the youngest of 179 entrants — when he spun off in wet conditions late in the race. The season concluded more positively with a fourth in class at the finale, lifting the squad to twelfth in the Silver standings.
Goethe ran a double campaign in 2021, contesting both the GT World Challenge Europe Endurance Cup and the Sprint Cup with WRT. In the Endurance Cup, partnered by James Pull and Stuart Hall, the team took a podium at the opening round at Monza and eventually finished fifth in the Silver Cup standings. The Sprint Cup season was more difficult, yielding just one podium at Misano.
The 2022 season was Goethe's breakthrough year. He opened with a second place at the Dubai 24 Hour before returning to ROFGO Racing with Team WRT for both the Endurance and Sprint cups, driving the Audi R8 LMS Evo II alongside Thomas Neubauer and Jean-Baptiste Simmenauer in the endurance rounds.
In the Endurance Cup, Goethe took his first outright car racing victory at Imola — a Silver Cup class win that he described as "the perfect way to start." The team then took Silver Cup victory at the 24 Hours of Spa and clinched the title with a round to spare after finishing third in class at the Hockenheimring. The season concluded with a class win at Barcelona, leaving the team on 125 points — 49 clear of second place. Goethe and Neubauer were crowned GT World Challenge Europe Silver Cup champions.
In the Sprint Cup that year, Goethe and Neubauer finished third in the Silver standings after a run of podiums including an overall third place at Misano, where Goethe held off Audi factory driver Christopher Haase in the closing stages.
Goethe moved to Garage 59 in 2023, competing in the Pro class with a McLaren 720S GT3 Evo. He also partnered his brother Oliver, father Roald, and others to win the GT4 class at the Dubai 24 Hours. The main season campaigns in the Endurance and Sprint cups were lower-key. In 2024 he remained with Garage 59, finishing sixth in the Sprint Cup standings alongside Tom Gamble after ten top-ten finishes in the ten Sprint Cup races.
In 2025 Goethe returned to the Sprint Cup podium at championship level, finishing third overall in the standings with two wins and four podiums. He also contested the FIA GT World Cup and the Endurance Cup, where he claimed a pole position.
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