While in high school in Kumamoto, the young Torahiko studied under Natsume Sōseki and science teacher Takuro Tamaru. In 1903, he graduated from the Environmental Physics Department of Tokyo Imperial University with chief honors. Finally in 1908, Terada obtained his Doctor of Science Degree and was elected to the position of an associate professor at Tokyo Imperial University. From there, he went to study abroad at the University of Berlin. Later he studied at Seismological Research Institute and at Research Institute of Aviation to become a specialist in terrestrial physics. In 1911, Terada made the trek back home to Japan by way of Paris, the UK and the United States.
When he returned to Japan, he was assigned to oceanography studies by the Ministry of Agriculture and Commerce. His results were published in the book Umi no Butsurigaku, published in 1913. Around this same period, Terada became heavily involved in studies of x-ray diffraction. Inspired by the work of Max von Laue, Terada devised a technique for greatly accelerating the photography process used for data gathering in these studies. However, Terada failed to get his results sent to Nature (journal) in time due to the distance of Japan from the publisher's location. Consequently, the 1915 Nobel Prize in Physics was awarded to William Henry Bragg and William Lawrence Bragg, who had come to the same discoveries through their research. Terada turned away from X-ray diffraction studies and did not encourage his students to pursue the course. Despite this setback, Terada was still awarded the 7th Imperial Prize of the Japan Academy for his work in 1917.
In 1922, Terada attended the welcome party for Albert Einstein during the physicist's visit to Japan.
In 1923 the Great Kantō earthquake struck, prompting Terada to seriously begin investigations of the causes of the phenomenon. This led to the development of a new field of earthquake studies. In 1924, Terada was elected to the position of senior researcher at RIKEN Institute. In 1926, he founded the Earthquake Research Institute at the Tokyo Imperial University and served as one of the senior professors there. His research continued to develop and gain attention, and in 1928 he was elected as one of senior staff of Japan's Imperial Academy.
In 1935, Terada began suffering from a bone tumor. He died on December 31, at the age of 57.
In 1897, Terada met and courted student Natsuko Sakai, who was to become his first wife. In 1902, Natsuko Sakai died, prompting Terada to move on. In 1903, he courted Hiroko Hamaguchi, who was to become his second wife. In 1917, his second wife, Hiroko, died. After recovering, he courted Shin Sakai in 1918, who was to be his third and final spouse.