The government spends billions of dollars a year sending students to college to make a better life for themselves, but it does little to shepherd students toward what is arguably even more important: picking a degree that will ensure a large return on their expensive college investment.

Over the course of a career, college graduates earn $1 million more than high school graduates on average. But the highest-paying majors earn $3.4 million than the lowest-paying ones, according to a new report from Georgetown University's Center on Education and the Workforce.

In summary, a college degree helps students earn more, but it's even more helpful when students pick the right major. Once a degree is completed, graduates still need to work hard to command a high salary, and a graduate degree might not be all that helpful.

For example, a Petroleum Engineering major who earns the median salary in that major for 40 years will make $5.4 million over the course of his or her career. Art History majors will earn $2 million over a 40-year career at median salary.

The study also found that the salary benefits of a graduate degree depend on the field of study. For example, a graduate degree in health and medical preparatory programs raises the median salary from $54,000 to $128,000 a year. In contrast, a graduate degree in architectural engineering raises the median salary by only $1,000 a year.

Some bachelor's degrees pay even more than some graduate degrees. Median wage with a Computer Science bachelor's is $83,000. A graduate degree in Social Work garners only $71,000 a year for those in the 75th percentile of earners.

Over the course of a career, a worker's wage will generally rise, and the difference in salaries between majors will grow even larger.

While it is often said that the decision whether to go to college is the most important predictor of future earnings, the report shows it really depends which major a student chooses. "Not all Bachelor's degrees are created equal," the authors wrote. A bachelor's degree in Studio Arts, where the 25th percentile earns $29,000 a year, might not be the path to high earnings a student had in mind.

Still, even with a typically high-paying bachelor's degree, graduates have to work hard to earn a lot. The 25th percentile in engineering degrees earns a $54,000 salary, while the 75th percentile in education degrees earns $60,000 a year.

Even then, plenty of other factors come into play. "College graduates' wages are also influenced by whether they work in the for-profit, nonprofit, or public sector; which industry they work in; and whether they pursue lifelong learning opportunities and employer training that further hone their career-related skills," the authors wrote. "Usually working in an occupation aligned with a college field of study enhances earnings and working outside of one's field of study reduces earnings–but not always."

The study was co-authored by Anthony Carnevale, Ban Cheah, and Andrew Hanson, all with Georgetown.