The Wisconsin Alumni Research Foundation, the patent licensing arm of the University of Wisconsin-Madison, said the verdict was important to guard its inventions from unauthorized use.
The jury had earlier decided that Apple incorporated patented microchip technology into some iPhones and iPads without permission.
Apple said it would appeal and declined to comment further.
The jury set the amount – about $165 million less than the foundation had claimed – after about three hours of deliberations.
University of Wisconsin-Madison computer sciences professor Gurindar Sohi, one of the inventors of the microchip technology – designed to boost the performance of computer processors – was in the federal court in Madison, Wisconsin, for the decision.
“For Dr. Sohi, I hope you felt that your invention was vindicated,” District Judge William Conley said.
Carl Gulbrandsen, managing director of the Wisconsin Alumni Research Foundation, said: “This is a case where the hard work of our university researchers and the integrity of patenting and licensing discoveries has prevailed.
“The jury recognized the seminal computer processing work that took place on our campus.”
The patent infringement case relates to use of the technology in the iPhone 5s, 6 and 6 Plus – but an additional lawsuit making the same claim against Apple’s newest models, the 6S and 6S Plus, has also been filed.
In 2008, the University of Wisconsin sued Intel over the same patent. That case was settled out of court for an undisclosed sum.
Apple’s annual revenue in 2014 was $182 billion.
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