RRKidz already offers Reading Rainbow in app form. After the show ended, Mr. Burton, who had been the host, and his business partner Mark Wolfe formed a company that bought rights to Reading Rainbow and its library of hundreds of books. (The Buffalo public television station WNED-TV, the series’ original co-producer, receives royalties from the venture.)

The app, introduced in June 2012, offers video field trips hosted by Mr. Burton and charges subscription fees for access to the library. Mr. Burton said children were now reading 139,000 books on average each week through the app, which he said is “on the cusp” of profitability.

More homes and schools have access to the web than tablets, Mr. Burton said. In addition to financing the web-based version, the crowdfunding money would subsidize its use in an as-yet-undetermined number of classrooms that have financial need.

RRKidz also wants to develop curriculum materials for teachers to use with the site, and a tool for them to track the reading progress of an entire classroom. The consumer-focused app, already used by some teachers, tracks just five readers on each account.

“Teachers love Reading Rainbow,” Mr. Burton said, adding that some told him as much at a recent “Star Trek” convention. “We really want to put a version of the app in their hands that works for them,” he said. The web version is expected to be available in homes by the end of the year and in schools in mid-2015, he said.