Both forms are correct by US writing standards. The main consideration when it comes to using “all right” versus “alright” is the purpose of your writing and how it might be received by your reader. 

Some posit that “alright” is an appropriate spelling for informal usage, like in a text message or brief email to a coworker or in fiction writing to characterize colloquial dialogue. Conversely, the use of “all right” is better suited for formal correspondences, such as in a professional report, official business letter, or academic paper.

There are currently two forms of this word because the English language is continuously changing, and historically, words often had many different forms before they became standardized. For example, “altogether” was once written as “all together,” “all-together,” and “alltogether.”

The two-...