The service is part of a new "pro" version of the data search and analysis engine to be launched on Wednesday.
Chief executive Stephen Wolfram said it was his firm's "biggest single step" since launching the computational tool two-and-a-half years ago.
Users need to pay for advanced features. The firm said it hoped this would become its main source of money.
At present, users of Wolfram Alpha's free "knowledge engine" are able to ask it plain language questions or input mathematical equations. The site then computes answers, making reference to the firm's restricted store of verified information where appropriate.
Under the pro version, users can upload their own data sets or other information which can then be cross-referenced against the company's own records.
'Program on the fly'
Mr Wolfram gave an example of providing the site with murder statistics for different countries in the world. The advanced service was then able to compute murder rates based on its own knowledge of the various states' population sizes, and offered maps and other readouts showing comparisons.
"What's happening is you are giving freeform input, and Wolfram Alpha is creating a program on the fly to create the interactivity that you use," he said.
Results can then be exported as customisable graphs, 3D interactive objects and other formats for use elsewhere.
Mr Wolfram also showed off the site's ability to cope with pictures uploading a picture of an ostrich. After a short pause the site provided information about dominant colours in the photo and other characteristics. Limited editing functions were possible including user-defined blurs and edge tracing.
The site can also provide linguistic analysis. Mr Wolfram demonstrated its ability to provide information about sentence lengths and the most common words used in an uploaded text of Alice in Wonderland.
Wolfram Alpha pro screenshot The site can accept scanned text - and then analyse its contents
Other types of analysable data include sounds, 3D object designs and molecules. In total about 60 different formats are compatible with the site.
Subscription fees
For the time being, size limits will apply - any file requiring minutes, rather than seconds, worth of analysis will be rejected. However, Mr Wolfram said that might change in the future.
He also said there were ambitions to add features such as the ability to count identical objects in a photo, such as buttons - and even report what it showed.
"We hope to offer more elaborate image recognition - but it's a tough problem," Mr Wolfram said.
The British-born inventor said his firm was already profitable thanks to Wolfram Alpha app sales, deals to provide the service to third parties and licences for its Mathematica software that powers its website.
However, he said he hoped plans to charge users for subscriptions to the new service would alter its business plan.
The standard fee will be $4.99 (£3.15) a month and $2.99 for students.
"We would like it to be the dominant revenue stream as our personal model is to provide services straight to users," he said.
Apple's iPhone 4S will continue to access the basic version of the service - but mobile apps will be made available to help smartphone and tablet users access the advanced engine for a charge.
The announcement was welcomed by one UK-based university lecturer.
"What's already on the market are relatively expensive stand-alone software products that can cost several thousand pounds for a licence - even to an academic," said Professor Alan Woodward, from the department of computing at the University of Surrey.
"Not all professors or students do data analysis on a regular basis - but would like access ad hoc.
"This kind of software-as-a-service will be useful to people in social sciences, engineering, management studies and a wide range of other disciplines."
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