## TL;DR

The results from cognitive research are largely statistical. You will not find a single canonical source for your question that can be expressed as a fixed percentage and that will be accurate across all domains.

There are, however, some generally-accepted rules of thumb for task switching, interrupted flow, and operational overhead. Each of these items is lightly touched on in the sections below in order to provide you with a starting point for your own research.

## Task Switching

Interruptions are a form of task switching. The American Psychological Association [says][1]:

> [S]hifting between tasks can cost as much as 40 percent of someone's productive time.

In other words, the more task-switching someone needs to do, the less they will get done. It's a direct hit to productivity, although the precise amount of the reduction may vary by person or situation.

## Cost of Interrupted Flow

Keep in mind that interruption overhead isn't just the amount of time someone is being actively interrupted. It also includes the amount of time necessary to resume [flow][2], and to recoup any cognitive framework and working memory they were using for the task.

This [related question][3] on Programmers Stack Exchange quotes from *Peopleware: Productive Projects and Teams* which posits a **minimum of 15 minutes** (in addition to the actual time spent on the interruption) to resume flow, but it's important to note that this is stated as a minimum, rather than as an average or a maximum. In practice, that means an interruption at a critical moment could potentially result in the entire rest of the day being wasted due to interruptions in flow, but your personal mileage will certainly vary greatly in this regard.

## Organizational and Framework Overhead

In addition to task switching, you'll want to take organizational and process overhead into account. Please see [this related answer][4] for a more complete discussion of overhead other than that which is strictly related to interruptions and task-switching.


  [1]: http://www.apa.org/research/action/multitask.aspx
  [2]: http://en.wikipedia.org/wiki/Flow_%28psychology%29
  [3]: https://softwareengineering.stackexchange.com/a/105895/57614
  [4]: http://pm.stackexchange.com/a/10650/4271