Difference between PowerPivot, PowerQuery and PowerBI

Power Query

Power Query is a self-service ETL (Extract, Transform, Load) tool which runs as an Excel add-in. It allows users to pull data from various sources, manipulate said data into a form that suits their needs, and load it into Excel.

Power Pivot

Power Pivot is an in-memory data modelling component that enables highly-compressed data storage and extremely fast aggregation and calculation. It is also available as part of Excel, and can be used to create a data model within an Excel workbook. Power Pivot can load data itself, or can have data loaded into it by Power Query. It is extremely similar to the SSAS (SQL Server Analysis Services) Tabular model, which is like a server-based version of Power Pivot.

Power View

Power View is an interactive visualisation tool which provides users with a drag-and-drop interface allowing them to build quick and easy visualisations of the data in their Excel workbooks (using the Power Pivot data model).

Power BI

Power BI is a SaaS service which enables business users to service their own business intelligence needs. It provides built-in ability to connect to SaaS services like Salesforce and many others. It provides connectivity to on-premises and cloud sources using a combination of direct query and periodic data refreshes. It is available as a freemium service. It is the successor to 'Power BI for Office 365' that was based on Microsoft's Office 365 and SharePoint Online products, and, through Excel 2013, encompasses Power Query, Power Pivot, and Power View.

Power BI (with O365 and SharePoint Online) provides a site where users can upload and share their created content with other users, as well as manage gateways into enterprise data source, enable data refresh, and advanced features like Q&A, which allows natural language querying of data models.

Microsoft has also released a standalone Power BI Desktop application, which ties together Power Query, Power Pivot, and Power View in a standalone application, removing the Excel 2013 constraint. Power BI Desktop is available for free.

It is also possible to achieve a lot of the functionality of Power BI using on-premise SQL Server 2012+, Excel 2010+ and SharePoint 2010+, if cloud-based is not an option for you.

Simple answer:

PowerBI=PowerQuery+PowerPivot+PowerView

Alternate answer:

If 

[PowerQuery]="Clean Data/M language" and [PowerPivot]="Calculations/DAX language" and [PowerView]="Data visualization"

then 

[PowerBI]=concatenate ("PowerQuery","-","PowerPivot","-","PowerView")

else "Excel"

Hope this answers the question :)

Power View is an interactive data exploration, visualization, and presentation experience that encourages intuitive ad-hoc reporting. Power View is a feature of Microsoft Excel 2013, and of Microsoft SharePoint Server 2010 and 2013 as part of the SQL Server 2012 Service Pack 1 Reporting Services Add-in for Microsoft SharePoint Server Enterprise Edition.

Power Map for Excel is a three-dimensional (3-D) data visualization tool that lets you look at information in new ways. A power map lets you discover insights you might not see in traditional two-dimensional (2-D) tables and charts.