Floor and Ceiling Functions

The floor function takes a floating point number and returns the first integer which is less than or equal to that number.

The ceiling function takes a floating point number and returns the first integer which is greater than equal to that number.

The notation for the floor and ceiling functions is shown below:

Whilst the floor and ceiling functions appear to be similar to rounding, they represent a strict set of rules, whilst rounding functions vary according to application.

Sample values for both functions are shown in the table below:

x	floor(x)	ceiling(x)
-1.5	-2.0	-1.0
-1.0	-1.0	-1.0
-0.5	-1.0	0.0
0.0	0.0	0.0
0.5	0.0	1.0
1.0	1.0	1.0
1.5	1.0	2.0

In graphic form:

Spreadsheets

The floor and ceiling functions in Excel and Google Docs work with multiples of a given number, e.g. floor(5.4,2) returns 4, whilst ceiling(5.4,2) returns 6.

Programming Languages

These functions are found in most programming languages, e.g. C++ (they were not present in VB6, but were introduced in vb.net).