Floor and Ceiling Functions Calculator

Floor and Ceiling Functions with Step-by-Step Solutions

Calculate the floor \( \lfloor x \rfloor \) and ceiling \( \lceil x \rceil \) of any real number. Complete step-by-step explanation shown for every calculation.

What are Floor and Ceiling Functions?

Floor Function: \( \lfloor x \rfloor \) is the greatest integer less than or equal to \( x \).

Ceiling Function: \( \lceil x \rceil \) is the smallest integer greater than or equal to \( x \).

Examples:
\( \lfloor 2.1 \rfloor = 2 \)    \( \lceil 2.1 \rceil = 3 \)
\( \lfloor 3 \rfloor = 3 \)    \( \lceil 3 \rceil = 3 \)
\( \lfloor -0.5 \rfloor = -1 \)    \( \lceil -0.5 \rceil = 0 \)
\( \lfloor 0 \rfloor = 0 \)    \( \lceil 0 \rceil = 0 \)

Enter a real number \( x \):

Floor Function

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\( \lfloor x \rfloor \)

Ceiling Function

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\( \lceil x \rceil \)

Enter a number and click "Calculate"

Step-by-step solution will appear here after calculation.

Floor and Ceiling Functions Calculator

Floor and Ceiling Functions with Step-by-Step Solutions

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