Floor Function Calculator

Floor Function Calculator

Compute the greatest integer less than or equal to x, with comparisons to ceiling, rounding, and truncation.

Last updated: June 2026 | By Patchworkr Team

Floor Function
The floor function rounds down to the greatest integer less than or equal to x. Negative inputs round toward negative infinity.
Result
Floor
3
Ceiling
4
Round
4
Trunc
3
Fractional
0.7000
floor(3.7) = 3

What floor means

Floor returns the greatest integer that does not exceed the input. It is different from truncation when the input is negative.

Fractional part

The fractional part is x - floor(x), and it is always between 0 and 1 for real x.

Formula and example

floor(x) = greatest integer less than or equal to x

Example: floor(3.7) = 3 and floor(-2.3) = -3.

Worked Example

Evaluate floor(-2.3).

1. The exact value is -2.3.

2. The greatest integer less than or equal to -2.3 is -3.

3. This is different from truncation, which would give -2.

Final answer: -3

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