Floor Function Calculator

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Enter any real number: positive, negative, integer, or decimal. The calculator applies the floor function and related operations.
Choose "All functions" to see how floor compares with ceiling, rounding and truncation for the same input.
Floor - greatest integer <= xx is closer to the next integer up
3

The largest integer less than or equal to x. Written as floor(x) or the floor symbol.

Ceiling - smallest integer >= x4
Round (nearest integer)4
Truncate (toward zero)3
Fractional part0.7
Floor of -x-4
Floor3
Ceiling4
Round4
Truncate3

floor(3.7) = 3

  • floor(3.7) = 3 because 3 is the largest integer that is still less than or equal to 3.7.
  • The ceiling is 4: the smallest integer that is greater than or equal to 3.7.
  • The fractional part is 0.700000, which is x minus its floor: 3.7 - 3 = 0.700000.
  • Standard rounding gives 4, which differs from the floor because the fractional part is at or above 0.5.

Next stepFor any real x, the floor always satisfies: floor(x) <= x < floor(x) + 1.

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