By Zencalcy Editorial TeamLast reviewed About us
The floor function ⌊x⌋: the largest integer ≤ x. Rounds down toward −∞ — so ⌊−3.2⌋ = −4. Whole numbers stay unchanged.
Round down to the nearest integer — negatives handled correctly.
floor(x) = largest integer n with n ≤ x
| Symbol | Meaning |
|---|---|
| x | Any real number |
⌊4.7⌋ = 4, ⌊−4.3⌋ = −5, ⌊7⌉ = 7.
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Same for positives; for negatives floor goes further down (⌊−4.3⌋ = −5) while truncation gives −4.
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Content updated: September 2026