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floor() 

floor(x)
Returns numeric· Updated May 12, 2026· Base Functions
numericroundingmathbase

floor() rounds numeric values down to the nearest integer, toward negative infinity. It’s part of R’s base package and essential for numerical computations requiring integer discretization.

Syntax

floor(x)

Parameters

ParameterTypeDefaultDescription
xnumeric—A numeric vector to round down

Technical Details

The floor function follows the mathematical definition: for any real number x, floor(x) is the greatest integer less than or equal to x.

Key behaviors:

  • Positive numbers: floor(3.7) returns 3 (moves left on number line)
  • Negative numbers: floor(-2.3) returns -3 (moves left on number line, away from zero)
  • Integers unchanged: floor(5) returns 5 (already an integer)

Examples

Basic Usage with Vectors

# Positive numbers
floor(3.7)
[1] 3
# Vector input
floor(c(1.1, 2.5, 3.9, 4.0))
[1] 1 2 3 4

Handling Negative Numbers

# Negative numbers round toward negative infinity
floor(-1.5)
[1] -2
# More examples
floor(-0.1)
floor(-3.7)
floor(-10.0)
[1] -1
[1] -4
[1] -10

The key insight: floor(-1.5) returns -2 because -2 is the largest integer less than or equal to -1.5.

Statistical Binning

# Create continuous data
heights <- c(162.3, 175.8, 183.2, 155.9, 168.7, 172.4, 180.1)

# Bin into 10-unit intervals
floor(heights / 10) * 10
[1] 160 170 180 150 160 170 180
# Create discrete age groups from continuous age data
ages <- c(23.5, 34.2, 45.8, 19.9, 67.1, 52.3)
age_groups <- floor(ages / 10) * 10
age_groups
[1] 20 30 40 10 60 50

This pattern is commonly used for creating histogram bins or demographic categories.

Integer Division Pattern

# Integer division: 7 divided by 3
7 %/% 3
[1] 2
# This is equivalent to:
floor(7 / 3)
[1] 2
# Works with vectors too
a <- c(17, 23, 31, 45)
b <- c(5, 4, 6, 7)

# Integer division using floor()
floor(a / b)
[1] 3 5 5 6

This pattern is useful when you need quotient-only division in calculations.

Common Patterns

Ceiling comparison:

# floor vs ceiling
x <- 2.7
c(floor = floor(x), ceiling = ceiling(x), round = round(x))
 floor ceiling round 
     2       3     3

Data preprocessing:

# Normalize to [0, 1] range then discretize
values <- c(0.12, 0.55, 0.89, 0.34, 0.67)
floor(values * 5)  # 5-level discretization
[1] 0 2 4 1 3

See Also