The ceil function returns the smallest integer that is greater than or equal to a given number. It is commonly used to round numbers up to the nearest whole number.

In Mathematics

• The ceiling function maps a real number $ x $ to the least integer greater than or equal to $ x $, denoted $ \lceil x \rceil $.

• Example: $ \lceil 2.3 \rceil = 3 $, $ \lceil -2.3 \rceil = -2 $.

In Programming Languages

• JavaScript: Math.ceil(x) returns the smallest integer greater than or equal to x.
  Example: Math.ceil(7.004) → 8, Math.ceil(-7.004) → -7.

• C/C++: ceil() (from <cmath> or <math.h>) returns the smallest integer not less than the argument.
  Example: ceil(2.3) → 3.0, ceil(-2.3) → -2.0.

• Python: math.ceil(x) returns the smallest integer not less than x.
  Example: math.ceil(2.3) → 3.

• PHP: ceil($num) rounds up to the next highest integer.
  Example: ceil(5.1) → 6.

• SQL (Oracle, PostgreSQL, etc.): CEIL(n) or CEILING(n) returns the smallest integer ≥ n.
  Example: CEIL(2.3) → 3.

• Excel: CEILING(number, significance) rounds a number up to the nearest multiple of significance.
  Example: CEILING(4.42, 0.05) → 4.45 (rounds up to nearest nickel).

Key Notes

• For negative numbers, ceil rounds toward zero (e.g., ceil(-2.3) = -2).

• The function always returns a floating-point value in most languages, even if the result is a whole number.

• It is the opposite of the floor function, which rounds down to the nearest integer.