Ceiling Function Calculator
Calculate the ceiling function ⌈x⌉ — the smallest integer greater than or equal to x.
Formula
⌈x⌉ = smallest integer n such that n ≥ x
- For positive non-integers: ⌈x⌉ = floor(x) + 1.
- For integers: ⌈n⌉ = n (no rounding needed).
- For negative numbers: ⌈-2.3⌉ = -2 (rounds toward zero).
Ceiling of 2.3
Inputs
- x: 2.3
⌈2.3⌉ = 3 (smallest integer ≥ 2.3). ⌊2.3⌋ = 2 (largest integer ≤ 2.3).
Frequently asked questions
What is the ceiling function?
⌈x⌉ rounds a number up to the nearest integer. ⌈2.1⌉ = 3, ⌈-2.1⌉ = -2.
How does ceiling differ from rounding?
Ceiling always rounds up; regular rounding rounds to the nearest integer (5.4 rounds to 5, but ⌈5.4⌉ = 6).
What is ceiling of a negative number?
⌈-2.7⌉ = -2 (rounds toward zero). ⌊-2.7⌋ = -3 (rounds away from zero).
Where is ceiling used in programming?
In loops to determine iteration count, pricing (always round up to next unit), pagination, and resource allocation.