Ceil
Ceil
Ceil[ expr ] rounds a value up to the nearest integer, or to a given number of decimals.
Usages
Ceil[ expr ]
Ceil[ expr ] returns the smallest integer that is greater than or equal to the value of expr. expr can be any expression with a numerical value.
| Example | in | out |
|---|---|---|
Round 3.1 up. |
Ceil[ 3.1 ] |
4 |
| For negative numbers, rounding up goes towards zero. | x := -3.5 |
r = -3 |
| An integer stays the same. | Ceil[ 4 ] |
4 |
| A fraction. | Ceil[ 7/2 ] |
4 |
| An expression with a numerical value. | Ceil[ Sqrt[5]+0.3 ] |
3 |
Ceil[ expr, n ]
Ceil[ expr, n ] rounds up to n decimals. A negative n rounds up to tens, hundreds, and so on.
| Example | in | out |
|---|---|---|
Round up to 2 decimals. |
Ceil[ 3.14159, 2 ] |
3.15 |
| Round up to hundreds. | Ceil[ 1234.5, -2 ] |
1300 |
Ceil[ list ]
If the argument is a list, each element is rounded up.
| Example | in | out |
|---|---|---|
| Round up each element. | Ceil[ {1.2, 2.5, -0.5} ] |
{2, 3, 0} |
Options
OmitTrailingZeroes
If set to False, the result is displayed with exactly n decimals, including zeros at the end. Default: True.
| Syntax | Example | rendered |
|---|---|---|
Ceil[ expr, n, OmitTrailingZeroes=>False ] |
Ceil[ 3.1, 2, OmitTrailingZeroes=>False ] |
|
Ceil[ 3.1, 2 ] |
Details
| Invalid input | Result |
|---|---|
Ceil[ x ] |
Left unevaluated: the argument must have a numerical value. |
Ceil[ 3.1, 1.5 ] |
Error: The second argument of Ceil must be an integer, but is 1.5 |
Ceil[ 3.1, 1, 2 ] |
Error: Ceil must have 1 or 2 arguments, but has 3 |