# How to use the CEILING function

**What is the CEILING function?**

The CEILING function rounds a number up to its nearest multiple.

The number is rounded down if both the number and multiple is negative. The number is rounded up if the number is negative and multiple is positive.

#### Table of Contents

## 1. Introduction

**What is a multiple?**

In mathematics a multiple is a number that can be divided evenly by another number with no remainder. For a number to be a multiple it must be divisible by x with 0 remainder.

For a number x, multiples of x are numbers like 2x, 3x, 4x and so on. For example, 20 is a multiple of 4 since 20/ 4 = 5 with no remainder.

**How to round numbers?**

Rounding is a method to simplify a number by reducing its digits while keeping its approximate value close to the original value.

There are a few common ways to round:

- Round to a set number of decimal places, rounding 2.13579 to 2 decimal places gives 2.14.
- Round up or down to the nearest integer, rounding up 2.3 gives 3. Rounding down 2.3 gives 2.
- Round to a set increment, rounding to the nearest 10 rounds 17 to 20.
- Round to significant figures, rounding 2.333 to 3 significant figures gives 2.33.

When rounding, look at the first digit after where you want to round. If it's 5 or more, round up. If less than 5, round down. Rounding makes numbers cleaner and easier to work with in many everyday situations, however, they may also cause rounding errors like rounded values can compound errors. Rounding measurements and constants may reduces precision. It is better to round numbers after performing calculations than before.

**What is a decimal place?**

A decimal place refers to each position held by a digit in a number. The first decimal place is the tenths place (1/10), the second is the hundreds place (1/100) and so on.

**What is an integer?**

An integer is a whole number that can be positive, negative, or zero, but not a fraction or decimal.

**What is a "a set increment"?**

A "set increment" is a fixed regular number interval that is used as the rounding value or unit.

- Rounding to the nearest 10 uses a set increment of 10. Valid rounded values are ..., -20, -10, 0, 10, 20, 30, ...
- Rounding to the nearest 0.5 uses a set increment of 0.5. Valid values are ..., 2.0, 2.5, 3.0, 3.5, ...

**What other Excel functions round numbers?**

ROUND | Rounds a number to a specified number of digits |

ROUNDUP | Rounds a number up, away from zero |

ROUNDDOWN | Rounds a number down, towards zero |

MROUND | Rounds a number to the nearest multiple of a specified value |

CEILING | Rounds a number up to its nearest multiple. |

ODD | Returns number rounded up to the nearest odd integer. |

EVEN | Rounds a number up to the nearest even whole number. |

FIXED | Rounds a number to the specified number of decimals, lets you ignore comma separators. |

## 2. Syntax

CEILING(*number*, *significance*)

number |
Required. The value you want to round. |

significance |
Required. The multiple to which you want to round. |

## 3. Example 1

**Round up a numbers to the nearest multiple based on this table?**

number | significance |

22 | 5 |

-48 | 10 |

3.13 | 1 |

1.57 | 0.25 |

12345.67 | 1000 |

-1.57 | -0.25 |

1.57 | -0.25 |

The formula in cell E3 rounds the numbers in cell range B3:B9 based on the corresponding significance values specified in cell range C3:C9.

Formula in cell E3:

Here is how the calculations are made:

- The number is 22 and the significance is 5, the nearest multiples are to 22 are 20 and 25. The CEILING function rounds 22 up to 25 if both the number and significance are positive values.
- The number is -48 and the significance is 10, the nearest multiples are to -48 are -40 and -50. The CEILING function rounds -48 up to -40 if the number is negative and the significance is a positive value.
- The number is 3.12 and the significance is 1, the nearest multiples are to 3.13 are 3 and 4. The CEILING function rounds 3.13 up to 4 if the number is positive and the significance is a positive value.
- The number is 1.57 and the significance is 0.25, the nearest multiples are to 1.57 are 1.5 and 1.75. The CEILING function rounds 1.57 up to 1.75 if the number is positive and the significance is a positive value.
- The number is 12345.67 and the significance is 1000, the nearest multiples are to 12345.67 are 12000 and 13000. The CEILING function rounds 12345.67 up to 13000 if the number is positive and the significance is a positive value.
- The number is -1.57 and the significance is -0.25, the nearest multiples are to -1.57 are -1.5 and -1.75. The CEILING function rounds -1.57 down to -1.75 if the number is negative and the significance is a negative value.
- The CEILING function returns a #NUM error value if the number is positive and the significance is a negative value.

## 4. Example 2

**Calculate the total cost of items, rounding up the price of each item in cell range B3:B9 to the nearest nickel (0.05)?**

Here are the arguments:

- number: B3:B9 (A cell reference to all numerical values to be evaluated)
- significance: 0.05 (nearest nickel)

Formula in cell C13:

The following table shows the source data and the converted data:

number | Convert |

0.09 | 0.1 |

0.27 | 0.3 |

0.49 | 0.5 |

0.16 | 0.2 |

0.36 | 0.4 |

0.07 | 0.1 |

0.48 | 0.5 |

The total is 0.1 +.3 + 0.5 + 0.2 + 0.4 + 0.1 + 0.5 equals 2.1

## 5. Example 3

**Determine the number of full weeks between two dates, rounding up assuming cell B3 contains the start date and cell B6 contains the end date?**

Formula in cell C13:

This formula will calculate the number of days between the two dates, round up to the number of days based on a weekly interval (7). Lastly, divide by 7 to get the number of weeks.

Excel handles dates as whole numbers which makes it easy to calculate the difference between the start date and the end date. The difference is 45553-45393 equals 160 days. The nearest multiples are 154 and 161, the CEILING function rounds the number up to 161. Divide this by seven to get then number of weeks. 161/7 equals 23 weeks.

### Explaining formula

#### Step 1 - Calculate the difference between the end date and the start date

The minus character lets you perform subtraction in an Excel formula.

B6-B3 becomes 45553-45393 = 160

#### Step 2 - Round up to the nearest multiple of 7

CEILING(B6-B3,C11)

becomes

CEILING(160,7) returns 161.

#### Step 3 - Round up to full weeks

The division character lets you calculate the ratio between two numbers in an Excel formula.

CEILING(B6-B3,C11)/7

becomes 161/7 = 23 (weeks).

### Functions in 'Math and trigonometry' category

The CEILING function function is one of 61 functions in the 'Math and trigonometry' category.

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