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.

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:

1. 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.
2. 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.
3. 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.
4. 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.
5. 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.
6. 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.
7. 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).

6. Function not working

CEILING returns the #VALUE! error value if either argument is non-numeric.

6.1 Troubleshooting the error value

When you encounter an error value in a cell a warning symbol appears, displayed in the image above. Press with mouse on it to see a pop-up menu that lets you get more information about the error.

1. The first line describes the error if you press with left mouse button on it.
2. The second line opens a pane that explains the error in greater detail.
3. The third line takes you to the "Evaluate Formula" tool, a dialog box appears allowing you to examine the formula in greater detail.
4. This line lets you ignore the error value meaning the warning icon disappears, however, the error is still in the cell.
5. The fifth line lets you edit the formula in the Formula bar.
6. The sixth line opens the Excel settings so you can adjust the Error Checking Options.

Here are a few of the most common Excel errors you may encounter.

#NULL error - This error occurs most often if you by mistake use a space character in a formula where it shouldn't be. Excel interprets a space character as an intersection operator. If the ranges don't intersect an #NULL error is returned. The #NULL! error occurs when a formula attempts to calculate the intersection of two ranges that do not actually intersect. This can happen when the wrong range operator is used in the formula, or when the intersection operator (represented by a space character) is used between two ranges that do not overlap. To fix this error double check that the ranges referenced in the formula that use the intersection operator actually have cells in common.

#SPILL error - The #SPILL! error occurs only in version Excel 365 and is caused by a dynamic array being to large, meaning there are cells below and/or to the right that are not empty. This prevents the dynamic array formula expanding into new empty cells.

#DIV/0 error - This error happens if you try to divide a number by 0 (zero) or a value that equates to zero which is not possible mathematically.

#VALUE error - The #VALUE error occurs when a formula has a value that is of the wrong data type. Such as text where a number is expected or when dates are evaluated as text.

#REF error - The #REF error happens when a cell reference is invalid. This can happen if a cell is deleted that is referenced by a formula.

#NAME error - The #NAME error happens if you misspelled a function or a named range.

#NUM error - The #NUM error shows up when you try to use invalid numeric values in formulas, like square root of a negative number.

#N/A error - The #N/A error happens when a value is not available for a formula or found in a given cell range, for example in the VLOOKUP or MATCH functions.

#GETTING_DATA error - The #GETTING_DATA error shows while external sources are loading, this can indicate a delay in fetching the data or that the external source is unavailable right now.

6.2 The formula returns an unexpected value

To understand why a formula returns an unexpected value we need to examine the calculations steps in detail. Luckily, Excel has a tool that is really handy in these situations. Here is how to troubleshoot a formula:

1. Select the cell containing the formula you want to examine in detail.
2. Go to tab “Formulas” on the ribbon.
3. Press with left mouse button on "Evaluate Formula" button. A dialog box appears.
   The formula appears in a white field inside the dialog box. Underlined expressions are calculations being processed in the next step. The italicized expression is the most recent result. The buttons at the bottom of the dialog box allows you to evaluate the formula in smaller calculations which you control.
4. Press with left mouse button on the "Evaluate" button located at the bottom of the dialog box to process the underlined expression.
5. Repeat pressing the "Evaluate" button until you have seen all calculations step by step. This allows you to examine the formula in greater detail and hopefully find the culprit.
6. Press "Close" button to dismiss the dialog box.

There is also another way to debug formulas using the function key F9. F9 is especially useful if you have a feeling that a specific part of the formula is the issue, this makes it faster than the "Evaluate Formula" tool since you don't need to go through all calculations to find the issue..

1. Enter Edit mode: Double-press with left mouse button on the cell or press F2 to enter Edit mode for the formula.
2. Select part of the formula: Highlight the specific part of the formula you want to evaluate. You can select and evaluate any part of the formula that could work as a standalone formula.
3. Press F9: This will calculate and display the result of just that selected portion.
4. Evaluate step-by-step: You can select and evaluate different parts of the formula to see intermediate results.
5. Check for errors: This allows you to pinpoint which part of a complex formula may be causing an error.

The image above shows cell reference B3 converted to hard-coded value using the F9 key. The CEILING function requires numerical values which is not the case in this example. We have found what is wrong with the formula.

Tips!

• View actual values: Selecting a cell reference and pressing F9 will show the actual values in those cells.
• Exit safely: Press Esc to exit Edit mode without changing the formula. Don't press Enter, as that would replace the formula part with the calculated value.
• Full recalculation: Pressing F9 outside of Edit mode will recalculate all formulas in the workbook.

Remember to be careful not to accidentally overwrite parts of your formula when using F9. Always exit with Esc rather than Enter to preserve the original formula. However, if you make a mistake overwriting the formula it is not the end of the world. You can “undo” the action by pressing keyboard shortcut keys CTRL + z or pressing the “Undo” button

6.3 Other errors

Floating-point arithmetic may give inaccurate results in Excel - Article

Floating-point errors are usually very small, often beyond the 15th decimal place, and in most cases don't affect calculations significantly.

Functions in 'Math and trigonometry' category

The CEILING function function is one of 62 functions in the 'Math and trigonometry' category.

Excel function categories

Excel categories

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