Square Roots and Powers in Excel (SQRT, POWER, ^)
By ExcelReady TeamUpdated 6 min read
The short answer
To find a square root in Excel, use =SQRT(A2), so =SQRT(16) returns 4. For powers, use the caret: =A2^2 squares a number and =A2^3 cubes it. POWER does the same: =POWER(A2,2). For other roots, raise to a fraction, such as =A2^(1/3) for a cube root. SQRT of a negative number returns #NUM!.
Key takeaways
- =SQRT(number) returns the square root: =SQRT(81) is 9.
- The caret ^ means 'to the power of': =5^2 is 25 and =2^10 is 1024.
- Any root is a fractional power: =27^(1/3) is 3. Keep the fraction in brackets.
- SQRT of a negative number returns #NUM!; use =SQRT(ABS(A2)) if you need the size only.
- Excel works out -3^2 as 9, because the minus sign is applied before the power.
On this page+
To find a square root in Excel, type =SQRT(A2). For powers you use the caret symbol ^: =A2^2 squares a number and =A2^3 cubes it. Every other root, such as a cube root, is a power with a fraction. This guide shows all three tools (SQRT, POWER and ^), the order Excel works them out in, and how to fix the #NUM! error.
How to find a square root in Excel#
Use the SQRT function with one argument: the number or the cell that holds it.
=SQRT(number)| Formula | Result |
|---|---|
=SQRT(16) | 4 |
=SQRT(2) | 1.41421356 |
=SQRT(A2) where A2 is 20.25 | 4.5 |
A practical use: if a square room has an area of 20.25 m² in A2, =SQRT(A2) gives the length of one wall, 4.5 m.
SQRT works in every version of Excel, on Windows, Mac and the web. If you're new to typing formulas, start with the lesson on your first formulas: every formula begins with an equals sign, and without it Excel shows your text instead of a result. The guide to why a formula shows as text covers that problem.
How to square a number or raise it to a power#
Use the caret ^, which means "to the power of". On most keyboards you type it with Shift+6.
| Formula | Meaning | Result |
|---|---|---|
=5^2 | 5 squared | 25 |
=A2^3 where A2 is 4 | 4 cubed | 64 |
=2^10 | 2 to the power of 10 | 1024 |
=10^-2 | A negative power: 1/100 | 0.01 |
The POWER function does exactly the same job with a different shape:
=POWER(number, power)So =POWER(5,2) is 25, the same as =5^2. Most people use ^ because it's shorter. POWER can be easier to read when the power itself is a long calculation.
How to calculate a cube root or any other root#
Any root is a power with a fraction. The square root is the power 1/2, the cube root is 1/3, the fourth root is 1/4.
| Root | Formula | Result for 64 |
|---|---|---|
| Square root | =64^(1/2) or =SQRT(64) | 8 |
| Cube root | =64^(1/3) or =POWER(64,1/3) | 4 |
| Sixth root | =64^(1/6) | 2 |
The brackets around the fraction are essential. Excel works out powers before division, so =64^1/3 means 64 to the power of 1, divided by 3, which is 21.33. With the brackets, =64^(1/3) returns 4.
The same idea gives the average yearly growth rate of an investment, which is a fractional power of the total growth. See the CAGR formula guide for that use.
The order Excel uses for powers#
Excel follows a fixed order of operations, and two details surprise people.
- Negation comes before powers.
=-3^2returns 9, not -9. Excel applies the minus sign to 3 first, then squares -3. Write=-(3^2)if you want -9. - Powers are worked out left to right.
=2^3^2returns 64, because Excel calculates (2^3)^2. In school maths, the same expression often means 2^9. Add brackets to make your meaning clear.
After powers come multiplication and division, then addition and subtraction. So =2+3^2 is 11, and =(2+3)^2 is 25. When in doubt, add brackets. They never hurt.
How to fix the #NUM! error with SQRT#
SQRT returns #NUM! when the number is negative, because a negative number has no real square root. You have three options:
- Fix the data. Often a negative value is a sign error in the source.
- Use the size only:
=SQRT(ABS(A2))takes the square root of the number without its sign. For -16 it returns 4. - Skip negatives:
=IF(A2<0,"",SQRT(A2))leaves the cell blank instead of showing an error.
The same happens with a fractional power: =(-16)^(1/2) also returns #NUM!. If you hit this inside a longer formula, check which part has turned negative before the power is applied.
If SQRT shows an old result that doesn't change when you edit the inputs, the workbook may be on manual calculation. The guide to formulas not updating explains how to switch it back.
A worked example: Pythagoras in Excel#
The diagonal of a right-angled triangle is the square root of the sum of the two sides squared. With the width in A2 and the height in B2:
=SQRT(A2^2+B2^2)| Width | Height | Diagonal |
|---|---|---|
| 3 | 4 | 5 |
| 6 | 8 | 10 |
| 5 | 12 | 13 |
| 9 | 12 | 15 |
Fill the formula down the column (Windows: Ctrl+D; Mac: ⌘D) and each row updates. The same pattern works for screen sizes, ramps and distances on a grid.
Square roots in other everyday formulas#
Powers and roots appear in more places than maths homework. Area and volume use ^2 and ^3. Compound growth uses ^ with the number of years. Standard deviation is a square root of the variance, which Excel's STDEV functions calculate for you.
Scientific notation is another place powers appear. Excel may show a very large number such as 2^40 as 1.09951E+12, which means 1.09951 × 10^12. The value is stored in full; widen the column or apply a Number format to see every digit. You can also type large numbers this way: entering 3E6 in a cell stores 3,000,000.
For invoices, you rarely need powers, but you'll use the same operators and order of operations; see building an invoice with formulas. Percentages follow the same rules too, covered in the Excel percentage formula guide. Everything here works the same in Excel desktop and Excel for the web.
Practise it#
Operators and order of operations are the building blocks of every formula you'll write in a test. Practise your first formulas in a live spreadsheet: you type the formula and it checks it instantly. Then try the Pythagoras exercise on this page, and take the Excel screening quiz to check your basics.
Try it yourself
This is a live spreadsheet. Type the formula in the green cell and press Enter.
A ladder leans against a wall. Use Pythagoras to find the length of the diagonal in row 4. Click C4 and take the square root of A4 squared plus B4 squared.
| A | B | C | D | |
|---|---|---|---|---|
| 1 | Diagonal | |||
| 2 | ||||
| 3 | ||||
| 4 | ||||
| 5 | ||||
| 6 | ||||
| 7 | ||||
| 8 |
Tip: Square each side with ^2, add them, then wrap the sum in SQRT.
Practise this in a lesson
Frequently asked questions
What is the formula for square root in Excel?
Use =SQRT(number), for example =SQRT(A2) or =SQRT(144), which returns 12. You can also write =A2^(1/2), which gives the same result.
How do I square a number in Excel?
Use the caret: =A2^2. You can also use =POWER(A2,2) or =A2*A2. All three return the same value.
How do I calculate a cube root in Excel?
Raise the number to the power of one third: =A2^(1/3) or =POWER(A2,1/3). For 27 the result is 3. The brackets around 1/3 are required.
Why does SQRT return #NUM!?
The number is negative, and a negative number has no real square root. Use =SQRT(ABS(A2)) to take the root of its size, or check the data for a sign error.
How do I type a squared symbol in Excel?
For a label like m², type m2, select only the 2 in the formula bar, open Format Cells and tick Superscript. This only works in text cells, not in numbers or formulas.