TL;DR — To raise a number to a power, Excel gives you three interchangeable tools: the
^operator (=2^10), thePOWER(number, power)function, andSQRT(number)for the one specific power of ½. They compute the same math — pick by readability. Roots are just fractional exponents: a cube root is^(1/3). Two precedence traps bite almost everyone:=-3^2returns9, not-9, and=27^1/3returns9, not3— always wrap the exponent in parentheses.SQRTof a negative number is#NUM!.
=2^10 ' -> 1024 the ^ operator
=POWER(2, 10) ' -> 1024 the function form (identical result)
=SQRT(144) ' -> 12 square root = ^(1/2)
=27^(1/3) ' -> 3 cube root — note the parentheses
=POWER(B2/A2, 1/5) - 1 ' -> 5-year CAGR (a root in disguise)
Powers and roots feel like calculator territory, but in a spreadsheet they turn a column of raw numbers into growth rates, distances, and standard deviations. The functions are simple; what trips people up is a pair of operator-precedence rules that make a correct-looking formula quietly wrong. Get those two rules and this whole corner of Excel becomes dependable.
What you'll learn
- The mental model:
^,POWER, andSQRTare one operation with three faces - Why roots are fractional exponents — and there is no
CUBEROOTfunction - The
=-3^2 = 9trap: unary minus binds tighter than^ - The
=27^1/3 = 9trap:^binds tighter than/ - Why
SQRT(-4)is#NUM!, and theSQRT(ABS(x))fix - The one formula worth memorizing: POWER as CAGR
The mental model: one operation, three faces
Exponentiation is a single idea — multiply a number by itself power times — and Excel exposes it three ways that return byte-for-byte identical results:
=5^3 ' -> 125
=POWER(5, 3) ' -> 125
=5*5*5 ' -> 125
So the choice is never about correctness, only ergonomics. Use the ^ operator
for quick inline math where the formula stays readable (=radius^2*PI()). Reach for
POWER when the exponent is itself a calculation or a cell reference, where a
bare ^ would get lost in a dense expression — POWER(base, rate/12) reads better
than base^(rate/12) buried mid-formula. And SQRT is nothing more than a named
shortcut for the single most common exponent, ^(1/2). There's no deeper magic to
learn — but there are two precedence rules that decide whether the math you typed
is the math Excel runs.
Roots are fractional exponents (and there's no CUBEROOT)
The one conceptual leap worth making: a root is a power with a fractional
exponent. The square root is the ½ power, the cube root is the ⅓ power, and the
nth root is the 1/n power. This is the whole reason Excel needs only SQRT plus
the operator — everything else falls out of fractions:
=SQRT(144) ' -> 12 the ½ power, named
=144^(1/2) ' -> 12 the same thing, spelled out
=27^(1/3) ' -> 3 cube root
=32^(1/5) ' -> 2 fifth root
=POWER(32, 1/5) ' -> 2 fifth root, function form
People go hunting for a CUBEROOT function and there isn't one — you don't need it,
because ^(1/3) is the cube root. That mental model (root = 1/n power) is what
lets you take any root of anything without memorizing new function names. It also
sets up the single most important warning in this article, which is entirely about
where those parentheses go.
The precedence trap #1: =27^1/3 returns 9, not 3
Type =27^1/3 expecting a cube root and Excel hands you 9. Nothing is broken —
the ^ operator binds tighter than /, so Excel reads 27^1/3 as (27^1)/3,
which is 27/3 = 9. The fractional exponent you meant never happened.
The fix is one pair of parentheses, and it is not optional:
=27^1/3 ' -> 9 WRONG: computed as (27^1)/3
=27^(1/3) ' -> 3 RIGHT: the exponent is 1/3
Rule: whenever the exponent is itself an expression — a fraction, a subtraction, a
cell divided by something — wrap it in parentheses. This is the number-one reason
"my nth-root formula is way off" and it produces a plausible number, not an error,
so nothing flags it. If parentheses-in-exponents feel fussy, that's exactly when
POWER(27, 1/3) earns its keep: the function form makes the exponent a clearly
separated argument, and the trap disappears.
The precedence trap #2: =-3^2 returns 9, not −9
Here is the Excel quirk that catches every programmer and math student who moves in:
=-3^2 ' -> 9 Excel: unary minus binds TIGHTER than ^
=-(3^2) ' -> -9 what you probably meant
=0-3^2 ' -> -9 subtraction behaves normally
In standard mathematical notation and in nearly every programming language, -3^2
means "the negative of three squared" = -9. Excel is the odd one out: it applies
the unary minus first, squaring -3 to get +9. So a formula copied from a
textbook, a Python script, or a colleague's mental model can flip sign silently.
The defense is a habit: when a negative sign sits in front of a base you're about
to raise, decide out loud whether you want (-x)^n or -(x^n) and parenthesize
accordingly. Note this only affects a leading minus — =5-3^2 is 5-9=-4 as
you'd expect, because there the minus is subtraction, not negation.
SQRT of a negative is #NUM! — and the ABS bridge
SQRT refuses negative inputs, because it deals only in real numbers:
=SQRT(-4) ' -> #NUM!
=SQRT(ABS(-4)) ' -> 2 take the root of the magnitude
If a value could be negative and you want the root of its size, wrap it in
ABS to guarantee a non-negative input. The same limit hits
fractional powers of negative bases: =(-8)^(1/3) returns #NUM! even though the
real cube root of −8 is −2, because Excel evaluates fractional powers through
logarithms, which are undefined for negatives. The clean workaround borrows the
sign-and-magnitude idea from the ABS & SIGN guide:
=SIGN(-8) * ABS(-8)^(1/3) ' -> -2 odd root of a negative, done right
The one formula to memorize: POWER as CAGR
If you take a single practical thing from this page, make it this. Compound annual
growth rate — the honest "what steady yearly rate turns the start value into the end
value" — is an nth root, and POWER writes it in one line:
=POWER(EndValue / StartValue, 1 / Years) - 1
=POWER(2200000 / 1000000, 1/5) - 1 ' -> 0.1706 ~17.1% CAGR over 5 years
Read it through the mental model: the total growth ratio is End/Start; the 1/Years
exponent takes the Years-th root of that ratio to find the per-year multiplier;
subtracting 1 turns the multiplier into a percentage. It's exponents and roots doing
real financial work. (There's a second, logarithmic way to get the same answer, which
the EXP, LN & LOG guide covers — handy when you're solving
for the number of years instead of the rate.)
The judgment call
Don't overthink which tool to use: ^ for quick inline powers, POWER when the
exponent is computed or the formula is already crowded, SQRT for the ½ power it
names. They can't disagree on the answer. The failures here are never about picking
the "wrong" function — they're about the two precedence rules, so build the habits
that neutralize them: parenthesize any exponent that isn't a bare number, and
parenthesize any base that starts with a minus. Those two reflexes cover essentially
every powers-and-roots bug you'll ever hit. And when you catch yourself reaching for
these to compute repeated multiplication of a whole range, remember
PRODUCT and SUMPRODUCT exist for that.
How ExcelMaster helps
The traps on this page are exactly the kind a formula assistant should absorb for
you. Tell ExcelMaster "compute the 5-year CAGR from these start and end values"
and it writes POWER(End/Start, 1/Years)-1 with the exponent parenthesized
correctly — no ^1/3-style slip. Ask for "the cube root of column C" or "the
distance √(dx²+dy²)" and it places every parenthesis where the precedence rules
demand, and guards negative inputs with ABS when your data could go below zero. You
describe the result; it handles the operator-precedence minefield.
Frequently asked questions
What is the POWER function in Excel?
=POWER(number, power) raises number to the exponent power — =POWER(2, 10)
returns 1024. It's the function form of the ^ operator (=2^10 gives the same
result). Use POWER when the exponent is a calculation or cell reference and the
^ would be hard to read inside a longer formula.
How do I calculate a square root or cube root in Excel?
For a square root use =SQRT(number), e.g. =SQRT(144) → 12. For a cube root,
raise the number to the ⅓ power with the exponent in parentheses: =27^(1/3) → 3,
or =POWER(27, 1/3). Any nth root is =number^(1/n). There is no separate
CUBEROOT function — fractional exponents cover every root.
Why does =27^1/3 give 9 instead of 3 in Excel?
Because the ^ operator has higher precedence than /, Excel evaluates 27^1/3 as
(27^1)/3 = 9. You must wrap the fractional exponent in parentheses: =27^(1/3)
returns the cube root, 3. Whenever an exponent is itself an expression,
parenthesize it.
Why does =-3^2 return 9 in Excel instead of -9?
In Excel, the unary minus binds tighter than the ^ operator, so =-3^2 is read
as (-3)^2 = 9 — the opposite of standard math and most programming languages. To
get "negative of three squared," write =-(3^2), which returns -9.
How do I take the square root of a negative number in Excel?
SQRT returns #NUM! for negative inputs because it works only with real numbers.
If you want the root of the magnitude, use =SQRT(ABS(number)). For an odd root of a
negative value (like a cube root), use =SIGN(number)*ABS(number)^(1/n) to keep the
sign.
Tested in
Tested in: Excel 365 (Windows 11) — last verified 2026-07-10.
Related guides: Excel ABS & SIGN · Excel EXP, LN & LOG · Excel ROUND · Excel SUMPRODUCT