Suppose my cell A1 in an Excel spreadsheet holds the number 3. If I enter the formula
=  A1^2 + A1
in A2, then A2 shows the number 12, when it should show 6 (or 9+3)
Why is that? How can I prevent this misleading behaviour?
Suppose my cell A1 in an Excel spreadsheet holds the number 3. If I enter the formula
=  A1^2 + A1
in A2, then A2 shows the number 12, when it should show 6 (or 9+3)
Why is that? How can I prevent this misleading behaviour?
Short answer
To solve this problem, just add a 0 before the equal sign
= 0  A1^2 + A1
or add a couple of parenthesis to force the standard order of operations
=  (A1^2) + A1
or replace the minus sign by its common interpretation of multiplication by 1
= 1 * A1^2 + A1
Detailed explanation
Under Excel's conventions,
=  3^2
equals (3)^2 = 9, while
= 03^2
equals 09 = 9.
Why adding just a 0 changes the result?
Not preceded by a minuend, the minus sign in 3^2 is considered a negation operator, which is a unary operator (with only one argument) that changes the sign of the number (or expression) that follows. However, the minus sign in 03^2 is a subtraction operator, which is a binary operator that subtracts what follows 
from what precedes 
. According to Excel's conventions, the exponentiation operator ^
is computed after the negation operator and before the subtraction operator. See "Calculation operators and precedence in Excel", section "The order in which Excel performs operations in formulas".
The standard mathematical convention is that the exponentiation is computed before both negation and subtraction or, more simply stated, ^
is computed before 
. Shamefully, Excel chose different conventions from those of algebra rules, school textbooks, academic writing, scientific calculators, Lotus 123, Mathematica, Maple, computations oriented languages like Fortran or Matlab, MS Works, and... VBA (the language used to write Excel's macros). Unfortunately, Calc from LibreOffice and Google Sheets follow the same convention for compatibility with Excel. However, placing an expression in Google's search box or bar give excellent results. If you press enter, the order of computations will be given by using parentheses. A discussion where a mathematician kills the arguments of a "computer scientist" defending the precedence of negation over exponenciation: http://mathforum.org/library/drmath/view/69058.html
General Workarounds
If you want to compute
 anything ^ 2,
add a 0 before the equal sign
0  anything ^ 2
or add a couple of parenthesis to force the standard order of operations
 ( anything ^ 2 )
or replace the minus sign by its common interpretation of multiplication by 1
1 * anything ^ 2
A comment to another answer says that the only case you have to be aware of the the nonstandard precedence rule is where a minus sign follows an equal sign (=). However, there are other examples, like =exp(x^2) or =(2^2=2^2), where there isn't a minuend before the equal sign.
Thanks to @BruceWayne for proposing a short answer, which I wrote at the beginning.
You may be interested in According to Excel, 4^3^2 = 4096. I this correct?
A bit more succint than Rodolfo's Answer, you can use:
=(A1^2)+(A1)
(Edit: I totally didn't see it was a self question/answer.)
A leading 
is considered part of the first term.
=3^2
is processed as (3)^2 = 9
With a zero at the start it is instead treated as normal subtraction.
=03^2
is processed as 0  3^2 = 9
And if you have two operators, then the same thing will happen.
=03^2
is processed as 0  (3)^2 = 9
and
=0+3^2
is processed as 0 + (3)^2 = 9
The expression =  A1^2 + A1
is specific to Excel so must follow Excels rules. Contrary to some other answers here, there is no correct order of precedence. There are merely different conventions adopted by different applications. For your reference, the order of precedence used by excel is:
: Range
<space> intersection
, union
 Negation
% Percentage
^ Exponential
* and / Multiplication and Division
+ and  Addition and Subtraction
& Concatenation
= < > <= >= <> Comparison
Which you can override using parentheses.

can be unary or binary. But that doesn't imply an order of operations. Other languages get this right: in Python, Ruby, Octave, Awk, and Haskell (the first five languages with an exponentiation operator that came to mind), 3 ** 2
always evaluates to 9
. Why? Because that is the correct answer.
– wchargin
Dec 22 '18 at 10:27
You can have it either way:
=A1^2+A1
will return a 12, but:
=0A1^2+A1
will return a 6
If you feel that returning 12 violates common sense; be aware that Google Sheets does the same thing.
=A1A1^2
also returns 6
– Gary's Student
Dec 18 '18 at 19:09
Because Excel is interpreting your equation as:
(x)^2 + x
When you wanted:
(x^2) + x
To prevent this sort of undesired behavior, I find the best practice is to make heavy use of parenthesis to define your own priority system, since negation is not the same as subtraction, and thus not covered by PEMDAS. An example would be like:
((x^2))+x
It might be overkill, but this is how I guarantee Excel behaves the way I want.
x  x^2
. This ensures the  is interpreted as the binary subtraction operator.
– Xalorous
Dec 21 '18 at 13:00
Alternatively, you could just do
= A1  A1^2
because y + x = xy
The expression  A1^2
contains two operators, namely the unary negation operator 
and the binary exponentiation operator ^
. With the absence of any parenthesis, there could be two interpretations. Either:
(A1^2)
or:
(A1)^2
The first one says first do the exponentiation with operands A1
and 2
, and then do the negation on that.
The second one says first do the negation on operand A1
, and then use exponentiation on the result of that and 2
.
As was said in the comments to the question, Powers have higher priority than minus signs in any sane environment. Which means, it is best if a system assumes the first one.
However, Excel prefers the second one.
The lesson is, if you are unsure whether your environments is sane or not, include the parenthesis to be on the safe side. So write (A1^2)
.
This is not a problem with excel but with exponents and negatives. When you take a number and raise it to an even power, you cancel the negative sign.
x^2 + x == (x * x) + x
x = 3 => (3 * 3) + 3
== 9 + 3 => 12
You need to use parenthesis and multiple by 1
1 * (x^2) + x
x^2
where x is 3 and x^2
where x is 3. x^2+x
will never reach 12: wolframalpha.com/input/?i=x%5E2%2Bx
– Thomas Weller
Dec 20 '18 at 7:49
x^2+x where x =3 This is an example of a quadratic equation The equation can be written like this: 3*3+3 :Multiplication takes precedence over addition so result will be written as follows: 9 + 3 :Why =9 because a negative number x a negative number gives a positive result. This can be verified using any calculator, slide rule, or any computer mathematics program Final result 9 + 3 = 12
It is just a really simple maths.
Rule 1. Even multiplications of negative numbers, would output a positive result:
minus * minus = plus
minus * minus * minus = minus
minus * minus * minus * minus = plus
This is due to the fact, that minuses cancel each other in pairs.
Rule 2. The power of every number identifies that this number will be multiplied by itself a number of times.
(2)^n, where n=2 => 2*2 = 4
(2)^n, where n=2 => (2)*(2) = 4
And if you can see Rule number 1..
(3)^n, where n=3 => (3) * (3) * (3) = 9 * (3) = 27
Rule 3. Multiplication and Division have higher priority, than addition and subtraction.
3*5+2 = 15+2 = 17
3*(5+2) = 3*7 = 21
And there is the answer of your question:
Combining all 3 rules from before:
x^2 + x, where x=3 => 3^2+3 = 9+3 = 12
My advice to you is to spend some time every year and keep refreshing the fundamental rules of mathematics.
It is in fact a skill you can maintain and stay on top of a large portion of the world, only by knowing basic maths.
+*/
, but not unary operators like 
or +
. Precedence of the power operator is higher than *
and /
but unary operators have even higher precedence
– phuclv
Dec 23 '18 at 3:45