POWER Function in Excel

In mathematics we had exponents which were the power to a given any base number, in excel we have a similar inbuilt function known as POWER function which is used to calculate the power of a given number or base, to use this function we can use the keyword =POWER( in a cell and provide two arguments one as number and another as power.

Power in Excel

A Power in Excel is a Math/Trigonometric function computes and returns the result of a number raised to a power. Power Excel function takes two arguments the base (any real number), and the exponent (power, that signifies how many times the given number will be multiplied by itself). This means that, for example, 5 multiplied by a power of 2 is the same as 5 x5.

Formula of POWER Function

Explanation of POWER Function in Excel

Power in Excel takes both the argument as a numeric value, hence the arguments passed are of integer type where Number is the base number and the Power is the exponent. Both the arguments are required and are not optional.

We can use the Power function in excel in many ways, like for mathematical operations, power function equation and can be used to compute the relational algebraic functions.

 

How to Use POWER Function in Excel

Excel POWER function is very simple and easy to use. Let understand the working of POWER in excel by some examples.

POWER in Excel Example #1

For example, we have an power function equation y=x^n (x to the power n), where y is dependent on the value of x and n is the exponent. We also want to draw the graph of this f(x, y) function, for given values of x and n=2. The values of x are:

So, in this case, since the value of y depends upon the nth power of x, we will calculate the value of Y using the POWER function in Excel.

• 1^st value of y will be 2^2 (=POWER(2,2)
• 2^nd value of y will be 4^2 (=POWER(4,2)
• ……………………………………………………………
• ……………………………………………………………
• 10^th value of y will be 10^2 (=POWER(10,2)

Now, selecting the values of x and y from range B4:K5, select the graph (in this we have selected the Scatter graph with smooth lines) from the insert tab.

So, we get a linear exponential graph for the given POWER Function equation.

POWER in Excel Example #2

In algebra, we have the quadratic POWER Function equation, that is represented as ax²+bx+c=0, where x is unknown and a, b and c are the coefficients. The solution of this POWER Function equation gives the roots of the equation that is the values of x.

The roots of the quadratic POWER Function equation are computed by following mathematical formula

• x = (-b+ (b²-4ac)^1/2)/2a
• x = (-b- (b²-4ac)^1/2)/2a

b²-4ac is termed as discriminant and it describes the number of roots a quadratic POWER Function equation has.

Now, we have some list of quadratic POWER Function equation given in Column A and we need to find the roots of the equations.

^ is called the exponential operator used to represent the power (exponent). X² is same as x^2.

We have five quadratic POWER Function equation and we will be solving them using the formula with the help of the POWER function in excel to find out the roots.

In the first POWER Function equation, a=4, b=56 and c = -96, if we mathematically solve them using the above formula, we have the roots -15.5 and 1.5

To implement this in excel formula, we will use the POWER function in Excel and the formula will be

• =((-56+POWER(POWER(56,2)-(4*4*(-93)),1/2)))/(2*4) will give the first root and
• =((-56-POWER(POWER(56,2)-(4*4*(-93)),1/2)))/(2*4) will give the second root of the equation

So, the complete formula will be,

=”Roots of equations are”&” “&((-56+POWER(POWER(56,2)-(4*4*(-93)),1/2)))/(2*4)&” , “&((-56-POWER(POWER(56,2)-(4*4*(-93)),1/2)))/(2*4)

Both the formulas are concatenated together with String “Roots of equation are”.

Using the same formula for other POWER Function equation we have,Output:

POWER in Excel Example #3

So, for different mathematical calculations, we can use POWER function in Excel.

Suppose, we have to find out the compound interest for which the formula is

Amount = Principal (1 + r/n)^nt

• Where r is the rate of interest, n is number of times interest is compounded per year and t is the time
• If an amount of $4000 is deposited into an account (saving) at an interest rate of 5% annually, compounded monthly, the value of the investment after 5 years can be calculated using the above compound interest formula.
• Where Principal = $4000, rate = 5/100 that is 0.05, n =12 (compounded monthly), time =5 years

Using the compound interest formula and implementing it into excel formula using the POWER function in Excel we have the formula

=B2*(POWER((1+(B3/B5)),(B4*B5)))

So, the investment balance after 5 years is $5.133.43

POWER in Excel Example #4

According to Newton’s gravitation law, two bodies at a distance of r from their center of gravity attracts each other in the universe according to a gravitational POWER Excel formula

F = (G*M*m)/r²

Where F is the magnitude of the gravitational force, G is called the gravitational constant, M is the mass of first body and m is the mass of second body and r is the distance between the bodies from their center of the gravity.

Let us calculate the magnitude of gravitational force by which the Sun pulls the Earth

• Mass of Sun is 1.98*10^30 kg
• Mass of Earth is 5.97*10^24 kg
• The distance between Sun and the Earth is 1.496 x 10^11 meters
• Gravitational constant value is 6.67*10^-11 m³kg^-1s^-2

In excel, if we want to calculate the gravitational force, we will be again using the POWER in Excel that can operate over big numeric values.

• So, using the POWER in Excel we can convert the scientific notation values into the POWER Excel formula
• 1.98*10^30 will be represented as 1.98*Power(10,30), similarly other values.
• So, the POWER Excel formula to calculate the force will be =(6.67*POWER(10,-11)*1.98*POWER(10,30)*5.97*POWER(10,24))/POWER(1.496*POWER(10,11),2)

Since the value obtained as force is a big number Excel expressed it scientific notation. To change it into a fraction, change the format to the fraction

Output:

So, Sun pulls the Earth with a force of magnitude 35229150283107900000000 Newton.

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