SQL SERVER – Result of EXP (Exponential) to the POWER of PI – Functions Explained

SQL Server can do some intense Mathematical calculations. Following are three very basic and very necessary functions. All the three function does not need explanation. I will not introduce their definition but will demonstrate the usage of function.

SELECT PI()
GO
SELECT POWER(2,5)
GO
SELECT POWER(8,-2)
GO
SELECT EXP(99)
GO
SELECT EXP(1)
GO

Results Set :
PI
———————-
3.14159265358979
PowerEg1
———–
32
PowerEg2
———–
0
ExpEg1
———————-
9.88903031934695E+42
ExpEg2
———————-
2.71828182845905
Now the Questions asked in the Title of the Article – What is the result of EXP to the POWER of PI

SELECT POWER(EXP(1), PI())
GO

Results
———————-
23.1406926327793

What the POWER of PI Example Shows

The last query raises e, the value EXP(1) returns, to the power of pi. The answer, about 23.1407, is a well known number in mathematics, called Gelfond’s constant. You can get the same result in a shorter way with EXP(PI()), because EXP(x) simply means e raised to x.

If you flip it around, POWER(PI(), EXP(1)) returns about 22.4592. So e raised to pi is a little bigger than pi raised to e, which is a fun question to ask a friend who likes numbers.

There is one trap worth knowing. The result type of POWER follows the type of its first argument. That is why POWER(8, -2) in the examples returns 0: the input is an integer, so the real answer, 0.015625, is cut down to an integer. A decimal input does not fully fix it either, because POWER(8.0, -2) returns 0.0, keeping only one digit after the point like the input. For fractional results, pass a float, like POWER(CAST(8 AS FLOAT), -2).

Also remember that PI(), EXP() and a float POWER() work with approximate numbers. The number of digits you see can differ between tools, so do not expect the last digit to match a calculator exactly.

These functions have a few friends worth knowing. LOG() is the reverse of EXP(), LOG10() is the base 10 logarithm, SQRT() gives a square root, SQUARE() multiplies a number by itself, and ROUND() helps when you want to show fewer digits. Try each one with a small value you can check in your head, and you will remember them much better.

Published by Pinal Dave on SQLAuthority. More of my work at pinaldave.com.