# Standard Deviation to Variance Calculator

Standard Deviation s=

### Solution:

Enter the Standard Deviation in the above Box.
Next, press Solve to find the Variance.

### What is the difference between Variance and Standard Deviation?

Both Variance and Standard Deviation are Measures of Spread in Statistics.
The Variance is the Sum of the Squared Differences between the given Data and their Mean.
Taking the Square-Root of the Variance then gives the Standard Deviation. The Standard Deviation tells us by how much the data differ from the mean, the average distance from the mean. As formulas:

### Example for computing both Variance and Standard Deviation?

Say we are given 2,3,4 . Their mean is 3 since {2+3+4 \over 3} = 3 .
The Squared Differences between the data and mean are
(2-3)^2 + (3-3)^2 + (4-3)^2 = 1+0+1=2 .
Dividing that by the number of data points, here 3, yields s^2=2/3=0.666 as the variance.
Finally, take the Square Root of the Variance to find the Standard Deviation s= \surd (0.666)=0.81649658092 .

### How do you find Variance from Standard Deviation?

To find Variance we have to Square the Standard Deviation.
Reason: Standard Deviation is s , the Variance is s^2 .

### How do you find Standard Deviation from Variance?

To find Standard Deviation we have to take the Square Root of the Variance.
Reason: The Variance is s^2 , the Square of the Standard Deviation is s .

### What is the Difference between Population Variance and Sample Variance?

When computing Population Variance we divide by the Population Size N (as shown in the image above).
When computing Sample Variance we divide by the Sample Size N-1 instead (for technical reasons) .