Standard Deviation Calculator

Use Population σ when you have data for an entire group. Divides by N.

Population SD (σ)
Variance (σ²)
Mean
Count (N)
Sum
Range
Min
Max

Frequently Asked Questions

What is the symbol for standard deviation?

The symbol for population standard deviation is σ (lowercase Greek letter sigma). For sample standard deviation, the symbol is s. In casual writing and medical journals, you will often see SD written out. In Excel, the function names use STDEV as the abbreviation.

How do you figure out standard deviation by hand?

To calculate standard deviation manually: (1) Find the mean by adding all values and dividing by the count. (2) Subtract the mean from each value, then square each result. (3) Add up all the squared values. (4) Divide by N (for population) or N−1 (for sample) to get the variance. (5) Take the square root of the variance. This gives you σ or s respectively.

How do I calculate standard deviation in Excel?

In Excel, type =STDEV(A1:A10) in any empty cell, replacing A1:A10 with your data range. This returns the sample standard deviation (divides by N−1). For population standard deviation, use =STDEVP(A1:A10) or the newer =STDEV.P(A1:A10).

What is variance vs standard deviation?

Variance (σ²) is the average of the squared differences from the mean. Standard deviation (σ) is the square root of variance. The key difference is units: if your data is in pounds (£), the variance is in pounds-squared (£²) — which is hard to interpret — while the standard deviation is back in pounds (£).

What is standard deviation in A-Level maths?

In A-Level Statistics, standard deviation measures the spread of a distribution. You use the formula σ = √(Σ(x − μ)² / N) for population SD. A-Level also covers the normal distribution N(μ, σ²), where σ directly determines the width of the bell curve. Sample SD uses N−1 as divisor (Bessel's correction).

Is a higher or lower standard deviation better?

Neither is inherently better — it depends on your goal. In quality control, a lower SD is better as it means products are consistently made to specification. In investment, a lower SD means lower risk. Context always determines whether high or low SD is desirable.

MB

Written by Mustafa Bilgic — UK Statistics Specialist

Mustafa specialises in statistics, data analysis, and financial mathematics for UK audiences. This calculator and guide are reviewed for accuracy against ONS statistical methodology and A-Level curriculum requirements.

Understanding Standard Deviation

Standard deviation is a statistical measure that quantifies the amount of variation or dispersion in a set of data values. A low standard deviation means data points cluster closely around the mean, while a high standard deviation indicates data is spread over a wider range.

How It Is Calculated

The calculation involves finding the mean of your data set, then determining how far each value deviates from that mean. These deviations are squared, averaged, and then the square root is taken. Population standard deviation uses all data points, while sample standard deviation divides by (n-1) instead of n to account for sampling bias.

Practical Applications

Finance: Standard deviation measures investment volatility. A stock with a high standard deviation has unpredictable returns, representing higher risk. Portfolio managers use it to balance risk and return.

Quality Control: Manufacturing processes use standard deviation to ensure products fall within acceptable tolerance ranges. The Six Sigma methodology aims for no more than 3.4 defects per million opportunities.

Education: Exam results with a small standard deviation indicate most students scored similarly, while a large standard deviation shows a wide spread of achievement levels.

Enter your data values into this calculator to instantly compute the mean, variance, and standard deviation for both population and sample data sets.

Official Sources

Data verified against official UK government sources. Last checked April 2026.