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. All of these — σ, s, SD, and STDEV — refer to standard deviation, just in different contexts.
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. Our calculator above shows each of these steps automatically when you click "Show Step-by-Step Workings".
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). The result appears as soon as you press Enter. You can also select your data and see the SD in Excel's status bar at the bottom of the screen by right-clicking and enabling "Std Dev".
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 (£), making it much more intuitive. So SD = √(Variance), and Variance = SD².
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, or the equivalent computational form σ = √(Σx²/N − μ²). 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), which is examined in A-Level Year 2 Statistics.
Neither is inherently better — it depends on your goal. In quality control (e.g. manufacturing), a lower SD is better as it means products are consistently made to specification. In investment, a lower SD means lower risk (but also potentially lower reward). In education, a very low SD might indicate all students scored similarly — which could be good (everyone learned) or bad (the test was too easy). Context always determines whether high or low SD is desirable.
The phrase "variance variance" sometimes appears in searches and typically refers to the concept of variance of the variance estimator — that is, how much the variance statistic itself varies from sample to sample. In simpler terms, it is a measure of the precision of your variance estimate. This is an advanced statistical concept. If you are at A-Level or early university level, you likely mean simply "what is variance" — which is the square of the standard deviation: Variance = σ².
=STDEV and =STDEV.S produce identical results — both calculate sample standard deviation using N−1 as the divisor. The only difference is that =STDEV.S is the updated, cleaner function name introduced in Excel 2010, while =STDEV is the legacy version kept for backwards compatibility. Microsoft recommends using =STDEV.S in newer spreadsheets, but =STDEV works in all versions including older ones.