i What this calculator does
This calculator works out the standard deviation, variance, and mean from your entered data points, using the sample standard deviation formula commonly applied to financial returns.
Enter up to five data points, and the calculator returns the mean, variance, and standard deviation, a foundational concept behind volatility measurement in trading.
This calculator is for educational purposes only and uses sample standard deviation (n-1). Not financial advice.
How to use the Standard Deviation Calculator
It works immediately. Change one value, leave the others, and the difference belongs to that change.
- 1. Value 1
- 2. Value 2
- 3. Value 3
- 4. Value 4
- 5. Value 5
The result panel reports:
- Standard Deviation Sample std dev (n-1)
- Variance Std dev squared
- Mean Average of all values
Alongside the headline figures, the calculator reports standard deviation, variance, mean, coefficient of variation. Those are the numbers that usually explain why the headline result came out where it did.
Beneath the result the calculation is broken out in order, so nothing about the method is hidden.
One caution worth stating. A calculator answers exactly the question you pose to it, and the quality of the answer is set entirely by the inputs. Figures taken from a single period, an optimistic forecast, or a sample too small to be meaningful will produce a precise number that is not a reliable one. Where the result will inform a real decision, run it at several plausible inputs and treat the spread as the answer rather than any single figure.
The same applies to comparisons. A figure is informative against a benchmark, a sector average or the same measure over the company's own history, and much less so on its own. That context is what turns a number into a judgement.
Frequently asked questions
What does a high standard deviation actually tell me?
A high standard deviation means your data points (like prices or returns) are widely spread from the average, in trading, this generally indicates higher volatility, a low standard deviation means values cluster tightly around the mean, indicating lower volatility.
Does this calculator use population or sample standard deviation?
This calculator uses sample standard deviation, dividing by n-1 rather than n, which is the more commonly used convention for financial data since you're typically working with a sample of returns, not the entire population.
How is standard deviation related to Bollinger Bands?
Bollinger Bands are calculated by adding and subtracting a multiple of standard deviation from a moving average, use this calculator to find your standard deviation first, then apply it in our dedicated Bollinger Bands Calculator.
Why do I need at least a few data points for a meaningful result?
Standard deviation with very few data points can be significantly skewed by a single unusual value, more data points generally produce a more statistically reliable and representative measure of genuine variability.
How does standard deviation relate to the Sharpe Ratio?
Standard deviation is the risk (denominator) component of the Sharpe Ratio formula, a lower standard deviation for the same return produces a higher, more favourable Sharpe Ratio, use our dedicated Sharpe Ratio Calculator to combine both.
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