> For the complete documentation index, see [llms.txt](https://help.quantower.com/quantower/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://help.quantower.com/quantower/analytics-panels/chart/technical-indicators/volatility/standard-deviation.md).
# Standard deviation
## Description
Standard deviation indicator statistic measures the dispersion of a price relative to its mean (mathematical expectation) and is calculated as the square root of the variance. It is widely used in finance and trading regardless of asset class or market. For example, if trader calculates a standard deviation of his performance report as the result, he will receive the measurement of volatility of his balance and equity; the higher STD means the greater drawdown he can expect.
In the case of price movement, higher STD means higher volatility of an instrument; for example, if we compare two assets, the asset with higher standard deviation will be riskier for an investment.
## Formula
Where:\
**N** - period of calculation(number of observations)\
**x** - price value
## Most useful cases
* **Volatility measurement** - the most useful case of STD usage is to determine statistical volatility; understanding of this value is very useful to find the best positions of potential stop-loss and take-profit levels. It protects existing positions from small price fluctuations and random breakouts of levels.
* **Divergence/Convergence** - Divergence/Convergence pattern is a form of price action when a new high(low) of the price is not confirmed with a new high of STD. This is a very good approach to find a weakness in the existing trend.
---
# Agent Instructions
This documentation is published with GitBook. GitBook is the documentation platform designed so that both humans and AI agents can read, navigate, and reason over technical content effectively. Learn more at gitbook.com.
## Querying This Documentation
If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.
Perform an HTTP GET request on the current page URL with the `ask` query parameter, and the optional `goal` query parameter:
```
GET https://help.quantower.com/quantower/analytics-panels/chart/technical-indicators/volatility/standard-deviation.md?ask=&goal=
```
`ask` is the immediate question: it should be specific, self-contained, and written in natural language.
`goal` is optional and describes the broader end goal you are ultimately trying to accomplish on behalf of the user. GitBook uses it to tailor the answer towards what is most useful for that goal.
The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.
Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.