This article throws light on volatility and how to measure it. It says volatility measures the degree to which a stock price moves. It also states that:
Standard Deviation is the most widespread measure of volatility used by traders and analysts. It explains how Standard Deviation is calculated.
A technical indicator called Bollinger Bands is used by chartists to analyze Standard Deviation over time. It also explains how the width of the Bollinger Band measures volatility.
Beta is a measure of a security's volatility relative to the wider market and how it's value determines volatility.
Volatility is measured as a the standard deviation of the stock. We have a 3 part series on Zerodha Varsity, explaining Volatility and its application in detail. Request you to check the same -
Part 1 - What is Volatility and how is it measured
Part 2 - Volatility & normal distribution
Part 3 - Volatility application
This is very clear and elaborately poised.