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Understanding the math.sqrt() Function in Pine Script

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The math.sqrt() function in Pine Script is a fundamental mathematical operation used to calculate the square root of a number. The square root of any non-negative number (x) is a unique non-negative value (y) such that (y^2 = x). This function is versatile and can handle various types of inputs, making it essential for financial analysis, especially when dealing with volatility or other calculations requiring square roots.

Syntax and Overloads

Pine Script provides several overloads of the math.sqrt() function to accommodate different data types and contexts within your scripts:

  • math.sqrt(number) → const float
  • math.sqrt(number) → input float
  • math.sqrt(number) → simple float
  • math.sqrt(number) → series float


  • number (const int/float): This argument represents the number from which the square root will be calculated. The function is designed to work with both constant and variable inputs, allowing for flexibility in scripting.


The math.sqrt() function returns the square root of the provided number as a floating-point value. Depending on the context of the input, the return type can vary among constant float, input float, simple float, and series float.


Let’s consider a simple example to demonstrate the use of math.sqrt() in Pine Script. Suppose we want to calculate the square root of a series of closing prices in a trading strategy. We could use the math.sqrt() function as follows:

indicator("Square Root Example", overlay=true)

// Calculate the square root of the closing price
sqrtClosePrice = math.sqrt(close)

plot(sqrtClosePrice, title="Square Root of Close Price", color=color.blue)

In this example, we calculate the square root of the closing price (close) using math.sqrt(close) and plot the result on the chart. This simple illustration shows how math.sqrt() can be applied to series data, which is common in financial time series analysis.

Understanding the Code

  • Version Declaration: //@version=5 specifies that the script uses version 5 of Pine Script, ensuring compatibility with the latest features and syntax of the scripting language used on the TradingView platform.
  • Indicator Declaration: indicator("Square Root Example", overlay=true) declares a new indicator named “Square Root Example”. The overlay=true parameter indicates that this indicator will be drawn directly on top of the price chart, as opposed to in a separate panel.
  • Square Root Calculation: sqrtClosePrice = math.sqrt(close) calculates the square root of the closing price for each bar on the chart. The math.sqrt() function is used to compute the square root, and close represents the closing price of each bar.
  • Plotting: plot(sqrtClosePrice, title="Square Root of Close Price", color=color.blue) plots the calculated square root of the closing price on the chart. The plotted line is titled “Square Root of Close Price” and is colored blue for clear visualization.

Key Features and Takeaways

  • Versatility: The math.sqrt() function supports various types of inputs, including constant, input, simple, and series data types.
  • Essential for Analysis: It’s crucial for calculating volatility, standard deviation, and other metrics requiring the square root operation in financial analysis.
  • Syntax Flexibility: Pine Script’s handling of different data types through overloads allows script developers to apply mathematical operations like square root calculation across diverse scenarios.

This function exemplifies Pine Script’s ability to incorporate fundamental mathematical operations seamlessly into financial indicator and strategy development, providing traders and developers with powerful tools for technical analysis.

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