## What is Absolute Value?

The absolute value of a real number is a measure of its distance from zero on the number line. It is denoted by two vertical bars enclosing the number and is written as |x|, where “x” is the real number. The absolute value of a number is always non-negative (greater than or equal to zero).

## All Formulae Related to Absolute Value

**Definition of Absolute Value**:- |x| = x if x is greater than or equal to 0.
- |x| = -x if x is less than 0.

**Triangle Inequality**:- |x + y| ≤ |x| + |y| for all real numbers x and y.

**Absolute Value of a Product**:- |x * y| = |x| * |y| for all real numbers x and y.

**Absolute Value of a Quotient**:- |x / y| = |x| / |y| for all real numbers x and y, where y is not equal to 0.

**Absolute Value of an Absolute Value**:- | |x| | = |x| for all real numbers x.

**Absolute Value of a Difference**:- |x – y| = |y – x| for all real numbers x and y.

**Absolute Value of the Opposite**:- |-x| = |x| for all real numbers x.

**Absolute Value of a Sum (Reverse Triangle Inequality)**:- |x + y| ≥ |x| – |y| for all real numbers x and y.

**Absolute Value and Inequality**:- If |x| < a, then -a < x < a for some positive real number a.

**Absolute Value and Squaring**:- |x|² = x² for all real numbers x.

## Applications of Absolute Value Calculator in Various Fields

Absolute value calculators, or calculators that can compute the absolute value of a number, are useful tools in various fields for performing calculations and solving problems. Here are some applications of absolute value calculators in different areas:

**Mathematics**:- Solving equations and inequalities that involve absolute values.
- Calculating distances and magnitudes in geometry and trigonometry.
- Analyzing sequences and series, such as finding the absolute values of terms in a sequence.

**Physics**:- Calculating the magnitude of vectors and complex numbers.
- Analyzing physical quantities, such as displacement, velocity, and acceleration.
- Solving problems related to wave amplitudes and electrical potentials.

**Engineering**:- Analyzing signals and waveforms in electrical and electronic circuits.
- Evaluating errors and uncertainties in measurements and calculations.
- Assessing the magnitude of forces and stresses in structural engineering.

**Computer Science**:- Implementing algorithms that involve absolute values, such as sorting algorithms.
- Evaluating differences and distances between data points in machine learning and data analysis.
- Handling boundary conditions and edge cases in software development.

**Statistics**:- Calculating measures of dispersion, such as the standard deviation.
- Assessing the magnitude of errors or residuals in regression analysis.
- Analyzing data distributions and outliers.

Last Updated : 27 February, 2024

Sandeep Bhandari holds a Bachelor of Engineering in Computers from Thapar University (2006). He has 20 years of experience in the technology field. He has a keen interest in various technical fields, including database systems, computer networks, and programming. You can read more about him on his bio page.

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