# Absolute Value Calculator

## 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

1. Definition of Absolute Value:
• |x| = x if x is greater than or equal to 0.
• |x| = -x if x is less than 0.
2. Triangle Inequality:
• |x + y| ≤ |x| + |y| for all real numbers x and y.
3. Absolute Value of a Product:
• |x * y| = |x| * |y| for all real numbers x and y.
4. Absolute Value of a Quotient:
• |x / y| = |x| / |y| for all real numbers x and y, where y is not equal to 0.
5. Absolute Value of an Absolute Value:
• | |x| | = |x| for all real numbers x.
6. Absolute Value of a Difference:
• |x – y| = |y – x| for all real numbers x and y.
7. Absolute Value of the Opposite:
• |-x| = |x| for all real numbers x.
8. Absolute Value of a Sum (Reverse Triangle Inequality):
• |x + y| ≥ |x| – |y| for all real numbers x and y.
9. Absolute Value and Inequality:
• If |x| < a, then -a < x < a for some positive real number a.
10. 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:

1. 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.
2. 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.
3. 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.
4. 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.
5. 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

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