Absolute Value Calculator

Category: Algebra and General
- October 22, 2025
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Calculate the absolute value of numbers. The absolute value of a number is its distance from 0 on the number line, regardless of direction (positive or negative).

Absolute Value Calculation

Calculate the absolute value of a single number (e.g., |x|).

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About Absolute Value

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is denoted by vertical bars around the number or expression, such as |x|.

Definition and Properties
  • Definition: |x| = x if x ≥ 0, and |x| = -x if x < 0
  • Non-negativity: |x| ≥ 0 for all x
  • Symmetry: |-x| = |x| for all x
  • Triangle inequality: |x + y| ≤ |x| + |y| for all x, y
  • Multiplicative property: |xy| = |x| · |y| for all x, y
Solving Absolute Value Equations

When solving an equation like |x| = a (where a > 0), there are two possible solutions:

  • x = a (the positive solution)
  • x = -a (the negative solution)

For more complex forms like |ax + b| = c (where c > 0), we get:

  • ax + b = c
  • ax + b = -c

Then solve each equation for x.

Solving Absolute Value Inequalities

There are two main types of absolute value inequalities:

  • |x| < a means x is between -a and a: -a < x < a
  • |x| > a means x is less than -a or greater than a: x < -a or x > a

What is the Absolute Value Calculator?

The Absolute Value Calculator is a handy tool that helps you find the absolute value of numbers or expressions. But what does "absolute value" mean? It’s simply the distance of a number from zero on the number line, regardless of whether it's positive or negative. For example, the absolute value of -5 is the same as the absolute value of 5, both equal to 5. This calculator allows you to explore different scenarios involving absolute values easily.

Calculate Single Values with Ease

One of the coolest features of the Absolute Value Calculator is its ability to compute the absolute value of a single number. You just need to enter a number, like -3 or 7, and the calculator will reveal the absolute value instantly. This is perfect for anyone studying basic Math or needing a quick reference for homework.

Work with Expressions Involving Absolute Values

The calculator also lets you evaluate complex expressions containing absolute value notation. For instance, you can input something like 2|x - 3| + 5. All you need to do is enter the expression and the value of x, and you'll get the result. This is especially useful for students tackling algebra homework or anyone dealing with equations that include absolute values.

solve equations with Absolute Values

Another fantastic function is solving equations that include absolute values, like |x| = 5. This calculator can help you find the possible solutions quickly. Since absolute value equations can have two solutions (positive and negative), you can easily see both results using this tool. It’s great for those learning to tackle equations in algebra.

Double Absolute Values Made Simple

If you’re curious about double absolute values, the Absolute Value Calculator has you covered too. By entering a number like -7.5, you can find the double absolute value, which is useful in various mathematical contexts. This feature allows for deeper exploration into the properties of absolute values and their applications.

Customise Your Results

The calculator also has advanced options to customise how results are displayed. You can choose how many decimal places you want, and even decide whether you want to see the calculation steps shown. This means you can tailor your experience to fit your learning style, making it easier to understand the steps taken to reach the result.

Visual Representation of Absolute Values

To further aid in understanding, the Absolute Value Calculator provides a visual representation of the results on a number line. This shows where the values are located, allowing you to see the distance from zero visually. It’s a fantastic way to grasp the concept of absolute value better, especially for visual learners.

Learn More About Absolute Value

Lastly, the calculator includes educational content about absolute value. It covers definitions, properties, and how to solve absolute value equations and inequalities. This means you not only get results but can also deepen your understanding of the concepts behind them. It's perfect for students or anyone wanting to brush up on their math skills.