Quick answer

Enter a real number x; the tool displays |x|, which is always ≥ 0.

Formula

  • |x| = x if x ≥ 0
  • |x| = −x if x < 0

Introduction

A dedicated calculator saves time when decimals are long or you want a fast homework check. It is not a substitute for understanding the piecewise rule, but it is an honest verifier.

Browser tools are useful when you are learning: you can test many inputs in a row and watch the pattern that negative values flip while positive values stay.

The Absolute Value Calculator lives on the home page at the calculator anchor. For manual steps first, see how to calculate absolute value. When you need many worked cases, open absolute value examples.

What the calculator does

It applies the standard definition: non-negative inputs stay, negative inputs flip, zero stays zero. The output is always ≥ 0.

Nothing is sent to a server. Your number stays on your device, which makes it useful for quick classroom checks and privacy-conscious study sessions.

The tool focuses on |x| for a single real input. Solving |x| = 5 or graphing y = |x − 2| still belongs on paper, with the calculator used to test candidate values.

Treat the display as the final magnitude. If your hand work disagrees, re-read the sign of the input before you change the formula.

Same math as your textbook

  • Input: any real x
  • Output: |x| ≥ 0
  • Rule: x if x ≥ 0, −x if x < 0

The tool does not replace understanding; it confirms arithmetic. Use it after you attempt the problem so your brain still does the thinking first.

Compare calculator output with your piecewise work line by line. Matching results build trust; mismatches usually mean a sign error inside the bars.

Pair numeric checks with the piecewise definition on paper so you know why the output is correct, not only that it matches.

Using the tool

  1. Open the home page. Scroll to the calculator section or follow the #calculator link from this article.
  2. Enter x. Type an integer, decimal, or fraction the field accepts. Try negatives on purpose.
  3. Read |x|. Compare the output to your paper work. If they differ, revisit the sign rule.
  4. Retry with new values. Test negatives, zero, large positives, and small decimals to build intuition.

Sample sessions

Enter x = −18.7. The tool should display |−18.7| = 18.7, matching the sign-flip rule.

Enter x = 0. Enter x = 1/3 if the field allows fractions. Each session should take only seconds.

After solving |x| = 12 on paper, test x = 12 and x = −12 in the tool to see both magnitudes are 12.