Quick answer

If x < 0, multiply by −1; otherwise keep x. The answer is always ≥ 0.

Formula

  • |x| = x when x ≥ 0
  • |x| = −x when x &lt; 0

Introduction

Most calculation errors come from forgetting to flip negative inputs inside the bars. A short checklist fixes that pattern on every problem.

You can calculate |x| by hand, in a spreadsheet, or with a browser tool. All methods should agree on the same non-negative result.

The Absolute Value Calculator confirms your work in one step. Review what is absolute value for the definition, then use the absolute value formula when you need notation on paper.

Before you calculate

Circle the number inside the bars. If the expression is more complex, simplify inside the bars first before applying the sign rule, unless the problem tells you to split cases instead.

Decimals and fractions follow the same rule as integers: only the sign matters, not how many digits appear after the decimal point.

Mental math works well for small integers: |−9| = 9 is immediate. For messy decimals, paper or a calculator reduces slips.

When you want a dedicated walkthrough of the home tool itself, open the calculator article in this series from the blog index.

Tooling choices

  • Mental math for small integers
  • Paper for multi-step expressions
  • Spreadsheet: =ABS(x) in Excel or Google Sheets
  • Home calculator for messy decimals

Pick the method that matches the problem and the time you have. On tests, teachers often want written steps even if you own a calculator.

Spreadsheet ABS functions apply the same definition as |x| in algebra. They are helpful for tables when you graph y = |x|.

Build speed with varied practice values before you jump to equations where the unknown sits inside the bars.

Calculation checklist

  1. Read x. Identify the value inside | |. For |3x − 1|, you may need to simplify or solve later; for plain |−2.75|, x is −2.75.
  2. Flip if needed. Negative x becomes positive; zero and positive x stay as they are.
  3. Write |x| = answer. State the result clearly with correct notation. Include units if the word problem uses them.
  4. Optional check. Enter the same x on the home tool or re-count on a number line.

Practice prompts

Find |−2.75|. Because −2.75 < 0, flip the sign: |−2.75| = 2.75.

Find |9/16|. The value is positive, so |9/16| = 9/16.

Find |π − 4|. First π − 4 is negative (about −0.86), so |π − 4| ≈ 0.86. Two-step expressions still end with one non-negative magnitude.