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Absolute Value Calculator

Instantly find |x| — the absolute value of any number, free.

Privacy: your files never leave your device. All processing happens locally in your browser.

How to use

  1. 1.Type any number into the input — negatives, decimals, and scientific notation like 1.2e4 are all accepted.
  2. 2.Read the absolute value |x| instantly in the result panel; it updates live as you edit, with no button to press.
  3. 3.Click Copy to put the result on your clipboard for homework, spreadsheets, or code.

About Absolute Value Calculator

The absolute value of a number is its distance from zero on the number line, written with vertical bars as |x|. Because distance is never negative, the absolute value is always zero or positive: |x| ≥ 0 for every real number x. This calculator returns |x| the moment you type a value — enter -8 and you get 8, enter 8 and you still get 8, enter 0 and you get 0.

The rule is simple. If x is positive, |x| = x (the number keeps its value). If x is negative, |x| = -x (the minus sign is dropped, which flips it to positive). If x is zero, |x| = 0. Formally, |x| = x when x ≥ 0 and |x| = -x when x < 0. A useful shortcut is |x| = √(x²): squaring removes the sign and the principal square root returns the non-negative root, giving the same answer.

Absolute value answers “how far,” not “which direction,” which makes it the natural tool for magnitude. In measurement, the absolute error between a measured value and a true value is |measured - true|; the sign tells you whether you over- or under-shot, but the size of the mistake is the absolute value. In geometry, the distance between two points a and b on a line is |a - b|, and the order of subtraction never changes the result. In physics and engineering, speed is the magnitude of velocity and amplitude is the absolute peak of a signal — both strip direction and keep size. Absolute value also defines the bars in inequalities like |x - 5| < 2, which describes every number within 2 units of 5, and it powers the L1 (Manhattan) distance and the mean absolute error used throughout statistics and data science.

This tool accepts any real number: whole numbers, decimals such as -3.14, and scientific notation such as 1.2e-4 or 6.02e23. It computes entirely in your browser, so nothing is uploaded and the result updates live as you edit. Very large inputs up to about 1.8 × 10^308 are supported; anything beyond that exceeds the range a computer can store and is flagged instead of silently rounding.

A few facts worth remembering: absolute value can never be negative, |x| = |-x| always (a number and its opposite share one absolute value), and |x| = 0 only when x itself is 0. Use the tool below to check homework, verify an error margin, or find a distance — type a number and read |x| straight from the result.

Frequently asked questions

What is the absolute value of a negative number?
Drop the minus sign and keep the digits: the absolute value of a negative number is its positive counterpart. For example, |-5| = 5 and |-3.14| = 3.14. Because absolute value measures distance from zero, a negative number and its positive twin (-5 and 5) share the same absolute value.
What is the absolute value of 0?
|0| = 0. Zero sits exactly at the origin of the number line, so its distance from zero is zero. It is the only number whose absolute value equals the number itself, and it is neither positive nor negative.
Can an absolute value be negative?
No. Absolute value is a distance, and distance is never negative, so |x| ≥ 0 for every real number. If an expression seems to give a negative absolute value, such as -|x|, the minus sign is applied outside the bars after the absolute value has already been taken.
How do you calculate absolute value by hand?
Check the sign of the number. If it is positive or zero, the absolute value is the number unchanged. If it is negative, remove the minus sign. Equivalently, compute √(x²), which squares the sign away and returns the non-negative root.
When do you use absolute value in real life?
Anytime you need size without direction. Common cases are measurement error |measured - true|, distance between two points |a - b|, the magnitude of a temperature or price change, and signal amplitude. Each one ignores whether the change was up or down and reports only how big it was.

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