Absolute Value Calculator

The absolute value calculator returns |x| for any real number the instant you type it. Absolute value is the distance of a number from zero on the number line — always a non-negative quantity, no matter which direction you count. Enter a positive or negative value and the tool strips the sign, keeps the magnitude, and plots the result on a visual number line so you can see a negative input reflected onto its positive twin.

Definition: |x| = x when x ≥ 0, and |x| = −x when x < 0. The result is never negative, and |0| = 0.

Where Absolute Value Is Used

Measuring Distance

The gap between two values is |a − b|, so the order of the numbers never makes the distance negative.

Errors & Deviations

Absolute error |measured − actual| ignores whether you over- or under-shot, focusing only on magnitude.

Programming & Physics

Speed from velocity, vector magnitudes, and tolerance checks all rely on the absolute value, written abs(x) in most languages.

How to Find |x| Step by Step

Enter Any Real Number

Type a positive or negative value — integers and decimals are both accepted. The calculation runs live as you type, with no submit button.

Read the Result

The formula line updates to show |x| = and the non-negative result appears below it instantly.

See It on the Number Line

The visual marks your original number and its absolute value, showing how a negative input is reflected across zero to its positive counterpart.

Key fact: |−5| and |5| both equal 5 — opposite numbers share the same absolute value because they sit the same distance from zero.

Calculator Features

Real-Time Calculation

Results appear the moment you type — no submit button and no page reload.

Visual Number Line

A clear diagram marks the original point, zero, and the reflected absolute value; the result point is hidden when the input is already non-negative.

Decimals & Negatives

Accepts any real number — fractional values and negatives alike — and shows results to up to 10 decimal places.

Private by Design

Every calculation runs in your browser — nothing is uploaded to a server.

Worked Examples

Expression	Result	Why
\|−7\|	7	−7 is 7 units from zero
\|7\|	7	Already non-negative, unchanged
\|−3.5\|	3.5	Decimals work the same way
\|0\|	0	Zero is its own absolute value
\|−100\|	100	Sign removed, magnitude kept

Private by design: all math is computed locally in your browser — your numbers never leave your device.

Absolute Value Questions Answered

What is absolute value?

Absolute value |x| is the value of x without regard to its sign. Geometrically it is the distance from zero on a number line, so it answers "how far?" rather than "which direction?".

How do you calculate the absolute value of a number?

Drop the sign and keep the magnitude: if the number is negative, remove the minus; if it is zero or positive, leave it unchanged. So |−8| = 8 and |8| = 8. In code the same operation is written abs(x).

Can absolute value be negative?

No. Absolute value is always non-negative (≥ 0). The only number whose absolute value is exactly 0 is zero itself; every other number gives a strictly positive result.

Why do |−5| and |5| give the same answer?

Both −5 and 5 sit exactly 5 units away from zero — one to the left, one to the right. Because absolute value measures distance only, opposite numbers always share the same absolute value.

Does it work with decimals?

Yes. Any real number is accepted, including decimals such as −3.5. The calculator removes the sign and keeps the magnitude, so |−3.5| = 3.5.

What is the difference between absolute value and modulus?

For a real number they mean the same thing — "modulus" is just another name for absolute value, so |x| and the modulus of x are identical. This tool works with real numbers; it finds |x| of a value rather than solving absolute-value equations.