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Enter a real or complex number to instantly calculate its absolute value (modulus).
Enter multiple numbers, separated by newlines, commas, or spaces. Each will be calculated individually.
Enter numbers to see absolute value results.
Overview
Understand what the tool solves, how it works, and the boundaries of its data.
The absolute value of a real number tells how far it is from zero on the number line, without keeping its direction. It is written with vertical bars: |x|. The rule is |x| = x when x ≥ 0, and |x| = −x when x < 0. So |−4.5| = 4.5, |4.5| = 4.5, and |0| = 0. The output is always nonnegative. OpenStax’s algebra text presents this piecewise definition and the number-line interpretation. The calculation uses the numbers you enter; it does not need a lookup table or external data.
Enter one real number to see its absolute value. Enter several numbers to get a value for each item, plus a separate sum of those absolute values. For example, −3, 2.5, 0 produces 3, 2.5, and 0; the displayed total is 5.5. This is |−3| + |2.5| + |0|, not the signed sum of the original inputs (which is −0.5).
Guide
Follow the workflow and verify inputs and outputs with practical examples.
Use a minus sign for negative values. Separate list entries with commas, spaces, semicolons, or line breaks; for instance, put one value on each line or enter −8, 3.14, 0.
Each separated entry is read as a single numeric value. If you want the absolute value of 3 − 5, first work out that expression and enter −2. A fraction such as −2/8 is not evaluated as division; enter its decimal value, −0.25.
For one value, the result is shown with a copy control. For multiple values, review the item-by-item results and the sum beneath them; the copy control copies the absolute values as a line-separated list. The solution steps show whether each value stays the same or changes sign.
A nonnegative input stays unchanged: |2.5| = 2.5. A negative input is replaced by its opposite: |−3| = −(−3) = 3. For a list, the final step adds the resulting nonnegative values. Absolute value does not round a decimal to an integer: |−3.14| = 3.14.
Use cases
See how the tool fits into real work and everyday tasks.
A student can enter positive values, negative values, and zero on separate lines, then compare each output with the rule for distance from zero.
If a list already contains signed deviations from a target, enter those deviations to see each magnitude and their combined magnitude. If you have target and measured values instead, subtract first; the list tool does not find those differences for you.
Paste a whitespace-, comma-, or semicolon-separated group to produce a corresponding list of magnitudes. The additional total can help answer “what is the sum of these absolute values?”
Q&A
Find concise answers to common questions and confusing cases.
It adds the absolute value of each valid entry. For −3, 2.5, 0, the individual outputs are 3, 2.5, and 0, and their total is 5.5.
No. The input is parsed as separate real-number values; it does not evaluate operations such as 3−5 or parse complex notation such as 3+4i. Calculate an expression first and enter its real-number result.
Items that do not parse as finite numbers are skipped. If nothing in the input parses as a number, there is no result to display. Check separators and remove labels or other text before pasting a list.
Numbers are handled with ordinary JavaScript numeric values and formatted for display. Ecma International’s specification states that integer values above 9,007,199,254,740,991 are not guaranteed to be represented exactly or distinguished from neighboring integers. See the precision note in “Notices” before relying on large integer results.
Notes
Review scope, result limitations, and important precautions before use.
This page calculates numerical absolute values; it does not solve absolute-value equations or inequalities, simplify algebra, calculate the distance between two values, or find complex moduli. List inputs are summed after each entry is made nonnegative. Display formatting can shorten decimal output, and very small or very large finite values may use scientific notation. For integers beyond 9,007,199,254,740,991, distinct source integers may no longer be represented distinctly by the underlying numeric format; the ECMAScript 2025 specification documents this safe-integer boundary. Use an exact-arithmetic method when every digit or strict decimal precision matters.
The sources above were checked on September 29, 2026. OpenStax supports the real-number definition; Ecma International’s 2025 specification supports the numeric precision boundary.
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