Find a number's distance from zero and see why its sign disappears. Its absolute value sits beside the working formula for a quick arithmetic check.
Absolute value measures distance on the number line. Distance has no direction, so |−14.6| and |14.6| are both 14.6 even though the original numbers lie on opposite sides of zero. For a connected concept in Absolute Value, see coordinate distance.
On this page, the displayed absolute value follows this definition rather than any similarly named measure.
Evaluate anything inside the absolute-value bars, locate that result on a number line, and read its distance from zero. A nonnegative result stays the same; a negative result is replaced by its opposite.
A temperature moves from 3°C to −5°C. The signed change is −8°C, while the magnitude of that change is |−8| = 8°C. Those statements answer different questions. This Absolute Value example can be compared with absolute error in a percentage.
Signed quantities turn up in temperatures, elevations, account changes, coordinates, and measurement errors. Absolute value is useful when the size of the difference matters more than whether the change was upward or downward.
Do not remove a negative sign before completing the expression inside the bars. For |4 − 11|, subtract first to get |−7|, then report 7. Also remember that −|6| is −6 because the outside minus remains.
Keep any applicable units beside the source values; the browser cannot detect a silent mismatch during absolute value.
Treat each labeled field as part of the definition, not merely an empty box. The field assignment determines what the displayed absolute value describes. Convert measured values to compatible units first and retain their original precision until the final rounding choice.
Moving the input through zero creates a sharp turning point: values approaching zero make the answer smaller, while values moving away on either side make it larger at the same rate. Predict that movement before recalculating the absolute value; disagreement points to an input-role or sign issue.
Report the absolute value at a precision justified by the inputs. A long browser decimal is computational detail, not evidence that the source values were measured that accurately. When an exact symbolic form is conventional, keep it beside the rounded value so later work is not forced to reuse an early approximation.
Absolute value is not the same as deleting every minus sign in a longer expression. It applies only to the expression enclosed by the bars after that expression has been evaluated. Here the requested quantity is specifically absolute value.
Keep the supplied input with the result, including any units and the final rounding place. The displayed formula then preserves how the absolute value was obtained.
No. A distance from zero is zero or positive.
It is 0 because zero is no units away from itself.
Only when x is nonnegative; for negative x, |x| equals −x.