Absolute Value Calculator

What this calculator does

So, you want the absolute value of a number, its size without any sign attached. This tool gives it. Enter any number, positive or negative, and it returns the absolute value, always as a number that is zero or greater.

One input, one button, and the sign is stripped away, leaving just the magnitude.

How to use it

1. Enter any number, positive, negative, or zero.
2. Press Calculate.

What absolute value means

The absolute value of a number is its size, ignoring whether it is positive or negative. It is written with two vertical bars around the number, so the absolute value of negative 7 is written as the bars around negative 7, and it equals 7. Positive numbers are left unchanged, negative numbers lose their minus sign, and zero stays zero. In short, absolute value answers the question "how big is this number?" without caring which side of zero it sits on. The result is never negative.

Distance from zero

The clearest way to understand absolute value is as a distance. Picture the number line with zero in the middle. The absolute value of a number is simply how far it sits from zero, measured as a plain distance. Negative 7 is seven steps to the left of zero, and positive 7 is seven steps to the right, but both are seven steps away, so both have an absolute value of 7. Distances are never negative, which is exactly why absolute value is never negative either. This distance picture is the idea behind everything absolute value is used for.

The simple rule

In practice the rule could not be simpler. If the number is positive or zero, its absolute value is the number itself, unchanged. If the number is negative, its absolute value is the number with the sign flipped to positive. That is the whole operation. The tool applies this directly: it reads your number and reports its distance from zero, which means dropping a minus sign if there is one and otherwise leaving the value alone.

A worked example

The absolute value of negative 7 is 7, because negative 7 is seven units from zero. The absolute value of positive 7 is also 7, since it too is seven units from zero. And the absolute value of 0 is 0, because zero is no distance from itself. Notice how the two versions of 7, one negative and one positive, collapse to the same answer once the sign is removed.

Where absolute value is used

Absolute value comes up wherever size matters but direction does not. It measures the gap between two numbers, since the distance between them is the absolute value of their difference, regardless of which is larger. It describes how far a measurement strays from a target, whether it overshoots or undershoots. It appears throughout algebra, physics, and statistics whenever a quantity should be reported as a magnitude. When an absolute value sits inside an equation to be solved rather than simply evaluated, the absolute value equation calculator handles that more involved task.

Questions people ask

What is the absolute value of a number?

Its size without a sign: how far it is from zero. The absolute value of negative 7 and of positive 7 are both 7.

Can an absolute value be negative?

No. Because it measures a distance from zero, it is always zero or greater.

What is the absolute value of zero?

Zero, since zero is no distance from itself.

How is it worked out?

A positive number or zero stays the same; a negative number has its sign flipped to positive.

What if the absolute value is inside an equation?

Then use the absolute value equation calculator, which solves equations containing an absolute value rather than just evaluating one.

References

On absolute value. The absolute value of a number is its distance from zero, and is always greater than or equal to zero.

1. Eric W. Weisstein, "Absolute Value," from MathWorld, a Wolfram resource, on the absolute value as the unsigned part of a number, never negative.
2. "More about Numbers," An Elementary Introduction to the Wolfram Language, on the absolute value, or positive part, of a number.