➖ Absolute Value Calculator

What is the Absolute Value Calculator?

Absolute value answers a simple question: how far is this number from zero, ignoring which side it sits on? On a number line, -7 and 7 are both seven units away from the origin, so both have an absolute value of 7. Formally, |x| equals x when x is zero or positive, and equals -x (the negation, which makes it positive) when x is negative. The notation uses two vertical bars around the value, and you will also hear it called the modulus of a number.

The key property is that the result is never negative. |0| is 0, and for every other number the output is strictly positive. This is why absolute value shows up wherever only the size of a quantity matters and the direction does not: the gap between two temperatures, the magnitude of an error, the speed of an object regardless of which way it travels. It turns a signed quantity into a plain non-negative size.

A point that trips people up is the difference between |-x| and -|x|. The first takes the absolute value of -x, which is positive; the second takes the absolute value of x and then negates it, which is negative (or zero). The bars act on whatever sits inside them first, so |3 - 8| = |-5| = 5, not -5. When an expression appears inside the bars, evaluate the inside completely, then take the distance from zero of that result.

When to use it

• Finding how far a number is from zero, regardless of its sign, for a homework or algebra problem.
• Measuring the size of a difference or error, such as |measured - expected|, where only the magnitude matters.
• Converting a column of signed values (temperature swings, profit and loss, sensor readings) into their non-negative sizes.
• Checking your own working when simplifying an expression that contains absolute value bars.

How to use the Absolute Value Calculator

1. Type a single number into the box, for example -7, to see its absolute value.
2. Or paste a list of numbers separated by commas, spaces or new lines to convert them all at once.
3. Read the absolute value (the distance from zero) from the result panel.
4. For a list, check the per-value table that shows each input next to its absolute value.

Formula & method

Worked examples

Absolute value of common inputs

Common mistakes to avoid

• Thinking absolute value can be negative. Absolute value is a distance, so it is never negative. If you ever get a negative answer, you have likely written -|x| (negate after) instead of |x|. The result of the bars alone is always 0 or positive.
• Splitting the bars across an operation. In |a - b| you must evaluate a - b first and then take the absolute value. |3 - 8| is |-5| = 5, not |3| - |8| = -5. The bars treat everything inside as one quantity.
• Confusing |-x| with -|x|. |-x| is the absolute value of -x, which is positive. -|x| is the absolute value of x with a minus sign placed in front, which is negative or zero. They are not the same thing.
• Mixing up the bar notation with brackets. The two vertical bars |x| are not parentheses or rounding. They specifically mean distance from zero, so |2.7| stays 2.7, it does not round to 3.

Glossary

Absolute value

The distance of a number from zero on the number line, written |x|. It is always zero or positive.

Modulus

Another name for absolute value: the modulus of a number is its size with the sign removed.

Number line

A straight line where every real number has a position; absolute value measures how far a number sits from the zero point.

Magnitude

The size of a quantity ignoring its direction or sign, which is exactly what absolute value reports.

Negation

Multiplying a number by -1. For a negative number, negation produces its positive absolute value.

Frequently asked questions