What is absolute value?

The absolute value of a number is its distance from zero on the number line, always expressed as a non-negative number. Written with vertical bars as |x|, it strips the sign: |7| equals 7 and |-7| also equals 7. The absolute value of zero is zero.

How do you calculate the absolute value of an expression like |3 minus 10|?

You evaluate the expression inside the bars first: 3 minus 10 equals -7. Then you take the absolute value of -7, which is 7. The absolute value bars act like brackets, so you always resolve what is inside them before applying the modulus.

What is the difference between absolute value and absolute error?

Absolute value is the mathematical operation |x| that returns the non-negative magnitude of any number. Absolute error is a specific application of absolute value used in measurement: it is the absolute value of the difference between a measured value and the true value, |measured minus true|. The absolute value calculator on this page handles both, since the difference mode computes |a minus b|.

Absolute Value Calculator

The absolute value of a number is its distance from zero on the number line, always returned as a non-negative quantity regardless of whether the original number is positive or negative. Written with vertical bars as |x|, it simply strips the sign: |7| equals 7, |-7| also equals 7, and |0| is 0. This idea scales up naturally: |3 minus 10| equals |-7| equals 7, which is the absolute difference between 3 and 10, or equivalently the distance between those two points on the number line. This calculator handles both uses. In single-number mode you enter one value and get back its absolute value, its distance from zero, and the sign of the original number. In difference mode you enter two numbers and the calculator evaluates the absolute value of their difference, |a minus b|, which is the same as the distance between a and b regardless of order. You can enter negative numbers, decimals, and zero in either field. The absolute value concept appears throughout mathematics and its applications: in error analysis it measures how far a measurement deviates from the truth; in statistics it appears in mean absolute deviation; in geometry it gives distances; in programming it is a built-in function for handling magnitudes. This tool is useful for students learning about absolute value for the first time, for checking arithmetic, and for quickly computing absolute differences between two quantities. It does not evaluate general algebraic expressions such as |x squared minus 5|; for those you would substitute a numeric value for x first.

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Number (or first value a)

Second value b (optional, for |a − b|)

7.5

absolute value

Distance from zero7.5

Sign of inputNegative

Expression| −7.5 |

Leave the second field blank for a single absolute value. Enter both fields to compute |a − b|, the distance between two numbers.

How it works

When only one value is entered the calculator returns Math.abs(a), which is a if a is positive or zero, or -a if a is negative. The distance from zero is identical to the absolute value. The sign label reports Positive, Negative, or Zero based on the original input. When a second value b is entered, the calculator computes |a minus b|: it subtracts b from a and then takes the absolute value of the result. This is commutative, meaning |a minus b| always equals |b minus a|, so the order you enter the values does not affect the distance result.

Worked example

Using the default value a = -7.5 with no second value: |-7.5| = 7.5. The number is 7.5 units from zero on the number line. The original number is negative. To also demonstrate the difference mode: enter a = 3 and b = 10 to get |3 minus 10| = |-7| = 7, confirming the distance between 3 and 10 is 7 units.

Related calculators

Absolute Error Calculator: apply absolute value to the difference between a measured and true value.
Percent Error Calculator: express that absolute error as a percentage of the true value.
Discriminant Calculator: classify quadratic roots using b squared minus 4ac.
Proportion Calculator: solve a/b = c/d for any missing value.

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