What this calculator does
Find how far any number is from zero. That distance is called its absolute value. So the absolute value of −7.5 is 7.5, and the absolute value of 7.5 is also 7.5.
You can enter a number or a simple expression such as 3 − 10 × 2. You can also find the distance between two numbers. The steps show how each answer comes about.
Where it's used
Why this math matters outside the classroom:
- Bank balances. A customer with a balance of −$40 reads the absolute value, 40, as the $40 owed to the bank.
- Temperature swings. A weather student finds that a change from −3 degrees to 5 degrees is |−3 − 5|, a swing of 8 degrees.
- Elevation differences. A hiker compares a spot 20 feet below sea level with a hill 35 feet above it, a gap of 55 feet.
- Measurement error. A lab student who expected 10 grams and measured 9.6 reports an error of |9.6 − 10|, or 0.4 grams.
Grade level and standards: Grades 6–7; Common Core State Standards for Mathematics 6.NS.C.7.c, 7.NS.A.1.c. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.
How to use it
- Choose a number, an expression, or the distance between two numbers.
- Type your values. Expressions can use + − × ÷ and brackets.
- Read the absolute value and where the number sits on a number line.
What the inputs mean
- Expression
- You can type * for times and / for divide. Letters aren't accepted, so this doesn't solve equations such as |x − 2| = 5.
Formula and method
|x| = x when x is 0 or more |x| = −x when x is less than 0 distance between a and b = |a − b|
The two straight bars mean absolute value, and x stands for any number. If x is already 0 or positive, it stays the same. If x is negative, the formula takes its opposite, which removes the minus sign.
The distance formula subtracts the numbers and then takes the absolute value. That's why the order doesn't matter. Going from −3 to 5 is the same length of trip as going from 5 to −3.
Worked example
You want the absolute value of 3 − 10 × 2.
- Multiply first: 10 × 2 = 20.
- Then subtract: 3 − 20 = −17.
- Drop the minus sign: |−17| = 17.
Result: The absolute value is 17. In the same way, |−7.5| = 7.5, and −3 and 5 are 8 apart.
Understanding the result
An absolute value is never negative. It measures size, not direction. A $20 debt and a $20 credit are on opposite sides of zero, but both have a size of 20.
Only 0 has an absolute value of 0. Every other answer has two numbers that could produce it, one on each side of zero.
Assumptions and limitations
- Expressions follow the usual order: brackets, then times and divide, then plus and minus, left to right.
- It works with plain numbers only. It doesn't solve equations or inequalities with a variable.
- Powers, roots and nested absolute value bars aren't accepted in expressions.
Frequently asked questions
Can an absolute value be negative?
No. It's a distance, and a distance can't be below zero. But −|5| is −5, since the minus sign sits outside the bars.
What's the absolute value of 0?
It's 0, because 0 is no distance from itself.
Is |a − b| the same as |b − a|?
Yes. The two differences are opposites, so they have the same size.
Do I work out what's inside the bars first?
Yes. The bars act like brackets. So |3 − 10| is |−7|, which is 7. It isn't 3 + 10.
How this calculator is checked
Method: Definition of absolute value. The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-31. Found a problem? Tell us.
Embed this calculator
Put this Absolute Value Calculator on your own website or blog for free. Paste this code where you want it to appear: