Absolute Value Calculator
Absolute Value Calculator
Find the absolute value of any positive number, negative number or zero. Absolute value measures distance from zero and is never negative.
Enter your values
Enter a number and select Calculate.
Absolute Value Calculator: Find the Absolute Value of a Number
Use this free absolute value calculator to find the absolute value of a positive number, negative number, decimal or zero. The absolute value of a number is its distance from zero on the number line, regardless of direction. It is always zero or positive, so a negative input produces a positive result while a positive input stays unchanged.
This absolute value finder is useful for maths homework, algebra, comparing numbers, understanding distance, and checking calculations involving positive and negative values. Simply enter your number to calculate its absolute value instantly.
What is absolute value?
Absolute value describes how far a number is from zero on the number line. Distance cannot be negative. For example, −8 is eight units to the left of zero and 8 is eight units to the right. Both numbers are eight units away from zero, so both have an absolute value of 8.
Absolute value formula
The absolute value of x is written as |x| and is defined using two cases:
|x| = −x, when x < 0
In simple terms, keep a non-negative number as it is. If the number is negative, change its sign to obtain its non-negative magnitude. The result can never be less than zero.
Examples of absolute value calculations
|−12| = 12. The number −12 is 12 units away from zero.
|4.75| = 4.75. A positive input remains unchanged.
|0| = 0. Zero has no distance from itself.
|−3.6| = 3.6. The negative sign is removed while the magnitude remains 3.6.
How to use this absolute value calculator
- Enter the number in the Number field. You can enter a positive number, negative number, decimal or zero.
- Select Calculate to find its absolute value.
- Read the result displayed below the calculator buttons.
- Select Clear to remove the current entry and calculate another number.
Absolute value rules and properties
- Non-negative result: Absolute value is always greater than or equal to zero.
- Opposite numbers: A number and its negative have the same absolute value, such as |9| = |−9| = 9.
- Zero: The absolute value of zero is zero.
- Multiplication: |a × b| = |a| × |b|.
- Division: For b ≠ 0, |a ÷ b| = |a| ÷ |b|.
- Addition inequality: |a + b| ≤ |a| + |b|.
Where is absolute value used?
Absolute value is used in algebra, equations and inequalities, coordinate geometry, statistics, and everyday comparisons. It can represent the distance between two points on a number line, the size of an error without its direction, or the magnitude of a change. For two real numbers a and b, the distance between them is |a − b|.
Frequently asked questions
1. What is the absolute value of a number?
It is the number's distance from zero on the number line. Distance is never negative, so absolute value is always zero or positive.
2. How do you calculate absolute value?
Keep the number unchanged if it is zero or positive. If it is negative, remove its negative sign. For example, |−6| = 6 and |6| = 6.
3. Can absolute value be negative?
No. Absolute value represents distance or magnitude, which cannot be negative. Its smallest possible value is zero.
4. What is the absolute value of a negative number?
It is the corresponding positive number. For example, the absolute value of −15 is 15.
5. What is the absolute value of zero?
The absolute value of zero is zero because zero is zero units away from itself: |0| = 0.
6. Do positive numbers change when taking absolute value?
No. A positive number remains the same because it is already non-negative. For example, |11| = 11.
7. What is the difference between absolute value and a negative sign?
A negative sign indicates direction or position to the left of zero. Absolute value gives only the non-negative magnitude, without that direction.
8. Can I calculate the absolute value of a decimal?
Yes. The same rule applies to decimals. For example, |−2.35| = 2.35 and |2.35| = 2.35.
9. What does |a − b| mean?
It represents the distance between two real numbers a and b on the number line. The result is non-negative regardless of which number is larger.
10. Is absolute value the same as squaring a number?
No. Absolute value gives the non-negative magnitude of a number. Squaring multiplies a number by itself. For example, |−3| = 3, while (−3)² = 9.
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