Free · Algebra calculators
Absolute Value of a Real Number
Find a real number’s nonnegative distance from zero.
- Formula & worked example
- Private in your browser
- No signup
Calculator inputs
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How to use this calculator
- Enter the known values in the units shown. Results update as you type.
- Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
- Use the worked example to check the method. Reset restores the starting fields.
Private by default
Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.
Formula and method
The absolute value of −7.25 is 7.25. Positive 7.25 has the same absolute value, and the absolute value of zero is zero.
|x| = x when x ≥ 0; |x| = −x when x < 0
Worked example
Enter these known values and leave the other values blank.
- Signed real number x
- -7.25
- Absolute value |x|
- 7.25
Assumptions and limitations
- The input is one real number. This does not parse or solve an absolute-value equation or inequality.
- The result is nonnegative and read-only. A magnitude alone generally cannot recover the original sign.
- The tool does not calculate the modulus of a complex number; that requires its real and imaginary components.
Common questions
Is absolute value the same as changing the sign?
Only a negative input changes sign. A positive input stays positive, and zero stays zero.
Why can I not recover the original number from |x|?
A positive magnitude corresponds to two possible real inputs, one positive and one negative. Zero is the only magnitude with one real input.
References
The calculation equations, inverse formulas, units, and input rules were imported from this source. Bookify provides the interface and equation solver.