Math
Complex multiplication
Multiply two complex numbers entered as real and imaginary components.
Calculators / Math / Complex number modulus
Complex number modulus calculator
Find the distance of a complex number from the origin of the complex plane.
On this page
Modulus5
Modulus squared25
Calculator controls
How to calculate
Find the distance of a complex number from the origin of the complex plane.
Modulus = sqrt(a^2+b^2); Modulus squared = a^2+b^2
Worked example
Real part: 3; Imaginary part: 4.
Modulus: 5 ; Modulus squared: 25 .
Assumptions and limits
The input represents a + bi. This tool gives magnitude; it does not report the phase angle.
Results are rounded for display; calculations use unrounded values. Read our calculation methodology.
Understanding the result
Find the distance of a complex number from the origin of the complex plane.
When this tool is useful
Modulus = sqrt(a^2+b^2); Modulus squared = a^2+b^2
Understanding your inputs
| Input | What to enter |
|---|---|
| Real part | Enter a number of at least -1000000000000 and no more than 1000000000000. |
| Imaginary part | Enter a number of at least -1000000000000 and no more than 1000000000000. |
Frequently asked questions
What assumptions does this calculation use?
The input represents a + bi. This tool gives magnitude; it does not report the phase angle.
How is the result calculated?
Modulus = sqrt(a^2+b^2); Modulus squared = a^2+b^2