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Complex Magnitude from Real and Imaginary Parts

Calculate the magnitude of a complex number from its real and imaginary components.

Author

Dr. Lucia Fernandez Vega

Math editorial contributor

Argentine astrophysicist from the University of Buenos Aires, contributing to exoplanet detection with the James Webb telescope

Reviewed by

Dr. Isabella Rossi

Math content reviewer

Italian neuroscientist at Sapienza University of Rome, studying the neural mechanisms of bilingual language processing

Last updatedFebruary 22, 2026

PublishedFebruary 22, 2026

On this page

  1. Reference values
  2. Calculator
  3. Reference table
  4. FAQs
  5. Methodology and review
  6. Related conversions

0 Real Part Real Part; 0 Imaginary Part Imaginary Part =

0 Magnitude

Representative value from the Complex Magnitude from Real and Imaginary Parts reference table.

Reference Values

Browse 81 reference values with individual detail pages for quick lookup.

Browse all reference values

Complex Magnitude from Real and Imaginary Parts

Calculate the magnitude of a complex number from its real and imaginary components.

Calculated Result

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Reference Table

Use this complete table for quick lookup and internal linking to specific value pages.

Complex Magnitude from Real and Imaginary Parts Reference
ScenarioMagnitude
-10 Real Part Real Part; -10 Imaginary Part Imaginary Part14.142136 Magnitude
-10 Real Part Real Part; -5 Imaginary Part Imaginary Part11.18034 Magnitude
-10 Real Part Real Part; -2 Imaginary Part Imaginary Part10.198039 Magnitude
-10 Real Part Real Part; -1 Imaginary Part Imaginary Part10.049876 Magnitude
-10 Real Part Real Part; 0 Imaginary Part Imaginary Part10 Magnitude
-10 Real Part Real Part; 1 Imaginary Part Imaginary Part10.049876 Magnitude
-10 Real Part Real Part; 2 Imaginary Part Imaginary Part10.198039 Magnitude
-10 Real Part Real Part; 5 Imaginary Part Imaginary Part11.18034 Magnitude
-10 Real Part Real Part; 10 Imaginary Part Imaginary Part14.142136 Magnitude
-5 Real Part Real Part; -10 Imaginary Part Imaginary Part11.18034 Magnitude
-5 Real Part Real Part; -5 Imaginary Part Imaginary Part7.071068 Magnitude
-5 Real Part Real Part; -2 Imaginary Part Imaginary Part5.385165 Magnitude
-5 Real Part Real Part; -1 Imaginary Part Imaginary Part5.09902 Magnitude
-5 Real Part Real Part; 0 Imaginary Part Imaginary Part5 Magnitude
-5 Real Part Real Part; 1 Imaginary Part Imaginary Part5.09902 Magnitude
-5 Real Part Real Part; 2 Imaginary Part Imaginary Part5.385165 Magnitude
-5 Real Part Real Part; 5 Imaginary Part Imaginary Part7.071068 Magnitude
-5 Real Part Real Part; 10 Imaginary Part Imaginary Part11.18034 Magnitude
-2 Real Part Real Part; -10 Imaginary Part Imaginary Part10.198039 Magnitude
-2 Real Part Real Part; -5 Imaginary Part Imaginary Part5.385165 Magnitude
-2 Real Part Real Part; -2 Imaginary Part Imaginary Part2.828427 Magnitude
-2 Real Part Real Part; -1 Imaginary Part Imaginary Part2.236068 Magnitude
-2 Real Part Real Part; 0 Imaginary Part Imaginary Part2 Magnitude
-2 Real Part Real Part; 1 Imaginary Part Imaginary Part2.236068 Magnitude
-2 Real Part Real Part; 2 Imaginary Part Imaginary Part2.828427 Magnitude
-2 Real Part Real Part; 5 Imaginary Part Imaginary Part5.385165 Magnitude
-2 Real Part Real Part; 10 Imaginary Part Imaginary Part10.198039 Magnitude
-1 Real Part Real Part; -10 Imaginary Part Imaginary Part10.049876 Magnitude
-1 Real Part Real Part; -5 Imaginary Part Imaginary Part5.09902 Magnitude
-1 Real Part Real Part; -2 Imaginary Part Imaginary Part2.236068 Magnitude
-1 Real Part Real Part; -1 Imaginary Part Imaginary Part1.414214 Magnitude
-1 Real Part Real Part; 0 Imaginary Part Imaginary Part1 Magnitude
-1 Real Part Real Part; 1 Imaginary Part Imaginary Part1.414214 Magnitude
-1 Real Part Real Part; 2 Imaginary Part Imaginary Part2.236068 Magnitude
-1 Real Part Real Part; 5 Imaginary Part Imaginary Part5.09902 Magnitude
-1 Real Part Real Part; 10 Imaginary Part Imaginary Part10.049876 Magnitude
0 Real Part Real Part; -10 Imaginary Part Imaginary Part10 Magnitude
0 Real Part Real Part; -5 Imaginary Part Imaginary Part5 Magnitude
0 Real Part Real Part; -2 Imaginary Part Imaginary Part2 Magnitude
0 Real Part Real Part; -1 Imaginary Part Imaginary Part1 Magnitude
0 Real Part Real Part; 0 Imaginary Part Imaginary Part0 Magnitude
0 Real Part Real Part; 1 Imaginary Part Imaginary Part1 Magnitude
0 Real Part Real Part; 2 Imaginary Part Imaginary Part2 Magnitude
0 Real Part Real Part; 5 Imaginary Part Imaginary Part5 Magnitude
0 Real Part Real Part; 10 Imaginary Part Imaginary Part10 Magnitude
1 Real Part Real Part; -10 Imaginary Part Imaginary Part10.049876 Magnitude
1 Real Part Real Part; -5 Imaginary Part Imaginary Part5.09902 Magnitude
1 Real Part Real Part; -2 Imaginary Part Imaginary Part2.236068 Magnitude
1 Real Part Real Part; -1 Imaginary Part Imaginary Part1.414214 Magnitude
1 Real Part Real Part; 0 Imaginary Part Imaginary Part1 Magnitude
1 Real Part Real Part; 1 Imaginary Part Imaginary Part1.414214 Magnitude
1 Real Part Real Part; 2 Imaginary Part Imaginary Part2.236068 Magnitude
1 Real Part Real Part; 5 Imaginary Part Imaginary Part5.09902 Magnitude
1 Real Part Real Part; 10 Imaginary Part Imaginary Part10.049876 Magnitude
2 Real Part Real Part; -10 Imaginary Part Imaginary Part10.198039 Magnitude
2 Real Part Real Part; -5 Imaginary Part Imaginary Part5.385165 Magnitude
2 Real Part Real Part; -2 Imaginary Part Imaginary Part2.828427 Magnitude
2 Real Part Real Part; -1 Imaginary Part Imaginary Part2.236068 Magnitude
2 Real Part Real Part; 0 Imaginary Part Imaginary Part2 Magnitude
2 Real Part Real Part; 1 Imaginary Part Imaginary Part2.236068 Magnitude
2 Real Part Real Part; 2 Imaginary Part Imaginary Part2.828427 Magnitude
2 Real Part Real Part; 5 Imaginary Part Imaginary Part5.385165 Magnitude
2 Real Part Real Part; 10 Imaginary Part Imaginary Part10.198039 Magnitude
5 Real Part Real Part; -10 Imaginary Part Imaginary Part11.18034 Magnitude
5 Real Part Real Part; -5 Imaginary Part Imaginary Part7.071068 Magnitude
5 Real Part Real Part; -2 Imaginary Part Imaginary Part5.385165 Magnitude
5 Real Part Real Part; -1 Imaginary Part Imaginary Part5.09902 Magnitude
5 Real Part Real Part; 0 Imaginary Part Imaginary Part5 Magnitude
5 Real Part Real Part; 1 Imaginary Part Imaginary Part5.09902 Magnitude
5 Real Part Real Part; 2 Imaginary Part Imaginary Part5.385165 Magnitude
5 Real Part Real Part; 5 Imaginary Part Imaginary Part7.071068 Magnitude
5 Real Part Real Part; 10 Imaginary Part Imaginary Part11.18034 Magnitude
10 Real Part Real Part; -10 Imaginary Part Imaginary Part14.142136 Magnitude
10 Real Part Real Part; -5 Imaginary Part Imaginary Part11.18034 Magnitude
10 Real Part Real Part; -2 Imaginary Part Imaginary Part10.198039 Magnitude
10 Real Part Real Part; -1 Imaginary Part Imaginary Part10.049876 Magnitude
10 Real Part Real Part; 0 Imaginary Part Imaginary Part10 Magnitude
10 Real Part Real Part; 1 Imaginary Part Imaginary Part10.049876 Magnitude
10 Real Part Real Part; 2 Imaginary Part Imaginary Part10.198039 Magnitude
10 Real Part Real Part; 5 Imaginary Part Imaginary Part11.18034 Magnitude
10 Real Part Real Part; 10 Imaginary Part Imaginary Part14.142136 Magnitude

Frequently Asked Questions

Common questions about Complex Magnitude from Real and Imaginary Parts, formulas, and typical use cases.

What does the Complex Magnitude from Real and Imaginary Parts calculator do?

It helps with converting rectangular complex coordinates into magnitude form.

What formula does the Complex Magnitude from Real and Imaginary Parts calculator use?

Complex magnitude |z| = √(a² + b²).

What inputs are valid?

Any finite real and imaginary values are valid.

When would I use this?

converting rectangular complex coordinates into magnitude form

Methodology and Review

This page combines a live calculator, precomputed reference values, and FAQ content from the same conversion definition to reduce mismatch between calculator output and lookup tables.

Editorial metadata (author, reviewer, and update date) is rendered on the page and in structured data. See our editorial policy, review process, and corrections policy.

For compliance-sensitive work, verify final values against project requirements, governing standards, and manufacturer documentation.