Convertools

Complex Phase (Degrees) from Real and Imaginary Parts

Calculate complex-number phase angle in degrees using atan2(imag, real).

Author

Prof. Ingrid Johansson

Math editorial contributor

Norwegian political scientist at the University of Oslo, studying democratic resilience in Nordic welfare states

Reviewed by

Prof. Kenji Tanaka

Math content reviewer

Japanese materials scientist at Kyoto University, known for breakthroughs in sustainable polymer research

Last updatedFebruary 22, 2026

PublishedFebruary 22, 2026

Table of Contents

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

0 Real Part Real Part; 1 Imaginary Part Imaginary Part =

90 deg

Representative value from the Complex Phase (Degrees) from Real and Imaginary Parts reference table.

Reference Values

Browse 80 reference values with individual detail pages for quick lookup.

Browse all reference values

Complex Phase (Degrees) from Real and Imaginary Parts

Calculate complex-number phase angle in degrees using atan2(imag, real).

Calculated Result

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Reference Table

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

Complex Phase (Degrees) from Real and Imaginary Parts Reference
ScenarioPhase Angle
-10 Real Part Real Part; -10 Imaginary Part Imaginary Part-135 deg
-10 Real Part Real Part; -5 Imaginary Part Imaginary Part-153.434949 deg
-10 Real Part Real Part; -2 Imaginary Part Imaginary Part-168.690068 deg
-10 Real Part Real Part; -1 Imaginary Part Imaginary Part-174.289407 deg
-10 Real Part Real Part; 0 Imaginary Part Imaginary Part180 deg
-10 Real Part Real Part; 1 Imaginary Part Imaginary Part174.289407 deg
-10 Real Part Real Part; 2 Imaginary Part Imaginary Part168.690068 deg
-10 Real Part Real Part; 5 Imaginary Part Imaginary Part153.434949 deg
-10 Real Part Real Part; 10 Imaginary Part Imaginary Part135 deg
-5 Real Part Real Part; -10 Imaginary Part Imaginary Part-116.565051 deg
-5 Real Part Real Part; -5 Imaginary Part Imaginary Part-135 deg
-5 Real Part Real Part; -2 Imaginary Part Imaginary Part-158.198591 deg
-5 Real Part Real Part; -1 Imaginary Part Imaginary Part-168.690068 deg
-5 Real Part Real Part; 0 Imaginary Part Imaginary Part180 deg
-5 Real Part Real Part; 1 Imaginary Part Imaginary Part168.690068 deg
-5 Real Part Real Part; 2 Imaginary Part Imaginary Part158.198591 deg
-5 Real Part Real Part; 5 Imaginary Part Imaginary Part135 deg
-5 Real Part Real Part; 10 Imaginary Part Imaginary Part116.565051 deg
-2 Real Part Real Part; -10 Imaginary Part Imaginary Part-101.309932 deg
-2 Real Part Real Part; -5 Imaginary Part Imaginary Part-111.801409 deg
-2 Real Part Real Part; -2 Imaginary Part Imaginary Part-135 deg
-2 Real Part Real Part; -1 Imaginary Part Imaginary Part-153.434949 deg
-2 Real Part Real Part; 0 Imaginary Part Imaginary Part180 deg
-2 Real Part Real Part; 1 Imaginary Part Imaginary Part153.434949 deg
-2 Real Part Real Part; 2 Imaginary Part Imaginary Part135 deg
-2 Real Part Real Part; 5 Imaginary Part Imaginary Part111.801409 deg
-2 Real Part Real Part; 10 Imaginary Part Imaginary Part101.309932 deg
-1 Real Part Real Part; -10 Imaginary Part Imaginary Part-95.710593 deg
-1 Real Part Real Part; -5 Imaginary Part Imaginary Part-101.309932 deg
-1 Real Part Real Part; -2 Imaginary Part Imaginary Part-116.565051 deg
-1 Real Part Real Part; -1 Imaginary Part Imaginary Part-135 deg
-1 Real Part Real Part; 0 Imaginary Part Imaginary Part180 deg
-1 Real Part Real Part; 1 Imaginary Part Imaginary Part135 deg
-1 Real Part Real Part; 2 Imaginary Part Imaginary Part116.565051 deg
-1 Real Part Real Part; 5 Imaginary Part Imaginary Part101.309932 deg
-1 Real Part Real Part; 10 Imaginary Part Imaginary Part95.710593 deg
0 Real Part Real Part; -10 Imaginary Part Imaginary Part-90 deg
0 Real Part Real Part; -5 Imaginary Part Imaginary Part-90 deg
0 Real Part Real Part; -2 Imaginary Part Imaginary Part-90 deg
0 Real Part Real Part; -1 Imaginary Part Imaginary Part-90 deg
0 Real Part Real Part; 1 Imaginary Part Imaginary Part90 deg
0 Real Part Real Part; 2 Imaginary Part Imaginary Part90 deg
0 Real Part Real Part; 5 Imaginary Part Imaginary Part90 deg
0 Real Part Real Part; 10 Imaginary Part Imaginary Part90 deg
1 Real Part Real Part; -10 Imaginary Part Imaginary Part-84.289407 deg
1 Real Part Real Part; -5 Imaginary Part Imaginary Part-78.690068 deg
1 Real Part Real Part; -2 Imaginary Part Imaginary Part-63.434949 deg
1 Real Part Real Part; -1 Imaginary Part Imaginary Part-45 deg
1 Real Part Real Part; 0 Imaginary Part Imaginary Part0 deg
1 Real Part Real Part; 1 Imaginary Part Imaginary Part45 deg
1 Real Part Real Part; 2 Imaginary Part Imaginary Part63.434949 deg
1 Real Part Real Part; 5 Imaginary Part Imaginary Part78.690068 deg
1 Real Part Real Part; 10 Imaginary Part Imaginary Part84.289407 deg
2 Real Part Real Part; -10 Imaginary Part Imaginary Part-78.690068 deg
2 Real Part Real Part; -5 Imaginary Part Imaginary Part-68.198591 deg
2 Real Part Real Part; -2 Imaginary Part Imaginary Part-45 deg
2 Real Part Real Part; -1 Imaginary Part Imaginary Part-26.565051 deg
2 Real Part Real Part; 0 Imaginary Part Imaginary Part0 deg
2 Real Part Real Part; 1 Imaginary Part Imaginary Part26.565051 deg
2 Real Part Real Part; 2 Imaginary Part Imaginary Part45 deg
2 Real Part Real Part; 5 Imaginary Part Imaginary Part68.198591 deg
2 Real Part Real Part; 10 Imaginary Part Imaginary Part78.690068 deg
5 Real Part Real Part; -10 Imaginary Part Imaginary Part-63.434949 deg
5 Real Part Real Part; -5 Imaginary Part Imaginary Part-45 deg
5 Real Part Real Part; -2 Imaginary Part Imaginary Part-21.801409 deg
5 Real Part Real Part; -1 Imaginary Part Imaginary Part-11.309932 deg
5 Real Part Real Part; 0 Imaginary Part Imaginary Part0 deg
5 Real Part Real Part; 1 Imaginary Part Imaginary Part11.309932 deg
5 Real Part Real Part; 2 Imaginary Part Imaginary Part21.801409 deg
5 Real Part Real Part; 5 Imaginary Part Imaginary Part45 deg
5 Real Part Real Part; 10 Imaginary Part Imaginary Part63.434949 deg
10 Real Part Real Part; -10 Imaginary Part Imaginary Part-45 deg
10 Real Part Real Part; -5 Imaginary Part Imaginary Part-26.565051 deg
10 Real Part Real Part; -2 Imaginary Part Imaginary Part-11.309932 deg
10 Real Part Real Part; -1 Imaginary Part Imaginary Part-5.710593 deg
10 Real Part Real Part; 0 Imaginary Part Imaginary Part0 deg
10 Real Part Real Part; 1 Imaginary Part Imaginary Part5.710593 deg
10 Real Part Real Part; 2 Imaginary Part Imaginary Part11.309932 deg
10 Real Part Real Part; 5 Imaginary Part Imaginary Part26.565051 deg
10 Real Part Real Part; 10 Imaginary Part Imaginary Part45 deg

Frequently Asked Questions

Common questions about Complex Phase (Degrees) from Real and Imaginary Parts, formulas, and typical use cases.

What does the Complex Phase (Degrees) from Real and Imaginary Parts calculator do?

It helps with finding phase angle from rectangular complex coordinates for ac and signal analysis.

What formula does the Complex Phase (Degrees) from Real and Imaginary Parts calculator use?

Phase angle (degrees) = atan2(imaginary, real) × 180 / π.

What inputs are valid?

Real and imaginary values can be any finite numbers except both zero at the same time.

When would I use this?

finding phase angle from rectangular complex coordinates for AC and signal analysis

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.