HomeCalculatorsElectricalRF & MicrowaveReflection Coefficient to Impedance Calculator
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Reflection Coefficient to Impedance Calculator

Convert complex Γ ↔ normalized z (Cartesian or polar Γ). Reports VSWR and return loss. Runs locally in your browser.

Instant result
Result
—

Enter values to calculate.

Inputs—
Mode—
Formula—
Trust summary CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance
Input interpretation
Enter values to calculate.
Result
—
Assurance
Engineering
Declared partition coverage
PASS · 3/3 declared partitions (polar-z, z-gamma, invalid-domain) · Matrix
Known limitations
  • Normalized passive loads; |Γ|≤1
  • Core CVP does not include live graph, viewport, or pointer interaction.
Model
Complex Γ ↔ normalized impedance.
Scope
Passive |Γ|≤1
Verification
Engine tested · Source checked · v1.0.0 · CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance· View Manifest · CVP overview · Specification
Versions
Calculation 1.0.0 · CVP protocol 1.0.0-proposed
CVP identity
1/1 property · digest 8c349af43258
Legacy regression
3/3 tests · Production surface contract 4/4
Reference
O1 model · O2 expected_values · O2 numerical_behavior
Interfaces
PASS · UI (SSR) / REST / MCP — ui-ssr is query-result HTML, not a live browser session.
Supplemental domain review
Internal · Pass
Named expert review
Not performed
CVP suite
2/2 golden · 1/1 CVP boundary · 1/1 invalid · 1/1 property · 1/1 cross-interface · 1/1 CVP contract · Manifest
Sources
  • Pozar Microwave Engineering — reflection coefficient
  • Collin — Foundations for Microwave Engineering — Reflection coefficient and VSWR
Sources
Evidence
1 legacy golden · 1 legacy boundary · legacy regression suite · 2/2 oracle-backed golden · 1/1 invalid · Artifact integrity PASS · CalculatorX physics/RF review
This calculator CURRENT · Public schema 1.0.0 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓
Semantic contract
PASS
Full verification

Manifest identity, reference classes, interfaces, suite, and production records.

Formulas

Core equations used by this calculator.

z from Γz = (1 + Γ) / (1 − Γ)
VSWRVSWR = (1+|Γ|)/(1−|Γ|)
iNormalized to system Z0. VSWR companion: /calc/electric/vswr for magnitude-only.

How to use

1

Choose conversion direction

z ↔ Γ, or polar Γ → z, depending on what you have.

2

Enter normalized impedance or Γ components

For polar input, provide magnitude and angle as labeled.

3

Read z or Γ

z = (1 + Γ)/(1 − Γ). |Γ| = 1 is a singularity (open/short extremes).

Example calculations

Common configurations with formula and result.

ϟ

|Γ|=0.5 ∠0°

real

z=(1.5)/(0.5)
z=3 · VSWR=3

Reflection Coefficient to Impedance calculator specification

Version 1.0.0 · Engine tested · Supplemental domain review · Internal · 2026-08-09

Calculation status

Review policy · Evidence · Reviewed by CalculatorX physics/RF review

Definition
z=(1+Γ)/(1−Γ) and Γ=(z−1)/(z+1). Polar mode: Γ = |Γ|∠θ.
What it calculates
Complex Γ ↔ normalized impedance.
Inputs
  • mode z-gamma|gamma-z|polar-z
  • z or Γ components
Outputs
  • z_r
  • z_i
  • gamma_r
  • gamma_i
  • VSWR
  • RL_dB
Formula
z=(1+Γ)/(1−Γ)
Assumptions
  • Passive |Γ|≤1
Units
  • normalized
Boundary conditions
  • |Γ|>1 → VALUE_OUT_OF_RANGE
  • z_r<0 → NEGATIVE_RESISTANCE_NOT_SUPPORTED (z_r=0 short allowed)
Example
|Γ|=0.5 → z=3 VSWR=3
Validation cases

1 published on this page · 3/3 tests · Production surface contract 4/4 · View evidence

  • polar-z mag=0.5 ang=0 → z_r=3 VSWR=3
Sources
  • Pozar Microwave Engineering — reflection coefficient
    Supports: Γ↔z
  • Collin — Foundations for Microwave Engineering — Reflection coefficient and VSWR
    Supports: Γ=(z−1)/(z+1); VSWR=(1+|Γ|)/(1−|Γ|)
Last reviewed
2026-08-09
Reviewed by
CalculatorX physics/RF review
Calculation version
1.0.0

Background

Interpretation and common distinctions.

Convert complex Γ ↔ normalized z.

Supported and not supported

Supported — Cartesian / polar Γ · VSWR/RL · API electrical.rf.gamma_z

Not supported — De-embedding fixtures, S-parameter chains

Agent / API notes

Capability id: electrical.rf.gamma_z · tool id: gamma-z · pin 1.0.0.

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Frequently asked questions

Key distinctions behind the calculation.

Can |Γ| exceed 1?

For passive loads no — API returns VALUE_OUT_OF_RANGE when |Γ| > 1.