SWR & Reflection Coefficient Calculator
Calculate Voltage Standing Wave Ratio (VSWR), reflection coefficient (Γ), and return loss from a complex load impedance Z = R + jX and a transmission line characteristic impedance Z<sub>0</sub>.
How to Use
- Enter the load resistance R (real part of Z) in ohms.
- Enter the load reactance X (imaginary part) — positive for inductive, negative for capacitive, zero for purely resistive.
- Enter the transmission line characteristic impedance Z<sub>0</sub> — typically 50 Ω (RF/radio), 75 Ω (TV/video), or 300/450 Ω (ladder line).
- Results: SWR (always ≥ 1), |Γ| (magnitude of reflection coefficient), return loss in dB, and reflection phase.
Show Work
Formulas
History of SWR and Transmission Lines
Oliver Heaviside developed the mathematics of waves on transmission lines in the 1880s, working out what became known as the "telegrapher\'s equations" while trying to explain signal distortion on long telegraph and telephone cables. His analysis showed that a wave traveling down a mismatched line produces a reflected wave, and the superposition of forward and reflected waves creates a standing-wave pattern with periodic voltage maxima and minima — hence standing wave ratio.
Before network analyzers existed, engineers measured SWR directly with a slotted line: a section of coax with a longitudinal slot through which a probe could measure the E-field amplitude at different positions. The ratio of max to min probe reading was the VSWR. The Hewlett-Packard 415B SWR meter (1960s) and the General Radio 874 series slotted lines were standard RF lab equipment for decades. Modern vector network analyzers replace all of it with direct S-parameter measurement at computer speed.
The 50-ohm coaxial standard emerged during WWII. Compromise coaxial line manufacturing at Western Electric balanced the competing requirements: minimum loss (optimum ~77 Ω in air-dielectric coax), maximum CW power handling (optimum ~30 Ω), and minimum voltage breakdown. 50 Ω minimized the combined figure of merit and has been the global RF test-equipment standard ever since. TV video kept 75 Ω because low signal loss dominated over power handling for long cable runs.
About This Calculator
Enter the load impedance as R + jX (real + imaginary parts in ohms) and the transmission line Z0. The tool computes the complex reflection coefficient Γ = (Z − Z0) / (Z + Z0), its magnitude and phase, the resulting VSWR = (1 + |Γ|) / (1 − |Γ|), and return loss RL = −20 log|Γ| dB.
For a quick sanity check on non-reactive loads, VSWR = R/Z0 when R > Z0 or Z0/R when R < Z0. For reactive loads, the full complex calculation is required. Everything runs client-side; no values leave your browser.
Frequently Asked Questions
What's a good SWR?
1:1 is perfect; 1.5:1 is excellent; 2:1 is acceptable for most amateur and commercial RF; above 3:1 most transmitters fold back their output to protect the final amplifier. Solid-state transmitters are especially sensitive — they can shut down entirely at SWR > 3.
Why 50Ω as the RF standard?
It\'s a compromise: a coaxial line with air dielectric has minimum loss at ~77Ω and maximum power handling at ~30Ω. 50Ω splits the difference, becoming the de-facto standard for radio, test equipment, and microwave systems since the 1940s. (Exception: TV/video uses 75Ω because minimum loss matters more than power handling in cable runs.)
What does reflection coefficient represent?
Γ is the complex ratio of the reflected wave\'s voltage amplitude to the forward wave\'s. |Γ| = 0 means perfect match (no reflection); |Γ| = 1 means complete reflection (open, short, or purely reactive load). The phase angle of Γ tells you whether the reflection is from an inductive (positive phase) or capacitive (negative phase) mismatch.
How does SWR relate to lost power?
Fraction of power reflected = |Γ|². At SWR 2:1, |Γ| = 1/3, so ~11% of the transmitter power bounces back up the line. At SWR 3:1, ~25% reflects. High SWR doesn\'t burn out the transmitter per se — it just wastes power and can overheat the finals.
What about complex loads?
Real antennas at off-resonance frequencies present Z = R + jX where X ≠ 0. The full formula Γ = (Z − Z<sub>0</sub>) / (Z + Z<sub>0</sub>) handles complex arithmetic correctly — but the SWR formula in terms of |Γ| is still the same. Matching networks (L-networks, Pi-networks, antenna tuners) transform a complex Z into the line\'s Z<sub>0</sub> for a low SWR.
Common Use Cases
Antenna Feedpoint Check
A 2m dipole measured at 14.2 MHz feedpoint: R = 75Ω, X = +5Ω into a 50Ω line → SWR ≈ 1.52, return loss 14 dB. Acceptable without matching.
Mobile Whip Match
A quarter-wave mobile whip on a car roof presents ~30Ω at resonance. SWR into 50Ω = 1.67 — low enough to work, high enough that a matching transformer improves efficiency 5–10%.
Production Line QA
RF cable assemblies are acceptance-tested for SWR on network analyzers. Typical spec: SWR < 1.25 over the operating band.
Satellite Downlink LNA
LNA input matched to 50Ω within SWR 1.1 over the operating band minimizes noise figure penalty — critical for weak-signal reception.
Troubleshooting
An SWR meter at the transmitter reading 3:1 when you expect 1.2 suggests feedline damage, water intrusion, or a connector failure somewhere between transmitter and antenna.
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