SWR and Reflection Coefficient
The standing wave ratio (SWR) is the number you see on your SWR meter and in every antenna specification. The reflection coefficient (Γ, or ρ — rho) is the underlying physical quantity that determines SWR. Return loss is the same information expressed in decibels, preferred by RF engineers. Reflected power percentage is what these numbers mean for your transmitter's efficiency.
These four quantities — SWR, reflection coefficient, return loss, and reflected power — all describe the same physical situation from different angles. Being able to convert fluently between them is a core skill for understanding antenna systems, and the four calculators in this lesson make it easy.
When a transmission line meets a mismatched load, the reflection coefficient Γ determines what fraction of the incident voltage is reflected. SWR, return loss, and reflected power percentage are all derived from |Γ|.
View LargerThe Reflection Coefficient
The voltage reflection coefficient Γ (gamma) is the ratio of the reflected voltage wave amplitude to the incident voltage wave amplitude at the load:
- Γ = voltage reflection coefficient (complex in general)
- ZL = load impedance (ohms, may be complex)
- Z₀ = characteristic impedance of the line (real for ideal line)
For the SWR and power calculations that follow, we use the magnitude |Γ|, also written as ρ (rho). For a purely resistive load:
- If ZL > Z₀: Γ is positive real, 0 ≤ Γ ≤ 1
- If ZL < Z₀: Γ is negative real, −1 ≤ Γ < 0
- If ZL = Z₀: Γ = 0 (perfect match)
- If ZL = 0 (short): Γ = −1
- If ZL = ∞ (open): Γ = +1
- For a complex load: Γ is complex, with |Γ| between 0 and 1
The magnitude |Γ| (always 0 ≤ |Γ| ≤ 1) is what determines SWR, return loss, and reflected power. The phase of Γ determines where along the line the voltage maxima and minima occur but does not affect the SWR value.
SWR from Reflection Coefficient
SWR is related to |Γ| by two equivalent formulas:
and the inverse:
|Γ| = (SWR − 1) / (SWR + 1)A 50-ohm line feeds a 150-ohm resistive load.
Γ = (150 − 50) / (150 + 50) = 100/200 = 0.500
SWR = (1 + 0.500) / (1 − 0.500) = 1.500 / 0.500 = 3.0:1
Check via inverse: |Γ| = (3.0 − 1) / (3.0 + 1) = 2/4 = 0.500 ✓
Calculator 1: SWR ↔ Reflection Coefficient
SWR and Reflection Coefficient Converter
Enter either SWR (≥ 1) or reflection coefficient magnitude |Γ| (0 to 1) to convert between them.
Return Loss
Return loss is the ratio of the reflected power to the incident power, expressed in decibels. A high return loss is good — it means very little power is being reflected. A low return loss is bad — it means a large fraction is being reflected.
Expressed in terms of SWR:
Return loss (dB) = 20 × log₁₀((SWR + 1) / (SWR − 1))And the inverse:
SWR = (10RL/20 + 1) / (10RL/20 − 1)- A matched load (SWR = 1:1) has infinite return loss
- Return loss 20 dB = |Γ| = 0.10, SWR = 1.22:1
- Return loss 14 dB = |Γ| = 0.20, SWR = 1.50:1
- Return loss 9.5 dB = |Γ| = 0.333, SWR = 2.00:1
- Return loss 6 dB = |Γ| = 0.501, SWR = 3.01:1
Return loss is the preferred metric in professional RF work, particularly in microwave engineering and antenna measurement. Vector network analyzers (VNAs) typically display S11, which equals the return loss (with a sign convention that makes S11 a negative number in dB for a reflection — so an antenna with 10 dB return loss displays S11 = −10 dB on a VNA).
Calculator 2: Return Loss from SWR
Return Loss and SWR Converter
Enter either SWR or return loss (dB) to convert between them.
Reflected Power
The fraction of the incident power that is reflected from a mismatched load equals the square of the magnitude of the reflection coefficient:
As a percentage:
% reflected = |Γ|² × 100 = ((SWR − 1) / (SWR + 1))² × 100Power delivered to load:
% delivered = 100 − % reflected = (1 − |Γ|²) × 100SWR 1.5:1 → |Γ| = (1.5-1)/(1.5+1) = 0.5/2.5 = 0.200 → reflected = 0.2² = 4.0% → delivered = 96%
SWR 2:1 → |Γ| = (2-1)/(2+1) = 1/3 = 0.333 → reflected = 0.333² = 11.1% → delivered = 88.9%
SWR 3:1 → |Γ| = (3-1)/(3+1) = 2/4 = 0.500 → reflected = 0.5² = 25.0% → delivered = 75%
SWR 5:1 → |Γ| = (5-1)/(5+1) = 4/6 = 0.667 → reflected = 0.667² = 44.4% → delivered = 55.6%
SWR 10:1 → |Γ| = 9/11 = 0.818 → reflected = 0.818² = 66.9% → delivered = 33.1%
An important nuance: this reflected power calculation assumes the source simply absorbs any returning reflected power without re-reflecting it. In a well-designed transmitter with a 50-ohm output impedance, this is approximately true. The reflected power returned to the transmitter is not "lost" from the antenna system perspective if the transmitter absorbs it (it becomes heat in the transmitter's output stage), but it does mean that only the delivered percentage of the transmitter's power actually reaches the load side of the junction.
Calculator 3: Reflected Power from SWR
Reflected Power Calculator
Enter SWR and transmitter output power to calculate reflected power, delivered power, and all related values.
Calculator 4: SWR from Load and Line Impedances
When you know the load impedance and the feedline characteristic impedance, you can calculate the SWR directly. For a purely resistive load, the calculation is straightforward. For a complex load (ZL = R + jX), you need the magnitude of the reflection coefficient.
SWR from Impedance Values
Enter the feedline characteristic impedance and the load impedance (with optional reactive component). The calculator returns the SWR and reflection coefficient.
Quick Reference Table
This table allows quick lookup of all four related quantities for common SWR values:
| SWR | |Γ| (rho) | Return Loss (dB) | Reflected Power (%) | Delivered Power (%) |
|---|---|---|---|---|
| 1.0:1 | 0.000 | ∞ | 0.0% | 100.0% |
| 1.1:1 | 0.048 | 26.4 dB | 0.2% | 99.8% |
| 1.2:1 | 0.091 | 20.8 dB | 0.8% | 99.2% |
| 1.5:1 | 0.200 | 14.0 dB | 4.0% | 96.0% |
| 2.0:1 | 0.333 | 9.5 dB | 11.1% | 88.9% |
| 2.5:1 | 0.429 | 7.4 dB | 18.4% | 81.6% |
| 3.0:1 | 0.500 | 6.0 dB | 25.0% | 75.0% |
| 4.0:1 | 0.600 | 4.4 dB | 36.0% | 64.0% |
| 5.0:1 | 0.667 | 3.5 dB | 44.4% | 55.6% |
| 7.0:1 | 0.750 | 2.5 dB | 56.3% | 43.8% |
| 10.0:1 | 0.818 | 1.7 dB | 66.9% | 33.1% |
| ∞ | 1.000 | 0 dB | 100.0% | 0.0% |
Note the disproportionate nature of SWR and reflected power: even SWR 3:1, which many beginners consider "very bad," only reflects 25% of the incident power. A matched load delivers 100% and SWR 2:1 delivers 89% — the difference is only 11%. This is why modern transceivers operate acceptably at SWR up to 2:1 or 3:1 without significant performance degradation. The problems with high SWR are more about increased feedline loss (especially on long, lossy coaxial cable runs) than about the reflection itself.
Test Your Knowledge
Answer the questions below to check your understanding. Every answer can be found in the lesson above.