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Reflection Coefficient Calculator

Enter the load and line impedances to find Γ, VSWR and return loss.

Result

0.2000
0.2000
1.500
13.979 dB
4.000%

How it is calculated

Inputs are the load impedance ZL and the line characteristic impedance Z0, both in ohms and both treated as purely resistive (real) values. The reflection coefficient is Γ = (ZL − Z0) / (ZL + Z0). From its magnitude |Γ| the tool derives VSWR = (1 + |Γ|) / (1 − |Γ|), return loss = −20·log10|Γ| in dB, and the share of reflected power |Γ|² × 100 in percent.

Γ is signed: positive when the load is above the line impedance, negative when below. A perfect match (ZL = Z0) gives Γ = 0, VSWR = 1.000 and return loss ∞ dB. A short circuit (ZL = 0) gives Γ = -1, VSWR ∞ and 0 dB return loss. ZL must be zero or more and Z0 above zero; otherwise there is no result. Reactive loads with a phase angle (complex impedance) cannot be entered.

Worked example

A 75 ohm load is connected to a 50 ohm line. Γ = (75 − 50) / (75 + 50) = 25 / 125 = 0.2000. VSWR = (1 + 0.2) / (1 − 0.2) = 1.2 ÷ 0.8 = 1.500. Return loss = −20·log10(0.2) = 13.979 dB. Reflected power = 0.2² × 100 = 4.000%, so about 96% of the power reaches the load.

Try this example →

Common mistakes

  • Swapping the load and the line: Γ then changes sign (a 25 ohm load on a 50 ohm line gives -0.3333), although |Γ|, VSWR and return loss stay the same. Enter the load as ZL and the line as Z0.
  • Reading a larger return loss as worse: return loss in dB is higher when the match is better, so 13.979 dB is better than 9.542 dB.
  • Confusing the magnitude with the signed value: the Γ line keeps the minus sign, while the |Γ| line is always positive. VSWR and return loss use only the magnitude.
  • Entering a complex antenna impedance such as 50 + j25: only the real value can be typed, so reactance is ignored and the result describes a purely resistive load.
  • Entering 0 for the line impedance or a negative load: both return no result, because a transmission line needs a positive characteristic impedance and the tool handles only passive resistive loads.

About this calculator

When a transmission line's characteristic impedance doesn't match the load impedance connected to it, some of the signal reflects back instead of being absorbed. The reflection coefficient Γ quantifies this: Γ = (Z_load − Z_line) / (Z_load + Z_line). From Γ, the Voltage Standing Wave Ratio (VSWR) = (1 + |Γ|) / (1 − |Γ|) and the return loss (dB) = −20·log₁₀|Γ| follow directly.

RF and microwave engineers use these three related numbers to check how well an antenna, filter, or component is matched to its feed line — a perfect match gives Γ = 0, VSWR = 1, and infinite return loss, while a poor match wastes transmitted power and can even damage a transmitter.

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Comments (1)

  • Editorial team

    To feel the scale, try a few loads on a 50 ohm line. A 75 ohm load reflects 4 percent of the power, which is a loss of only about 0.18 dB, while a 200 ohm load gives a VSWR of 4 and reflects 36 percent. Both inputs are treated as pure resistance, so an antenna with reactance is not covered. A positive sign means the load is above the line impedance. What load or antenna are you matching?

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