A decibel (dB) loss calculator quantifies signal attenuation in RF transmission lines, audio cables, and optical fibers. Because the decibel scale is logarithmic, you cannot simply subtract linear units like watts or volts to find your loss. Instead, you must use logarithmic ratios to determine how much signal degrades over a specific distance or through a specific component.
Below are the exact formulas, symbol definitions, real-world coaxial attenuation data, and step-by-step worked examples required to calculate dB loss accurately on the bench or in the field.
The Core dB Loss Formulas and Symbol Definitions
The calculation method depends on whether you are measuring power (watts) or amplitude/voltage (volts). Power uses a multiplier of 10, while voltage uses a multiplier of 20 because power is proportional to the square of the voltage ($P = V^2 / R$).
Power Loss Formula:
dB = 10 · log10(Pout / Pin)
Voltage/Amplitude Loss Formula:
dB = 20 · log10(Vout / Vin)
Cable Attenuation Formula:
LossdB = α · (d / Lref)
| Symbol | Definition | Standard Unit |
|---|---|---|
dB |
Decibel change (negative value indicates loss) | dB (dimensionless ratio) |
LossdB |
Positive magnitude of attenuation | dB |
Pin, Pout |
Input and output power | Watts (W) or milliwatts (mW) |
Vin, Vout |
Input and output voltage/amplitude | Volts (V) |
α |
Attenuation rate per reference length | dB / 100 ft (or dB / 100 m) |
d |
Total physical length of the cable | Feet (ft) or Meters (m) |
Lref |
Reference length for the attenuation rate | 100 (if α is per 100 ft) |
Real-World Coaxial Cable Attenuation Data
To use the cable attenuation formula, you need the α value for your specific cable at your operating frequency. Higher frequencies suffer greater skin effect losses. The table below provides standard attenuation rates for common 50-ohm coaxial cables at key RF frequencies.
| Cable Type | 100 MHz (FM/VHF) | 400 MHz (UHF/Ham) | 1 GHz (Cellular) | 2.4 GHz (WiFi) |
|---|---|---|---|---|
| RG-58 (Thin, flexible) | 1.20 dB/100ft | 2.50 dB/100ft | 4.80 dB/100ft | 9.00 dB/100ft |
| RG-8X (Mid-size, flexible) | 0.63 dB/100ft | 1.30 dB/100ft | 2.40 dB/100ft | 4.50 dB/100ft |
| RG-213 (Standard thick) | 0.39 dB/100ft | 0.80 dB/100ft | 1.50 dB/100ft | 2.90 dB/100ft |
| LMR-400 (Low-loss, rigid) | 0.22 dB/100ft | 0.45 dB/100ft | 0.77 dB/100ft | 1.40 dB/100ft |
Data sourced from standard Times Microwave and Belden specification sheets. Values assume standard copper-clad aluminum or bare copper center conductors at 20°C ambient.
Rearranged Forms for Reverse Engineering
When designing a system, you rarely just calculate the loss; you usually need to find the required input power, the maximum allowable cable length, or the expected output voltage. Use these rearranged forms to solve for the missing variable.
- Solve for Output Power:
Pout = Pin · 10(dB / 10) - Solve for Input Power:
Pin = Pout · 10(-dB / 10) - Solve for Output Voltage:
Vout = Vin · 10(dB / 20) - Solve for Input Voltage:
Vin = Vout · 10(-dB / 20) - Solve for Maximum Cable Length:
d = (LossdB / α) · Lref - Solve for Linear Power Ratio:
Ratio = 10(dB / 10)
Worked Examples: Calculating Signal Loss in Real Circuits
Example 1: RF Power Transmission (Cable Attenuation)
Scenario: You are setting up a 400 MHz UHF amateur radio transmitter. The transmitter outputs 50 Watts. You are using a 75-foot run of LMR-400 coaxial cable. What is the dB loss, and how much power actually reaches the antenna?
- Identify the attenuation rate (α): From the table above, LMR-400 at 400 MHz has an attenuation of 0.45 dB per 100 ft.
- Calculate total cable loss (LossdB):
LossdB = 0.45 dB/100ft · (75 ft / 100)
LossdB = 0.45 · 0.75 = 0.3375 dB
Note: Because this is a loss, the dB value for the power formula is -0.3375 dB. - Calculate Output Power (Pout):
Pout = 50 W · 10(-0.3375 / 10)
Pout = 50 · 10-0.03375
Pout = 50 · 0.9252
Pout = 46.26 Watts
Result: The cable introduces 0.3375 dB of loss, leaving 46.26 Watts at the antenna feed point.
Example 2: Audio Line Voltage Drop
Scenario: You are testing a long unbalanced audio cable. You inject a 2.0 VRMS 1 kHz sine wave at the source. At the receiving end, your oscilloscope reads 1.4 VRMS. What is the dB loss of the cable?
- Select the correct formula: Because we are measuring voltage (amplitude) and not power directly, we must use the 20-log formula.
- Plug in the voltage values:
dB = 20 · log10(Vout / Vin)
dB = 20 · log10(1.4 V / 2.0 V) - Calculate the ratio and logarithm:
dB = 20 · log10(0.70)
dB = 20 · (-0.1549) - Final multiplication:
dB = -3.098 dB
Result: The cable exhibits a signal loss of approximately 3.1 dB.
Assumptions, Unit Traps, and Realistic Magnitudes
When the Formulas Apply (and When They Don't)
The power formula (10 · log) assumes that the input and output impedances are identical (e.g., a 50-ohm source driving a 50-ohm load through a 50-ohm cable). If the impedance changes across the circuit, the power ratio will not match the square of the voltage ratio. In mismatched systems, you must measure actual power (using a wattmeter or directional coupler) rather than deriving it from voltage readings.
The voltage formula (20 · log) calculates amplitude loss regardless of impedance. It is the correct choice for audio line-level signals, oscilloscope probe attenuation, and high-impedance sensor outputs where power transfer is not the primary concern.
Unit Mistakes That Break the Math
- Mixing dB and dBm: dB is a relative ratio (a multiplier). dBm is an absolute power level referenced to 1 milliwatt. You can subtract dB from dBm (e.g., 30 dBm - 3 dB = 27 dBm), but you cannot plug a dBm value directly into the
Pinvariable of the linear power formula without first converting it to Watts or milliwatts. - Forgetting Length Scaling: Cable datasheets specify attenuation per 100 feet or 100 meters. If you multiply the datasheet value directly by your cable length in feet without dividing by 100, your calculated loss will be 100 times too high.
- Using Peak Voltage instead of RMS: When calculating audio or AC power loss, ensure both
VinandVoutare measured in the same domain (both RMS, or both Peak-to-Peak). Mixing RMS and Peak values will skew the ratio by a factor of $\sqrt{2}$, introducing a 3 dB error.
What a Realistic Answer Magnitude Looks Like
When using a dB loss calculator, you should immediately recognize if your answer violates the fundamental rules of logarithmic decay. Memorize these baseline magnitudes to sanity-check your results:
| dB Loss | Power Remaining | Voltage Remaining | Real-World Context |
|---|---|---|---|
| -1 dB | 79.4% | 89.1% | Short patch cable, high-quality connectors |
| -3 dB | 50.0% (Half) | 70.7% | Standard splitter loss, or long thin coax run |
| -6 dB | 25.0% | 50.0% (Half) | Two cascaded -3dB splitters |
| -10 dB | 10.0% | 31.6% | Severe attenuation; requires inline amplifier |
| -20 dB | 1.0% | 10.0% | Signal practically destroyed; 99% power lost as heat |
For practical RF system design, keep your total feedline loss under 3 dB at your target operating frequency. Beyond 3 dB of loss, you are converting more than half of your transmitter's expensive RF energy into heat inside the coaxial cable rather than radiating it from the antenna. For further reading on transmission line theory and practical antenna system design, consult the ARRL Transmission Lines guide.
