The attenuation calculator above handles loss that accumulates per unit length. You give it an attenuation coefficient — decibels per kilometre, decibels per metre or nepers per metre — and a path length, and it returns the total loss in decibels, the power that survives, the output level in dBm, and how far the signal would reach before exhausting a loss budget you set.
Arb Digital keeps each loss mechanism on its own page, because they are genuinely different physics. The free space path loss calculator handles loss that comes from a wave spreading out over distance, which grows with the square of range and has nothing to do with the medium. The sound attenuation calculator handles the acoustic case. This page owns the per-unit-length case: a signal losing a fixed number of decibels for every kilometre of material it passes through.
What This Attenuation Calculator Does
Attenuation is the reduction in a signal's power as it propagates. When the loss mechanism is absorption or scattering by the medium, the fractional loss per unit length is constant, which makes the power fall exponentially with distance. Take the logarithm of that exponential and you get a straight line, which is why the loss in decibels is simply the coefficient multiplied by the length.
That linearity in decibels is what makes the decibel worth using. Two spans in series multiply their power ratios but add their decibel losses, so a link budget becomes arithmetic you can do in your head. The same applies to connectors, splices and components: everything on the path contributes decibels, and they sum.
The tool works in either of the two conventions you will meet. Decibels per unit length is the engineering standard for cables and fibres. Nepers per metre is the physics standard, based on natural logarithms and applied to field amplitude rather than power, and one neper of amplitude decay is 8.6859 decibels of power loss. Getting that factor wrong is one of the most common quiet errors in this subject, so the tool converts explicitly.
How to Use It
- Get the coefficient from your own datasheet. Attenuation depends strongly on frequency or wavelength, and a figure quoted for one operating point does not carry across to another.
- Use the routed length, not the map distance. Slack coils, risers and service loops all count, and on a long run they add up to a real number of decibels.
- Enter the input power in whatever form you have it. Milliwatts, watts and dBm are all accepted, and the tool reports the output in both linear and logarithmic form.
- Set a realistic loss budget. It should be the difference between transmit power and receiver sensitivity, less whatever margin you intend to hold back.
- Add the discrete losses separately. This page gives you the distance-dependent part. Connectors, splices and splitters are fixed decibel amounts you add to the total.
The Formula: How Attenuation Is Calculated
Total attenuation in decibels is A = α × L, where α is the coefficient in decibels per unit length and L is the path length in the matching unit. The surviving power is Pout = Pin × 10−A/10, and in logarithmic units the output level is simply the input level in dBm minus A.
The decibel itself is ten times the base-ten logarithm of a power ratio, the definition set out on the Georgia State University HyperPhysics page on decibels. When the coefficient is given in nepers per metre it describes exponential decay of field amplitude, and converting to power decibels multiplies by 20 log10(e), which is 8.685889.
Specific attenuation expressed per unit length is how standards bodies publish medium loss. ITU-R Recommendation P.676, Attenuation by atmospheric gases and related effects, is a good example: it gives the specific attenuation of the atmosphere in decibels per kilometre as a function of frequency, pressure, temperature and water vapour, over a range from 1 to 1,000 GHz. The arithmetic on this page is exactly what you do with such a figure once you have it.
Work the defaults by hand. A coefficient of 0.2 dB/km over 80 km gives A = 16 dB. With 1 mW in, that is 0 dBm in and −16 dBm out, and the surviving power is 1 × 10−1.6 = 0.02512 mW, or 25.12 µW. That is 2.512 per cent of what went in. On a 25 dB budget the same coefficient reaches 25 ÷ 0.2 = 125 km, and the half-power point, where exactly 3 dB has been lost, sits at 15 km.
Why Decibels and Not Percentages
People often want the loss as a percentage, and it is available — the grid gives it — but it is the wrong tool for a link. Percentages do not add. Two spans that each pass 50 per cent of the power pass 25 per cent together, not zero. Decibels do add: two 3 dB spans make 6 dB, and that is the end of it.
The second reason is dynamic range. A long optical link can span more than ten orders of magnitude between transmit power and receiver sensitivity, and a scale on which that range is a hundred-odd decibels is far easier to work with than one on which it is a string of zeros. The logarithm compresses the range into numbers a person can hold.
A few landmarks are worth committing to memory. Three decibels is half the power. Ten decibels is a tenth. Twenty decibels is a hundredth, thirty is a thousandth. Anything else can be assembled from those: 16 dB is 10 plus 3 plus 3, which is a tenth of a quarter, which is 2.5 per cent — exactly the default result on this page.
Attenuation, Spreading and Why They Are Different
Two things called loss behave in completely different ways, and confusing them produces answers that are wrong by orders of magnitude.
Attenuation per unit length is what happens inside a medium. Each metre removes the same fraction, so the power decays exponentially and the loss in decibels grows linearly with distance. Doubling the length doubles the decibels.
Spreading loss is geometry. A wave radiating into free space spreads its power over a sphere whose area grows with the square of the distance, so power falls as an inverse square and the loss in decibels grows logarithmically with distance. Doubling the range adds 6 dB regardless of how far you already are. That is the case the free space path loss calculator handles.
A real radio link has both: spreading between the antennas plus atmospheric absorption per kilometre. A cable or fibre has essentially only the first kind, because the signal is guided rather than allowed to spread. Knowing which mechanism dominates tells you whether adding range costs you a fixed number of decibels per kilometre or a diminishing number.
What the Coefficient Depends On
The single most important thing to understand about an attenuation coefficient is that it is not a property of the cable alone. It is a property of the cable at a frequency.
In metallic cable, loss rises with frequency because of the skin effect, which confines current to a thinner and thinner layer at the conductor surface as frequency climbs, and because of dielectric loss in the insulation. A coaxial cable rated at a modest loss per hundred metres at low frequency can be several times worse an octave or two up.
In optical fibre the mechanisms are Rayleigh scattering, which falls steeply with increasing wavelength, and infrared absorption, which rises again beyond a point, with a water-related absorption feature between them. The result is a curve with minima, which is exactly why particular transmission windows became standard.
Temperature, bend radius, ageing, moisture ingress and installation damage all move the figure as well, and always in the direction of more loss. That is why a link is designed with margin rather than to the exact budget, and why measured loss on a commissioned link is compared against the calculated figure rather than assumed to match it. For the electrical characteristics that sit alongside loss, the cable impedance calculator and the crosstalk calculator cover the other two things that limit a cable run.
Arb Digital builds free tools like this one because useful pages earn attention. If you want tools, calculators or content built for your own audience, we can help.
Browse All Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Using a coefficient from the wrong frequency — attenuation is strongly frequency-dependent in every medium, and a figure quoted at one operating point can be several times off at another.
- Confusing nepers with decibels — one neper of amplitude decay is 8.686 dB of power loss. Treating them as interchangeable is an error of nearly nine to one.
- Adding percentages instead of decibels — power ratios multiply along a path. Only the logarithmic form adds, which is why link budgets are done in decibels.
- Forgetting the discrete losses — connectors, splices and splitters each cost a fixed number of decibels that this page does not include. Add them to the distance-dependent total.
- Designing with no margin — temperature, ageing, bends and repairs all move loss upward over the life of a link. A budget consumed exactly on day one is a budget already exceeded.
Related Free Tools From Arb Digital
For loss caused by spreading rather than by a medium, use the free space path loss calculator, and for the acoustic case use the sound attenuation calculator. Move between logarithmic and linear power with the dBm to watts converter and handle ratio arithmetic with the decibel calculator. For the rest of a cable's behaviour, see the cable impedance calculator and the crosstalk calculator, and for a radio link's transmit side see the EIRP calculator. The frequency converter keeps the operating point straight. Everything Arb Digital publishes is listed on the free online tools hub.
Frequently Asked Questions
Multiply the attenuation coefficient by the path length in matching units. A coefficient of 0.2 decibels per kilometre over 80 kilometres gives 16 decibels of loss. Then add the fixed losses of any connectors, splices or components on the same path.
Raise ten to the power of minus the decibels divided by ten. Three decibels leaves half the power, ten decibels leaves a tenth, twenty leaves a hundredth. Sixteen decibels leaves about 2.5 per cent, since it is ten plus three plus three.
A neper is based on the natural logarithm and describes decay of field amplitude, while a decibel is based on the base-ten logarithm and normally describes a power ratio. One neper of amplitude decay corresponds to 8.686 decibels of power loss.
Because the loss mechanisms do. In metallic cable the skin effect confines current to a thinner surface layer as frequency rises, and dielectric losses grow too. In optical fibre, scattering falls with wavelength while infrared absorption rises, which produces the transmission windows that systems are designed around.
No. Attenuation here means loss per unit length inside a medium, which grows linearly in decibels with distance. Free space path loss comes from a wave spreading over a growing sphere, so it grows logarithmically with distance and adds about six decibels every time the range doubles.
Divide the budget in decibels by the coefficient in decibels per unit length. A 25 decibel budget at 0.2 decibels per kilometre reaches 125 kilometres before anything else is counted, and connectors, splices and design margin reduce that in practice.
No. Loss increases over the life of an installation through temperature swings, ageing, additional bends and repair splices. Engineering practice is to hold back margin so that the link still works when those changes have accumulated rather than only on the day it was commissioned.
This tool is provided for educational and estimating use. It applies a uniform attenuation coefficient you supply over a path length and does not model dispersion, reflections, connector and splice losses, temperature effects or ageing, so treat its output as a first-pass estimate rather than a commissioned link budget or a measured result.
