Path Loss Calculator
The formula
What the radio path loss tells you
Signal attenuation over distance for a link design — free space for towers and backhaul, Hata for urban macro cells with clutter.
Calculation: FSPL = 32.44 + 20log d + 20log f; Hata = 69.55 + 26.16logf − 13.82loghb + (44.9 − 6.55loghb)logd. Enter your inputs and every substitution is shown below the result.
Reading the result
The Hata-minus-free-space gap is the tax the city charges: 20–30 dB at these distances means a link that works rural needs a relay downtown.
Rules of thumb: Urban 5 km at 900 MHz lands ≈ 147 dB; same path free space is ≈ 106 dB.
Limitations and best practice
Hata is calibrated 150–1500 MHz and 1–20 km; stretching it to 5 GHz or 200 m distances gives confident nonsense.
This calculator gives an estimate based on standard formulas; it is not professional financial, medical, legal or engineering advice. Verify anything you plan to act on with a qualified professional and your own records.
Frequently asked questions
Which model should I pick?
Why does the 3 dB rule appear here?
Source & methodology
Okumura-Hata empirical model (IEEE Trans. Veh. Technol., 1980); FSPL per standard radio texts.
How Path Loss works — and what your result really means
This page was written for one job: turning your own inputs into a defensible figure, with the working shown. Searchers land on a Path Loss page for three reasons — to plan, to compare options, and to check that somebody else’s arithmetic is honest. This tool serves all three, and everything after the calculator explains the model instead of hiding it.
Like most useful measures, Path Loss is a summary, and summaries hide as much as they reveal. The companion outputs and the input table are here to reopen what the headline compressed.
That makes documentation a feature. The steps block above exists so that the next engineer to read this page can verify not just the result but the reasoning — the difference between a number that gets acted on and one that gets argued with.
What makes a calculation page trustworthy is that its copy is derived from its own arithmetic: here path loss (chosen model) = 148.5 dB, recomputed every time a field changes, and the sensitivity section ranks the inputs that move the result — Distance first, at ≈1.1 % of the headline for a ten-percent error either way in that input. Work down the page and by the end you could re-derive the result in a spreadsheet from memory.
How Path Loss is computed, line by line
Here is the complete model this tool runs — FSPL = 32.44 + 20log d + 20log f; Hata = 69.55 + 26.16logf − 13.82loghb + (44.9 − 6.55loghb)logd — with each input explained below. If a competitor’s page gives you a different answer from the same inputs, this is the text that settles which of you is right.
Distance (km) (example value 4) is a plain measured quantity — the unit shown in the label is the unit the formula expects. Measure twice and use the unit the label asks for — length terms often scale the result geometrically.
Frequency (MHz) (example value 953) is a measured number in the unit named by the label; the formula does not convert for you. The example value is there to demonstrate the mechanics, not to describe your situation — overwrite it.
Base antenna height (m) (example value 29) is a plain measured quantity — the unit shown in the label is the unit the formula expects. Small measurement errors grow here: a length that is squared or cubed in the model magnifies a one-percent slip into a three-percent answer.
Environment (example value Urban macro (Hata)) is a choice rather than a quantity — pick the option that matches your situation, because the calculation path branches here. The example value is there to demonstrate the mechanics, not to describe your situation — overwrite it.
What each “Environment” choice actually does: Free space / rural LoS → 104.1 dB · Urban macro (Hata) → 148.5 dB — each value above is the model’s own output for that option, so the choice can be made on evidence rather than on what a category feels like it means.
The default Path Loss calculation, written out in full
Rather than describe the calculation, here it is end to end — every substitution in order, starting from the inputs above. Starting figures: Distance (km), Frequency (MHz), Base antenna height (m), Environment. The computed path loss (chosen model) comes out at 148.5 dB, which the interpretation band labels “Beyond typical cell radius”.
- FSPL = 32.44 + 20·log(4.0 km) + 20·log(953 MHz) = 104.1 dB
- Hata adds clutter: 69.55 + 26.16·logf − 13.82·loghb + (44.9−6.55·loghb)·logd = 148.5 dB
- Excess loss = 44.5 dB at 29 m antenna height
- RSL = 43 + 3 − 148.5 = -102.5 dBm
Free-space loss — 104.1 dB. This is the number experienced users quote when the headline alone would mislead.
Urban excess over free space — 44.5 dB. Compare it against the main result of 148.5 dB before drawing conclusions.
RSL at 43 dBm tx + 3 dBi rx — -102.5 dBm. Read next to the headline, this is the figure that shows the shape of the trade-off.
Frequency penalty vs 900 MHz — 0.5 dB. Compare it against the main result of 148.5 dB before drawing conclusions.
Overwrite any input above and every line of this example updates with it — the substitution is live, not a screenshot of somebody else’s numbers.
Scenario table: Path Loss at ±10 % and ±20 % of the key input
Read this table as the practical error bar on the headline figure. It answers the question people actually have after seeing a single number: how wrong could this be if the main input is off by ten or twenty percent?
| Distance setting | Path loss (chosen model) |
|---|---|
| 80 % of the example value | 145.1 dB |
| 90 % of the example value | 146.9 dB |
| example inputs | 148.5 dB |
| 110 % of the example value | 150.0 dB |
| 120 % of the example value | 151.3 dB |
Across 5 settings of Distance, the result spans 145.1 dB to 151.3 dB. A decision that only works at one row of this table is a decision waiting for an input to move. Reproduce it in the form above by editing Distance alone; the substitution steps will follow your figures exactly.
Sensitivity: which inputs change Path Loss the most
Generic advice says “it depends on your inputs”; this section says exactly how much. Each field was perturbed by ±10 % in isolation and the path loss (chosen model) recomputed, so the ranking below is measured rather than asserted. It is the fastest honest answer to “what matters most in Path Loss?” — and it is specific to these defaults, because sensitivity moves with the starting point.
- Distance: ten percent up gives 150.0 dB, ten percent down gives 146.9 dB — ≈1.1 % of the path loss (chosen model) either way
- Frequency: ten percent up gives 149.6 dB, ten percent down gives 147.3 dB — ≈0.8 % of the path loss (chosen model) either way
- Base antenna height +10 % → Path Loss = 147.8 dB · −10 % → 149.4 dB (the path loss (chosen model) shifts ≈0.5 %)
Distance is the dominant lever here: ten percent either way moves the result by about 1.1 %, from 146.9 dB to 150.0 dB. That is where a careless figure does the most damage, so check it against a source, and treat Frequency as the second priority (≈0.8 % per ten percent). Everything below that can stay approximate, which is a licence to stop chasing data that would not change the decision.
Reading the result: bands, zones and thresholds
A number on its own is trivia; a number against a range is intelligence. The default case lands in the “Beyond typical cell radius” band, and bands are deliberately wide because real situations overlap. How much of that band is luck? On Distance alone ten percent either way covers 146.9 dB to 150.0 dB. The practical reading rules: ask what would have to change to move you one band. If the answer is “a small, plausible input difference”, the band itself is not the finding — the uncertainty is.
Related measures answer related questions, and the distinctions matter: Path Loss is the quantity, Path loss (chosen model) is this tool’s reading of it, and the decision that follows belongs to neither of them separately.
How people get Path Loss wrong
Hata is calibrated 150–1500 MHz and 1–20 km; stretching it to 5 GHz or 200 m distances gives confident nonsense. This calculator gives an estimate based on standard formulas; it is not professional financial, medical, legal or engineering advice. Verify anything you plan to act on with a qualified professional and your own records.
Confusing a large number with an important one. Path Loss can be dominated by one input whose absolute value looks unimpressive, which is why this page ranks influence separately from magnitude.
One mistake is specific to this engine: assuming every input matters equally. The computation above shows Distance dominating — a careful figure there beats false precision everywhere else.
A final trap is presentation: reporting Path Loss to more decimal places than the inputs support. The tool prints what the arithmetic gives; you should quote only what your least precise field justifies.
Before you trust your Path Loss: a short checklist
- Compare the result with one independent method or published benchmark.
- Confirm the example values are plausible for your own situation before replacing them.
- Check Distance before anything else: it is the measured dominant input, ≈1.1 % of Path Loss per ten percent.
- Validate inputs against a live measurement, not datasheet peak figures.
- Record the date and the inputs alongside the number so future-you knows what was assumed.
- Run the ±10 % stress on the top two levers and check that your conclusion survives both.
How to use the Path Loss tool properly
Using a calculator well sounds trivial, but the difference between a decision-grade figure and a throwaway one lives entirely in the routine. The routine for Path Loss takes a minute to learn and applies to every input above.
Step 1 — one document, one pass. Open the statement, label or record that holds distance (km), frequency (mhz), base antenna height (m), environment and transcribe straight into the form. Transcription from a single source removes the mismatch errors that appear when figures are assembled from three different places. A figure nobody can reproduce is a figure nobody will act on twice.
Step 2 — enter the conservative case first. Resist the flattering scenario. Type the inputs you would defend in front of a sceptical reader, read the Path loss (chosen model) (148.5 dB for the example values), and note the verdict band. The input you reach for first is usually the one you measured longest ago.
Step 3 — play with the inputs on purpose. Ten percent up, ten percent down, one field at a time. Within a few minutes you will know this calculation better than most people who quote its results. The inputs are the part of the work that nobody else can do for you.
Step 4 — ask what would have to be true. Take the result you want and work backwards through the inputs until you find the assumption that produces it; then decide honestly whether that assumption is defensible. Note the assumption you are least sure about; that is where the real risk lives.
Step 5 — write the one-line memo. “Path loss (chosen model) = 148.5 dB on this date, from these inputs.” That line is the entire deliverable; everything else on this page is how you earned the right to write it. A figure nobody can reproduce is a figure nobody will act on twice.
Where Path Loss matters in practice
Most Networks & Storage disagreements are arithmetic disagreements in disguise. When Path loss (chosen model) of 148.5 dB sits on the table with its working shown, the conversation stops being about who sounds more confident and starts being about which input is wrong. If the answer changes your behaviour, it deserves a second run with different assumptions.
The audience for this page is people who need one trustworthy number before their next decision. In professional Networks & Storage practice the pattern is always the same — screen with Path Loss, then invest slow analysis only in whatever survives the screen. Note the assumption you are least sure about; that is where the real risk lives.
Re-running this page costs nothing and catches the slow drifts that never announce themselves. In Technology & Computing the expensive mistakes are rarely sudden; they are small changes in Distance (km) that nobody recalculated for a year. A figure nobody can reproduce is a figure nobody will act on twice.
Path Loss — frequently asked questions
What affects Path Loss the most?
The short answer: Distance. The longer answer is the sensitivity table on this page, where every numeric input was probed by ten percent and the path loss (chosen model) recalculated — Distance moved it furthest, by roughly 1.1 % (146.9 dB to 150.0 dB).
Which matters more: frequency or distance?
Distance, by a factor of about 1.4. Concretely: ten percent on Distance is worth ≈1.1 % of Path Loss, the same nudge on Frequency only ≈0.8 %. That ranking is re-computed for each page from that page’s own defaults.
How much does the “Environment” choice change the answer?
Across every option this tool offers, the path loss (chosen model) ranges from 104.1 dB (Free space / rural LoS) to 148.5 dB (Urban macro (Hata)) with all other inputs held at their example values. The per-option table is printed in the inputs section — this is a decision that genuinely moves the number, not a cosmetic dropdown.
What is a typical Path Loss?
With the example inputs on this page the result is 148.5 dB, labelled “Beyond typical cell radius”. “Typical” varies with situation, which is why every result here ships with its verdict band and its sensitivity list: they turn one figure into a range you can locate yourself inside.
How do I calculate Path Loss by hand?
Three steps: write the formula (FSPL = 32.44 + 20log d + 20log f; Hata = 69.55 + 26.16logf − 13.82loghb + (44.9 − 6.55loghb)logd), insert your values, and simplify. The worked example section shows exactly that chain for the default inputs; replicating it once on paper teaches you more about Path Loss than any number of calculator runs.
What happens to Path Loss if distance changes by 10 %?
On these inputs a ±10 % change in distance takes Path Loss to 150.0 dB against the 148.5 dB example — around 1.1 % of the headline. The same test on every other field is in the sensitivity section.
Is the Path Loss result of 148.5 dB good or bad?
Neither, on its own — the label “Beyond typical cell radius” is the band this figure falls in for the example inputs, and your own inputs will place you elsewhere on the same ladder. Judge the number against your history and your alternatives, and remember that a ten-percent error in Distance alone moves it by ≈1.1 %.
What affects Path Loss the most?
Sensitivity depends on where you start, but the inputs Distance (km) and Frequency (MHz) typically move Path Loss further than the rest because they enter the formula multiplicatively. If you can only measure two things well, measure those and hold the others at conservative defaults.
How do I calculate Path Loss manually?
Write down the inputs, then follow the printed steps in order — FSPL = 32.44 + 20log d + 20log f; Hata = 69.55 + 26.16logf − 13.82loghb + (44.9 − 6.55loghb)logd. A spreadsheet replicates it with two or three cells. The manual route is worth doing once to build intuition; after that the calculator saves time and eliminates transcription slips.
Which model should I pick?
LoS microwave → free space plus ducting margin; urban ground coverage → Hata or COST-231 for 1800+ MHz.
Why does the 3 dB rule appear here?
Loss grows 6 dB per distance doubling — cut range in half, get 6 dB back to spend on robust modulation.
Can this tool see the numbers I type?
It cannot. There is no submission step: the calculation happens in your browser and the result disappears when you close the page. Treat the fields above as a scratchpad rather than a form.
What the labels on this page mean
- Free-space loss
- 104.1 dB for the Path Loss worked case; it sits next to the main result because it carries context the headline leaves out.
- Urban excess over free space
- 44.5 dB on the example inputs — a companion figure printed beside the headline of Path Loss so that no result is read in isolation.
- RSL at 43 dBm tx + 3 dBi rx
- -102.5 dBm in the default Path Loss calculation — one of the secondary figures an experienced reader checks before trusting the primary number.
- Path loss (chosen model)
- The primary output of this tool: 148.5 dB for the default inputs, computed exactly from FSPL = 32.44 + 20log d + 20log f; Hata = 69.55 + 26.16logf − 13.82loghb + (44.9 − 6.55loghb)logd.
- Worked example
- The step-by-step substitution printed above, so the arithmetic can be re-derived by hand or in a spreadsheet.
- Verdict band
- The interpretation attached to a result (“Beyond typical cell radius” on these inputs), which turns a bare number into a position on a scale.
- Sensitivity (±10 %)
- How far the Path Loss moves when a single input is nudged ten percent either way; the ranked list on this page is computed live from this engine.
Where the Path Loss model comes from
The model is published arithmetic implemented exactly as written: FSPL = 32.44 + 20log d + 20log f; Hata = 69.55 + 26.16logf − 13.82loghb + (44.9 − 6.55loghb)logd. Source of record: Okumura-Hata empirical model (IEEE Trans. Veh. Technol., 1980); FSPL per standard radio texts. Any other implementation of this model should return the same figure for the same inputs. If one does not, the difference is in its assumptions — which this page prints and that one probably does not.
Treat the output as a precise answer to the question you typed: exact arithmetic, transparent formula, published source, no hidden rounding. What that buys you is reproducibility — two people, two browsers, the same arithmetic, and a printed trail from inputs to result that either of them can audit.
Next steps after the calculation
Re-run the calculation with your own figures, stress the two most sensitive inputs by ±10 %, and only then act on the result.
Whoever you are (people who need one trustworthy number before their next decision), the next step is the same: replace the example inputs with your own, note the date, and re-run whenever a figure moves. In Technology & Computing, a dated figure is a trend, and an undated one is a rumour.