Building entry loss calculator (ITU-R P.2109)
Building entry loss is how much weaker a signal is inside a building than just outside its façade. This calculator applies ITU-R P.2109-2 to traditional and thermally efficient buildings from 80 MHz to 100 GHz. It gives the loss not exceeded in a chosen share of buildings, plus the median and the 10 to 90 % spread.
A few common bands, not a full list. Picking one fills in the frequency. Typing another frequency switches back to custom.
P.2109-2 covers about 80 MHz to 100 GHz. Outside that range the results show “—”.
Thermally efficient means metal-coated (low-E) glass and foil-backed insulation. It is about the materials, not the age of the building. The other class is always drawn for comparison.
Angle of the path above the horizontal where it meets the wall. Only its size counts, so −30° and +30° give the same loss. The −90 to 90° range comes from the ITU-R reference code. Each degree adds 0.212 dB to the first component.
P % of buildings and indoor locations have a loss at or below the result. 50 % is the median. For coverage planning use a high P, such as 90 %.
Loss against probability at the chosen frequency and elevation angle, both axes linear. The solid green curve is the selected building class, the dashed grey curve the other class. The green dot is your probability and its loss, the hollow dot the other class at the same probability. Faint lines mark 10, 50 and 90 %. Read a point as “this share of buildings loses this much or less”.
P.2109-2 is a statistical model for sharing and compatibility studies, not a prediction for one building. It assumes an omnidirectional indoor antenna and ignores the azimuth of the path and whatever surrounds the building. Add clutter loss separately. The model was validated against data for P from 1 % to 99 %. Results are not clamped, so values near −3 dB at tiny P are part of the model.
How it works
- 01
Pick the frequency and building class
Traditional buildings lose more as the frequency rises. Thermally efficient buildings lose about 15 dB more from 1 to 6 GHz, and over 20 dB more at 28 GHz, because metal-coated glass and foil-backed panels reflect the wave. At 3.5 GHz the medians are 15.7 dB and 30.9 dB.
- 02
Build the two components
Each class combines two lognormal distributions. The first has median μ₁ = Lₕ + 0.212·|θ| and spread σ₁, the second μ₂ and σ₂. All four are short polynomials in log f, with f in GHz. Only μ₁ depends on the elevation angle.
- 03
Turn P into a quantile
F = Φ⁻¹(P) is the standard normal quantile of P. P = 10 % gives F = −1.28, 50 % gives 0 and 90 % gives +1.28. Then A = F·σ₁ + μ₁ and B = F·σ₂ + μ₂.
- 04
Power-sum the three terms
The loss is the power sum of A, B and a fixed C = −3 dB, so the largest term dominates. Because C never goes away, the result can dip below 0 dB at very low P and approach −3 dB. That is part of the model, not an error.
- 05
Read the spread, not one number
Between the 10 % and 90 % values, buildings of one class differ by 20 to 50 dB, more at high frequency. P.2109-2 asks for the whole distribution in sharing studies. The 10 % and 90 % values show how wide it is at your frequency.
Formulas
- LBEL — loss not exceeded at probability P, dB, for an omnidirectional indoor antenna, surrounding clutter excluded
- A = F·σ₁ + μ₁, B = F·σ₂ + μ₂ — the two lognormal components at P, dB
- C — fixed term, −3 dB
- Σ — sum over X = A, B and C, which adds their linear powers
- F = Φ⁻¹(P) — standard normal quantile of P (P as a fraction)
- Lₕ = r + s·log f + t·(log f)² — median for a horizontal path, dB
- θ — elevation angle at the façade, degrees, sign ignored
- σ₁ = u + v·log f, μ₂ = w + x·log f, σ₂ = y + z·log f — dB
- f — frequency, GHz
- traditional — 12.64, 3.72, 0.96 · 9.6, 2.0 · 9.1, −3.0 · 4.5, −2.0
- thermally efficient — 28.19, −3.00, 8.48 · 13.5, 3.8 · 27.8, −2.9 · 9.4, −2.1
Worked example
- log 28 = 1.447, so μ₁ = 20.03 dB, σ₁ = 12.49 dB, μ₂ = 4.76 dB, σ₂ = 1.61 dB
- F = Φ⁻¹(0.10) = −1.282
- A = −1.282 · 12.49 + 20.03 = 4.02 dB, B = −1.282 · 1.61 + 4.76 = 2.70 dB
- L = 10·log(2.525 + 1.862 + 0.501) = 6.89 dB, the SG3 workbook value (6.891 dB)
- Median 20.2 dB, 90 % value 36.1 dB. A thermally efficient building gives 19.5 dB at P = 10 %.
FAQ
- What does thermally efficient mean, and why does it matter for indoor coverage?
- It means metallised (low-E) glass and foil-backed insulation, and it costs roughly 15 dB of extra loss from 1 to 6 GHz. P.2109-2 classes buildings by materials, not by age. U-values below about 0.3 W/m²K for the walls and 0.9 W/m²K for the glazing point to it, and one poorly insulated window type can make a building behave as traditional. At 3.5 GHz the median is 15.7 dB for traditional and 30.9 dB for thermally efficient buildings.
- Why can the loss be negative?
- Because the model adds a fixed −3 dB term, and at very low P both lognormal terms fall far below it. The result then approaches −3 dB from above. The SG3 workbook itself lists −2.88 dB for a thermally efficient building at 2 GHz, 45° and P = 0.00001 %. Measurements do find indoor spots stronger than the outdoor reference. The calculator does not clamp the value.
- What P should I use for planning?
- For indoor coverage use a high P, such as 90 %, so the budgeted loss is exceeded in only one building in ten. For interference into or out of buildings use a low P, such as 10 % or less, because the leakiest buildings set the risk. P.2109-2 asks sharing studies to use the whole distribution. The median alone hides a spread of 20 to 50 dB.
- How does building entry loss differ from clutter loss and from the buildings in the simulator?
- Building entry loss is the wall the signal passes through to get inside. Clutter loss (ITU-R P.2108) is the extra loss from buildings and trees around a terminal that stays outdoors, and the two add up. Waveshed’s simulator treats buildings as outdoor obstructions that block or shadow the path. It does not model indoor penetration, so add the value from this page to its outdoor result when the receiver is inside.
- Do the wall orientation or a directional antenna change the result?
- Not in this model. P.2109-2 ignores the azimuth of the path relative to the façade and assumes an omnidirectional indoor antenna. Measurements at 32 GHz in two buildings in Korea found 5.3 dB more loss with a 10° beam antenna. The elevation angle does count, at 0.212 dB per degree.
Building entry loss starts where the outdoor signal ends. Waveshed computes that outdoor level over real terrain and building footprints, so you know what reaches the façade before you subtract this loss.
Map the outdoor signal →Related guides
- Including buildings — how the simulator uses building footprints, as outdoor obstructions
- LOS vs RF — where the outdoor signal level you start from comes from
Sources & further reading
- Recommendation ITU-R P.2109-2 (08/2023) — Prediction of building entry loss ↗ — equations (1) to (10) and Table 1, the model this calculator implements
- eeveetza/p2109 — MATLAB/Octave implementation of Recommendation ITU-R P.2109 (OFCOM) ↗ — reference code, functionally identical to the version published by Study Group 3. The −90 to 90° elevation range comes from its input checks.
- ITU-R Study Group 3 — Clutter and BEL workbook V2 (Excel) ↗ — sheet “BEL” for P.2109-2. The calculator matches its values to within 0.01 dB.
- Report ITU-R P.2346 — Compilation of measurement data relating to building entry loss ↗ — the measurements from 80 MHz to 73 GHz that the model was fitted to
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