How RouterMap works: model, calculations and sources

A technical note setting out every stage of RouterMap's estimate, from the geometry of the drawn home to the calibration against a household's own speed tests, with the constants used and the sources they rest on.

Dr Alex J. Martin-Smith, CMgr DBA · LinkedIn · Published 3 September 2026 · Version 1.0

1Purpose and scope

RouterMap estimates the Wi-Fi coverage a household can expect across a typical UK home of a chosen type, shows how that changes as the router moves, and finds the position that covers the most of the home. It is a site-general model in the sense used by ITU-R P.1238 (ITU-R, 2025): it describes a class of building from a small number of parameters rather than a surveyed building from a full description. Its outputs are estimates, and the interface says so. The point of setting the method out in full is that an estimate whose working is visible can be argued with, corrected, and calibrated; one whose working is hidden cannot.

Two design decisions shape everything that follows. First, walls are counted explicitly rather than absorbed into the distance term, following the multi-wall approach of COST 231 (Damosso & Correia, 1999), because the difference a doorway or a party wall makes is exactly what the household needs to see. Second, every constant is held in one place and treated as a published indicative value for its material or environment class, not as a measurement of any particular property. The calibration stage (Section 18) exists precisely because those values vary between real homes.

2Notation

3Generative geometry

Each floor of a home is defined only as a set of axis-aligned rectangles, one per room, that tile the floor's footprint exactly. Everything else is derived. Walls are generated from shared room edges and from the footprint boundary; doorways are punched as real gaps in the wall set; windows are placed on external edges of habitable rooms; furniture is placed procedurally by room type. The derivation guarantees that a room and its walls can never disagree and that no unlabelled space can exist.

Wall classes are assigned as follows. Footprint edges are external, except those flagged as shared with a neighbour, which are party. Internal edges are stud unless they lie on a declared structural line, in which case they are masonry. Where two circulation spaces meet (hall, stairs, landing) no wall is generated. Declared open-plan pairs receive a wide opening with short wall stubs. A room of type void represents space outside the home (a yard, a light well, eaves): it is excluded from every statistic, walls against it are external, and nothing opens onto it.

Doorways follow the way a house is actually connected. Every room opens onto a hall, landing or staircase where it shares an edge with one. Two rooms open onto each other only where British houses do that: kitchen to dining room, kitchen to utility, a through-lounge to its dining room, garage to utility, a bedroom to its own en suite, and any pair declared for a particular layout. Bedrooms do not open into bedrooms and a bathroom is not a corridor. This matters for the estimate, because a doorway is a gap in the wall set: an imaginary door between two bedrooms is a hole the model would let signal through. A short shared edge still receives a narrower door, and a validator confirms that every room on every floor is reachable and that no fallback door was needed.

Each layout declares its front door, or flat door, on the hall's external edge. The master socket, or the optical network terminal on full fibre, is placed just inside it, and the router starts beside the socket. That is where installers put them, because it is the shortest run for the cable from outside or from a riser in a corridor, and it is where most routers stay. The interface says so, because for most houses that corner is one of the worst places for a router to be.

Layout footprints are drawn to floor areas consistent with the English Housing Survey averages by dwelling type (Ministry of Housing, Communities and Local Government [MHCLG], 2020), so that a "semi-detached, 3 bed" in the checker is close to the average semi-detached house in England by area, not to a show home.

4Footprint from certificate data

Where a household supplies its own floor area, the chosen archetype is scaled by an affine transform of the room rectangles. Only the rectangles scale; walls, doorways, windows and furniture are re-derived at their true sizes, so a scaled plan retains 850 mm doorways and a 2 m bed.

Domestic Energy Performance Certificates (MHCLG, n.d.) record, per floor, the floor area A, the heat-loss perimeter P_h and the party wall length P_p. For a broadly rectangular footprint the total perimeter is P = P_h + P_p, and width and depth are the roots of

The solution is accepted only when both roots exceed 1.8 m and their ratio is below 4. The party wall length then identifies the shared elevation: whichever of x, 2x best explains P_p (within 20%) marks the depth of the house as shared on one or both sides. For a genuinely L-shaped footprint the discriminant is negative and the method falls back to scaling by area alone.

5The link budget

The received level at a point, for a given band, is

where FSPL(1 m, f) = 20 log₁₀(f) − 27.55 dB for f in MHz, the close-in free space reference at one metre used by the CI form of the log-distance model (Rappaport, 2002); β = 1 when the source and the point share a floor and 0.7 otherwise (Section 8); A_near is a small near-field term for what is touching the router (Section 22); and A_src is 0 for the router and −3 dB for a mesh point (Section 17). The distance d is three-dimensional, with the vertical component taken as s ⋅ 2.6 m less the difference between the router's height and a device height of 1.0 m, and floored at 1 m.

Transmit levels are typical of licence-exempt indoor equipment in the United Kingdom: 20 dBm EIRP at 2.4 GHz and 23 dBm at 5 and 6 GHz (Ofcom, 2026). L_c is 5 dB, representing the antenna of a phone or laptop and the body holding it.

6Distance exponent and clutter

ITU-R P.1238 tabulates a residential distance power loss coefficient of N = 28 at 2.4 GHz, that is n = 2.8, with walls absorbed into the coefficient (ITU-R, 2025). Because walls are counted explicitly here, the base exponent is lower, and it is made to depend on router height.

3GPP TR 38.901 distinguishes a device that is clutter-embedded, with its antenna below the average height of the surrounding clutter, from one that is clutter-elevated (3GPP, 2019). In a home the clutter is furniture, and its average height is taken as h_c = 0.95 m. The exponent is

with n₀ = 2.77, σ = 0.26 and δ the calibrated shift of Section 18 (zero by default). The four height settings map to h = 0.1, 0.5, 1.2 and 1.8 m, giving exponents of 3.02, 2.90, 2.70 and 2.52. Modelling height as a change in exponent rather than a fixed offset is the substantive choice: it makes the penalty for a low router grow with distance, so that height matters little in the same room and a great deal at the far end of the house.

7Wall attenuation

The direct path from source to point is tested against every wall segment on the relevant floor; each crossing adds the reference attenuation of that wall class. Reference values at 2.4 GHz are indicative of published ranges for the material class (COST 231; Damosso & Correia, 1999; ITU-R, 2025):

Frequency scaling κ(f) is 1.00 at 2.4 GHz, 1.45 at 5 GHz and 1.55 at 6 GHz. The construction multiplier α is 0.75 for newer timber-framed construction, 1.00 for the mixed block and stud of a standard UK house, and 1.30 for older solid brick. These three factors are applied multiplicatively to the sum of crossed-wall attenuations, so a solid-walled Victorian terrace on 5 GHz applies 1.45 × 1.30 = 1.89 times the reference value of each wall it crosses.

8Floors and stairwells

For s ≥ 1 storeys crossed, the floor loss is

with L_f = 12, 15 or 19 dB for newer, standard and solid construction. The sub-linear growth in s follows the empirical form of the COST 231 multi-floor term (Damosso & Correia, 1999). An open stairwell is a hole in the floor: where the horizontal distance from the router to the stairwell, a, and from the point to the stairwell, b, are both under 4 m, the relief is R_stairs = 7(1 − a/4)(1 − b/4) dB. Walls on the destination floor are counted at weight β = 0.7, because a path arriving through a floor at an angle does not fully cross every partition it passes over.

9Doorways

A doorway is a genuine gap in the wall set, 0.85 m wide, so a path through an open door picks up no wall loss. When the household indicates that internal doors are usually shut, a path through a doorway adds 3 dB. Open-plan openings add nothing in either case.

10Diffraction proxy

A pure straight-ray model draws knife-edge shadows behind every wall corner. Real signal diffracts around edges and reflects from surfaces. Rather than a full ray-tracing treatment, which P.1238 describes as a site-specific method requiring full building detail (ITU-R, 2025), the received-level grid is smoothed with a separable box filter of radius 0.42 m applied twice, which approximates a Gaussian kernel of similar width. This softens shadow edges while preserving the wall structure. It slightly under-states the benefit of reflections in open-plan rooms, and the limitations section says so.

11Noise floor and interference

Neighbouring networks do not reduce a household's received level; they raise the floor it must clear. Three environment classes set an effective noise floor N₀ of −95, −90 and −84 dBm for a quiet street, a typical street and a dense block of flats. The usable threshold is defined relative to it:

so that in the quiet case T = −67 dBm, a widely used design target for reliable Wi-Fi. In the dense case it rises to −56 dBm. The map therefore stays the same as the environment worsens, while the usable line moves inward and the throughput falls, which is what a household in a flat experiences.

12Throughput mapping

Achievable throughput is a bounded, saturating function of signal to noise ratio, in the spirit of Shannon (1948) but shaped to the stepped modulation and coding schemes of IEEE 802.11 (IEEE, 2021):

with R_max = 110, 620 and 900 Mb/s for the 2.4, 5 and 6 GHz bands and η = 0.55, 0.85 and 1.00 for the three router classes. The 8 dB offset is the SNR at which the lowest rate becomes available, the 35 dB span the SNR range over which rates climb to the maximum, and the exponent 1.7 reflects that throughput collapses far faster than signal as SNR falls. The result is capped at the household's broadband speed.

13Band and source selection

At every grid cell the model evaluates every (source, band) pair. It then does what a band-steering router does: among pairs whose level is at or above T, it selects the one with the highest throughput; only when no pair reaches T does it fall back to the strongest level. Colour and speed at a cell therefore come from the same band, and adding a faster band can never make a room appear worse. Adding a source, whether a better router or a mesh point, can only improve or leave unchanged every cell.

14Room statistics and verdicts

For each room the model gathers the grid cells within it and reports the median level, the median throughput, and the proportion of cells at or above T, denoted p_good. The room's verdict is a function of how much of its floor works, not of its centre alone:

Whole-home coverage is the area-weighted mean of p_good across rooms, with each room additionally weighted by type (living 1.35, office 1.30, bedroom 1.20, dining and kitchen 1.00, hall and landing 0.50, bathroom 0.45, utility 0.30, stairs 0.30, cloakroom 0.20, garage 0.15), so that a weak utility room costs less than a weak bedroom.

15Activity requirements

A room is judged fit for an activity when both its median throughput and its median level clear that activity's requirement. Stability matters as much as speed: a video call at 40 Mb/s on a level that keeps dipping is worse than one at 12 Mb/s that holds.

The plain-terms summary shown against each room is the highest tier the room satisfies, in the order: Everything; 4K and calls; Calls and HD; HD video only; Browsing only; Not much.

16Placement optimiser

Candidate router positions are sampled at 0.75 m spacing inside every room in which a router could realistically live (bathrooms, cloakrooms, garages and voids excluded), inset 0.35 m from the walls. Each candidate is scored against a sparse set of sample points at 1.15 m spacing across the whole home, weighted by room type and area. The objective is

where q(P) = 1 / (1 + e^{−(P − T)/3.2}) is a logistic soft version of the usable threshold, chosen so that the optimiser climbs the same quantity the headline reports rather than a different one; the worst-point term discourages solutions that abandon one room entirely; S_room is a small suitability bonus for halls, landings and living rooms and a penalty for kitchens and utility rooms; and C_cable = min(0.06, 0.0035(ℓ − 5)) for a cable run ℓ beyond 5 m. The cable run itself is estimated as 1.15 times the Manhattan distance from the master socket plus 4.5 m per storey plus 1 m, rounded up to a standard cable length. When the household asks for reachable spots only, candidates beyond 12 m are excluded. The top three candidates at least 1.8 m apart are reported.

17Mesh points and backhaul

A mesh point is a second source with A_src = −3 dB. Its link back to the router is evaluated with equation (2) and mapped to a backhaul throughput R_bh with equation (6). Throughput delivered by the mesh point at any cell is capped at 0.9 R_bh, because a wireless repeater cannot pass on more than it receives and spends part of its airtime doing so. This cap is what distinguishes a mesh point that helps from one placed so deep in the weak room that it repeats a weak signal. The automatic mesh suggestion considers only candidates whose link to the router is at or above −62 dBm, preferring landings and halls, and relaxes to −72 dBm with a warning only when nothing better exists.

18Calibration

Two parameters vary most between real homes: how much the walls take, μ, and how fast the signal falls away, δ. Given m measured throughputs M_j in identified rooms, taken from the router alone, the model minimises

over the bounded grid μ ∈ [0.5, 2.0] in steps of 0.1 and δ ∈ [−0.4, 0.4] in steps of 0.1, where R̂_j is the model's median throughput for room j. The error is taken in the log domain so that a 10 Mb/s miss in a weak room counts as much as a 100 Mb/s miss in a strong one. The regularisation terms express a mild preference for the typical home. Readings within 15% of the broadband speed are excluded, since they say more about the line than the Wi-Fi. A reading the fitted model still cannot bring within a factor of 2.5 is flagged as probably local: a large metal appliance beside the router, foil-backed plasterboard, or a router shut in a cupboard. Fitting takes under 100 ms in a browser.

19Measured advice

Each recommendation the checker makes that can be measured is measured, by re-running the whole model with that one change and reporting the difference in whole-home coverage: lifting the router to shelf height, opening the internal doors, moving to the best position, swapping for a tri-band router. Recommendations are shown only when the measured gain exceeds 0.5 percentage points. The escalation to mesh is triggered by a room condition, not an area percentage: it is raised when, at the best available position, any living room, bedroom, office, kitchen or dining room still has p_good below 0.5.

20Router catalogue

Transmit power for licence-exempt Wi-Fi is regulated (Ofcom, 2026), so routers do not differ much in how far a signal reaches. They differ in what they do with the power they are allowed: more spatial streams and beamforming buy a few decibels of effective gain at the edge of coverage, and each generation of the standard delivers more throughput per decibel of signal to noise ratio. The catalogue therefore maps every router onto the same four parameters used by the generic classes: the bands it offers, the number of spatial streams on 5 GHz, whether its aerials are external, and its generation.

with g_streams = 1.0, 1.5 or 2.0 dB for 2x2, 3x3 and 4x4 on 5 GHz, and η = 0.55, 0.85, 0.92 and 1.00 for Wi-Fi 5, 6, 6E and 7 (equation 6). The mapping is deliberately coarse. It is not a benchmark of any product; it is a way of placing a named router on the same scale as the generic classes so a household can pick the box it actually has.

Specifications are best efforts. They are taken from provider and manufacturer pages and from independent reviews and teardowns, checked on 4 September 2026, and they change without notice. Verified means generation, bands and streams were confirmed from such a source on that date; best efforts means generation and bands were confirmed and the stream count is assumed from the product class. Where sources disagreed the more detailed source was preferred and the disagreement is noted in the entry.

Coverage differences between these units are small: on the standard semi-detached layout with the router in the hall, every entry lands between 91% and 94% of floor area above the usable line. The throughput differences are large, from about 200 Mb/s average across the rooms for a Wi-Fi 5 hub to about 570 Mb/s for a tri-band Wi-Fi 7 unit on a 900 Mb/s line. That is the honest basis on which the checker recommends a router: not reach, but speed and stability.

21Limitations

• The model is site-general. It knows the class of a wall, not the wall.
• Reflections are not traced; the diffraction proxy under-states them in open-plan spaces.
• The antenna pattern is not modelled. A vertical dipole radiates weakly straight up and down, so the gain from raising a router is smaller directly overhead than equation (3) implies.
• Foil-backed plasterboard, underfloor heating mats, chimney breasts, metal-framed glazing and lath-and-plaster are not represented and can each shift a room by several decibels.
• Client devices differ. An older phone will do worse than the estimate and a recent laptop with a larger antenna better.
• Interference is modelled as a noise floor, not as channel-by-channel contention; a congested channel behaves worse than the class average.
• The room arrangement of an archetype is typical, not the household's own, even when the footprint has been scaled to theirs.

22Constants

23References

1. 3GPP. (2019). Technical Specification Group Radio Access Network; Study on channel model for frequencies from 0.5 to 100 GHz (Release 16) (TR 38.901 V16.0.0). 3rd Generation Partnership Project.
2. Damosso, E., & Correia, L. M. (Eds.). (1999). COST Action 231: Digital mobile radio towards future generation systems, final report (EUR 18957). European Commission.
3. IEEE. (2021). IEEE Standard for Information Technology: Telecommunications and information exchange between systems, local and metropolitan area networks, specific requirements. Part 11: Wireless LAN medium access control (MAC) and physical layer (PHY) specifications (IEEE Std 802.11-2020). Institute of Electrical and Electronics Engineers.
4. ITU-R. (2025). Recommendation ITU-R P.1238-13: Propagation data and prediction methods for the planning of indoor radiocommunication systems and radio local area networks in the frequency range 300 MHz to 450 GHz. International Telecommunication Union.
5. Ju, S., & Rappaport, T. S. (2023). 142 GHz multipath propagation measurements and path loss channel modeling in factory buildings. arXiv. https://arxiv.org/abs/2302.12142
6. Kacou, M., Guillet, V., El Zein, G., & Zaharia, G. (2018). A multi-wall and multi-frequency home environment path loss characterization and modeling. In Proceedings of the 12th European Conference on Antennas and Propagation (EuCAP 2018). Institution of Engineering and Technology.
7. Ministry of Housing, Communities and Local Government. (2020). English Housing Survey 2018 to 2019: Headline report. UK Government.
8. Ministry of Housing, Communities and Local Government. (n.d.). Energy Performance of Buildings Data: England and Wales [Data set]. https://epc.opendatacommunities.org/
9. Ofcom. (2026). UK Interface Requirement 2030: Licence exempt short range devices (IR 2030, April 2026). Office of Communications.
10. Rappaport, T. S. (2002). Wireless communications: Principles and practice (2nd ed.). Prentice Hall.
11. Shannon, C. E. (1948). A mathematical theory of communication. The Bell System Technical Journal, 27(3), 379–423.