LoRa & Meshtastic Link Budget and Fresnel Zone Calculator

The link budget is $P_{EIRP}=P_{TX}+G_{TX}-L_{TX}$ and $P_{RX}=P_{EIRP}+G_{RX}-L_{RX}-L_{misc}-L_{path}$, with powers in dBm and gains/losses in dB. Remaining design margin is $P_{RX}-S_{RX}-M_{required}$.

Sensitivity: Semtech SX1276/77/78/79, Rev. 7 (May 2020), Table 10, printed pp. 19–20: use the HF 125/250/500 kHz columns at SF7–SF12. Highest LNA gain, LnaBoost, split matched RX/TX paths, 25 °C, 1% packet error rate, 64-byte payload and coding 4/6 are the datasheet reference conditions. The table gives typical values, not guaranteed limits. External switch/feed losses are entered separately. Use manual sensitivity for other radios, frequencies or measured hardware.

Geometry: $\lambda=c/f$; $F_1=\sqrt{\lambda d_1d_2/D}$; effective-earth bulge $b=d_1d_2/(2kR)$ with mean $R=6371$ km. These are shallow-path approximations; the direct sight line joins antenna elevations. Clearance is sight-line height minus ground elevation and bulge; reserve is clearance minus $0.6F_1$. On each linear terrain segment the reserve is a linear term plus positive quadratic earth curvature minus a concave square-root Fresnel term, so it is strictly convex. Bounded Brent minimization finds each segment's interior minimum; both endpoints and the exact ridge are also tested. The minimum of all candidates drives clearance, the critical position and common antenna lift. Background-ground validity and direct sight-line clearance also use continuous minima. The plotted samples include the continuous extrema and are used only for drawing. Raising both antennas by the reported common lift removes the continuous deficit without changing path slope.

Propagation: ITU-R P.525-5 (2024), Annex §2, uses $L_{FS}=20\log_{10}(4\pi D/\lambda)$ with exact light speed. ITU-R P.526-15 (2019), §§2.1, 2.3 and 4.1, gives $\nu=-\sqrt{2}C/F_1$ and $J=6.9+20\log_{10}(\sqrt{(\nu-0.1)^2+1}+\nu-0.1)$ for $\nu>-0.78$; otherwise this planning approximation uses zero excess loss. Geometric mode adds J to free space for the one entered ridge, only within the diffraction-angle limit. The signed diffraction angle is the sum of the two ray elevation angles to the earth-adjusted ridge. This tool conservatively requires $|\theta|\leq0.2$ rad, following P.526-15 §4.1; an unsupported angle suppresses the knife-edge result and rejects that model.

Hata: original urban coefficients are 69.55 and 26.16; COST-231 uses 46.3 and 33.9. Both subtract $13.82\log_{10}(h_b)$ and the small/medium-city mobile correction and add $(44.9-6.55\log_{10}h_b)\log_{10}D$. Large-city Hata follows ETSI ETR 103 Annex B, printed p. 21: the low-frequency correction is specified for f ≤ 200 MHz and the high-frequency correction for f ≥ 400 MHz. The open interval 200–400 MHz is rejected; no interpolation or 300 MHz switch is assumed. COST metropolitan centres add 3 dB. Suburban and open corrections follow ECC Report 252 / SEAMCAT, pp. 362–363, equations 187–188, also for COST frequencies. The original Hata low-band coefficients differ slightly from SEAMCAT's rounded 69.6/26.2. This tool retains Hata's original coefficients. Total empirical loss is floored at free space, as SEAMCAT specifies. No knife-edge loss is added to empirical median loss.

The Hata comparison uses the selected family; in a geometric mode it shows original Hata for context. Invalid heights/frequencies produce a deliberate gap. Reference cases include published ETSI ETR 103 p. 9 intercepts and the exact half-field limit for a grazing edge; they are separate from property checks.

One-way, single-hop, far-field radio link with matched polarization unless an extra loss is entered. Antenna gains are relative to isotropic (dBi), entered in dB fields. Heights are above local ground; all ground elevations share one datum. The entered ridge is an ideal thin isolated knife edge for the diffraction estimate; straight terrain segments only illustrate the limited profile.

Effective-earth factor k = 4/3 is a user-changeable planning assumption, not a weather prediction. No automated terrain data, ground reflection, forest loss, rain loss, antenna pattern, interference, receiver desensitization or random fading is included. Hata gives median large-scale outdoor loss, not a surveyed obstacle model or availability guarantee. The free-space budget distance in the calculation sheet is a mathematical bound; it ignores curvature, diffraction and terrain and is not a promised range.

Preset airtime is the node's total transmission time, not airtime of one packet or the whole network. Input airtime includes retransmission and relay traffic. The metric/US viewer switch converts physical input and result units; profile chart axes explicitly retain their stated units.

Geometry: 0.05–100 km, frequency 150–2000 MHz, positive antenna heights, ridge strictly between endpoints. Antenna elevation difference is limited to 10% of path distance. Fresnel radii and vertical clearances use the shallow-path approximation. Minimum clearance and common lift come from continuous minimization on both entered terrain segments, including endpoints and the ridge. This removes sampling gaps in the entered profile; a real surveyed path may still contain unentered obstacles. Single knife-edge loss requires the magnitude of the computed diffraction angle to be at most 0.2 rad (about 11.5°); otherwise that model is rejected. The ridge estimate excludes multiple-edge and spherical-earth diffraction; a warning identifies background ground/earth encroachment.

Empirical models: original Hata is conservatively restricted to 150–1500 MHz (the original abstract also mentions 100 MHz); COST-231 Hata to 1500–2000 MHz. Both require distance 1–20 km, the higher antenna 30–200 m and above the local rooftop clutter, and the lower antenna 1–10 m. For original Hata in a large city, 200 < f < 400 MHz is additionally excluded, including from the comparison chart, because ETSI ETR 103 supplies no correction there. Bounds are enforced without clamping inputs or silently switching models. Quasi-smooth macrocell terrain is assumed. A 2 m / 2 m handheld path is outside these models. COST frequencies exceed SX127x capability; choose manual sensitivity for an engineering study with suitable hardware.

Dated regional screens — 2026-10-27: ERC Recommendation 70-03 compiled edition of June 2023 (amendments dated 16 June 2023), attached as s10 from the stable version URL https://docdb.cept.org/download/4358. The Annex 1 band entries on pp. 7–8 retain June 2022 page footers. The publication date is distinct from the preset review date, 27 October 2026; Meshtastic region settings were accessed on that review date. EU_868 uses 869.4–869.65 MHz, 500 mW ERP = 29.14 dBm EIRP, 10% airtime, and the Meshtastic 27 dBm conducted-power ceiling. EU 433 uses 433.05–434.79 MHz, 10 mW ERP = 12.15 dBm EIRP, 10% airtime, and the Meshtastic 10 dBm conducted-power ceiling. ERP-to-EIRP conversion uses 2.15 dB. This is the duty-cycle route; alternative LBT/AFA access is not assessed. National allocation and firmware channel plans can be narrower.

US 902–928 MHz screening follows 47 CFR 15.247: conditional conducted ceiling 30 dBm, reduced conservatively by transmit antenna gain above 6 dBi. 100% in the airtime screen means no generic duty-cycle cap has been applied; it does not waive hopping dwell time, bandwidth, power-spectral-density or certification requirements. Nominal 125/250 kHz non-hopping LoRa must not be assumed eligible for 1 W; use the module's grant and approved configuration. No preset certifies compliance. Custom mode does not check allocation or hardware approval. Check against the standard and national rules in force. Installation work belongs to a qualified person.