LoRa Link Budget Calculator — Sensitivity, Time on Air & Range

A LoRa link budget answers two questions at once: whether the packet arrives above the receiver's sensitivity, and how long it occupies the channel. Both are set by the spreading factor (SF), the bandwidth and the coding rate.

Sensitivity

LoRa spreads each symbol over $2^{SF}$ chips, which lets the demodulator work below the noise floor. Its sensitivity is the thermal noise in the bandwidth, plus the noise figure, plus the signal-to-noise ratio the spreading factor needs (Semtech AN1200.13, equation 1):

where $kT_0$ is −173.975 dBm/Hz at 290 K. The SX1276 datasheet gives $SNR_{SF}$ from −5 dB at SF6 to −20 dB at SF12, in steps of 2.5 dB. With a 125 kHz bandwidth and a 6 dB noise figure that is −124.5 dBm at SF7 and −137.0 dBm at SF12, which matches the −137 dBm in the datasheet's receiver table.

Time on air

The symbol time is $T_{sym} = 2^{SF}/BW$: 1.024 ms at SF7 and 32.768 ms at SF12 with 125 kHz. A packet is a preamble of $n_{preamble} + 4.25$ symbols followed by the payload symbols:

where $PL$ is the payload in bytes, $CR$ runs from 1 (4/5) to 4 (4/8), $CRC$ is 1 when the payload CRC is on, $IH$ is 1 for an implicit header, and $DE$ is 1 when low-data-rate optimisation is on. The datasheet makes that optimisation mandatory once the symbol time exceeds 16 ms, so the calculator switches it on by itself, at SF11 and SF12 with 125 kHz. A 10-byte packet at SF7 takes 41.216 ms; a 51-byte packet at SF12 takes 2465.792 ms.

Duty cycle

In much of the European 868 MHz band a device may transmit for at most 1% of the time (ETSI EN 300 220-2). After each packet it must then stay silent for $T_{off} = ToA\,(100/\delta - 1)$, which is 99 times the time on air at 1%. The calculator also gives how many packets an hour fit within the duty cycle.

Path loss and range

In free space the loss is $20\log_{10}(4\pi d f/c)$ (ITU-R P.525). For a gateway on a mast above the surrounding roofs, the Okumura–Hata model gives the median loss in a town,

with $f$ in MHz, $d$ in kilometres and the antenna heights $h_b$ and $h_m$ in metres, plus corrections for a large city, suburban areas and open country. The link margin is the received power less the sensitivity, and the maximum range is the distance at which it falls to zero.

Validity

The SNR limits are those of the SX1276/77/78/79, which covers 137 to 1020 MHz and bandwidths of 7.8 to 500 kHz; another LoRa radio may differ by a dB or two. Okumura–Hata holds from 150 to 1500 MHz, 1 to 20 km, base heights of 30 to 200 m and mobile heights of 1 to 10 m. Outside those ranges, including a maximum range beyond 20 km, the values are shown with a warning. The path loss is a median with no fading: the link margin is what remains for fading and obstructions. Spreading factors outside 6 to 12 and payloads outside 1 to 255 bytes are refused.