How Long Should a LoRa Antenna Be? 868 MHz and 915 MHz Lengths • The Science 360

A LoRa module arrives with a pad or a connector marked ANT and, often, no antenna. The usual fix is a piece of wire, and the usual question is how long to cut it. For 868 MHz the short answer is about 82 mm; for 915 MHz, about 78 mm. The longer answer explains why those numbers are a little shorter than a quarter of a wavelength, which frequency to cut for when LoRa hops between channels, and what the wire needs underneath it to work.

The antenna length calculator works out quarter-wave, half-wave and 5/8-wave lengths for any frequency and draws the antenna to scale beside the module; every length here comes from it. Why the trim depends on wire thickness, with a model of the feed impedance, is covered in quarter-wave antenna length.

Quick answerA quarter-wave LoRa whip is about 82.0 mm (3.23 in) for 868 MHz and 77.8 mm (3.06 in) for 915 MHz: a quarter of the free-space wavelength, cut about 5% shorter for end effect. A half-wave dipole is twice as long. Cut slightly long, trim, and give a whip a ground plane.

A quarter-wave whip for 868 MHz LoRa drawn to scale on a radio module over a ground plane: 82.0 mm with the 0.95 factor, beside a ruler, with the 86.3 mm free-space length dashed and the current largest at the feed — Figure 1. An 868 MHz quarter-wave whip, 82.0 mm, against a ruler. The dashed line is the full free-space quarter wavelength, 86.3 mm. The gold band shows the current, largest at the feed and zero at the tip. Open this in the calculator.

Which frequency to cut for

LoRa does not sit on one frequency. It uses a set of channels, and the antenna has to work across all of them. The LoRa Alliance's regional parameters document (RP002) sets the channel plans:

Europe (EU863-870): devices must be able to operate from 863 to 870 MHz, and every device implements three default channels at 868.1, 868.3 and 868.5 MHz.
North America (US902-928): 64 uplink channels from 902.3 to 914.9 MHz in 200 kHz steps, 8 wider uplink channels from 903.0 to 914.2 MHz, and 8 downlink channels from 923.3 to 927.5 MHz. The US rules for the band itself are in 47 CFR 15.247, which covers 902 to 928 MHz.

For an EU device, 868.3 MHz is the obvious centre. For a US device, the antenna both transmits near the bottom of the band and listens near the top, so 915 MHz, the middle of 902 to 928 MHz, is the sensible design frequency.

Frequency	Use	Wavelength	¼-wave whip (0.95)
863 MHz	EU band edge	347 mm	82.5 mm
868.3 MHz	EU default channels	345 mm	82.0 mm
870 MHz	EU band edge	345 mm	81.8 mm
902.3 MHz	US first uplink	332 mm	78.9 mm
915 MHz	US band centre	328 mm	77.8 mm
927.5 MHz	US last downlink	323 mm	76.8 mm

Across the EU band the length changes by less than a millimetre. Across the whole US plan it changes by about 2 mm, or 2.7%, which is why one antenna centred on 915 MHz serves both directions.

Step 1: the wavelength

A radio wave in air travels at very nearly the speed of light, which is exactly 299,792,458 m/s by definition of the metre (NIST). The wavelength is that speed divided by the frequency:

Wavelength at 868.3 MHz and 915 MHz

\begin{aligned}\lambda_{868} &= \frac{299{,}792{,}458}{868.3 \times 10^6} = 345.3\ \text{mm} \\ \lambda_{915} &= \frac{299{,}792{,}458}{915 \times 10^6} = 327.6\ \text{mm}\end{aligned}

A quarter of each: 86.3 mm and 81.9 mm.

Step 2: shorten it for end effect

Cut a wire to exactly 86.3 mm and it resonates a few percent below 868 MHz. The reason is end effect: the open tip of the wire has capacitance to its surroundings, which makes the element behave as if it were longer than it is. The US Army's 1953 technical manual TM 11-666, "Antennas and Radio Propagation", describes it and gives the standard correction: make the antenna about 5% shorter, so a half-wave antenna is

L = 0.95 \times \frac{492}{f} = \frac{468}{f}\ \text{feet}

with f in MHz. The quarter-wave version is 234/f. The same manual notes that the correction depends on the conductor: a thin wire changes the wave's behaviour less than a fat one. So 0.95 is a starting point, not a law, and the calculator lets you change it.

Quarter-wave whips with the 0.95 factor

\begin{aligned}L_{868} &= 0.25 \times 345.3 \times 0.95 = 82.0\ \text{mm} \\ L_{915} &= 0.25 \times 327.6 \times 0.95 = 77.8\ \text{mm}\end{aligned}

As a check, 234 ÷ 868.3 = 0.2695 ft = 82.1 mm, the same within the rounding of 468.

The same 868 MHz whip cut to the full free-space quarter wavelength, 86.3 mm, with no allowance for end effect — Figure 2. The same whip cut to the full 86.3 mm. It will work, but it resonates below the band. Open this in the calculator.

In practice, cut the wire a few millimetres long, connect it, and trim while watching the SWR or the received signal strength. If you cannot measure, cut to the 0.95 length; it is closer than the full quarter wave.

868 MHz and 915 MHz antennas are not interchangeable

The two bands are only 5.4% apart, so the antennas look alike: 82.0 mm against 77.8 mm, a difference of 4.2 mm. That is still about the same as the end-effect trim itself. A 915 MHz whip used at 868 MHz resonates above the band, and an 868 MHz whip used at 915 MHz resonates below it. Both will still radiate, but the mismatch costs range, so it is worth buying or cutting the antenna for the band you use.

A quarter-wave whip for 915 MHz LoRa: 77.8 mm (3.06 in), 4.2 mm shorter than the 868 MHz whip — Figure 3. The 915 MHz whip: 77.8 mm, 4.2 mm shorter than the 868 MHz one. Open this in the calculator.

Commercial antennas are usually marked with their band, and many of the short, stubby ones are not straight quarter-wave wires at all; they use a coil or a helix to fit the same electrical length into less space. Their physical length tells you little, so go by the marking.

The whip needs a ground plane

A quarter-wave whip is only half of an antenna. TM 11-666 describes the ground-plane antenna as a quarter-wave vertical radiator that "carries its own artificial ground": a metal disc or a set of rods at its base. The current flowing up the whip is matched by current in that ground, and without it the coax shield or whatever the board is connected to becomes the other half, with unpredictable results.

On a LoRa board the ground plane is the module's ground copper, the main board under it, or a metal case. For a wire antenna on a bare module, a few quarter-wave wires soldered to ground and spread out at the base will do the same job. The same manual notes that bending those radials down below horizontal raises the feed impedance toward 50 Ω, which suits ordinary coax.

A dipole for a gateway or a test

If there is no good ground plane, a half-wave dipole avoids the problem: two quarter-wave arms fed at the centre, each the same length as the whip.

Half-wave dipoles with the 0.95 factor

\begin{aligned}868.3\ \text{MHz} &: 164\ \text{mm, two arms of } 82.0\ \text{mm} \\ 915\ \text{MHz} &: 156\ \text{mm, two arms of } 77.8\ \text{mm}\end{aligned}

A half-wave dipole for 868 MHz fed by coax from the module: 164 mm tip to tip, two 82.0 mm arms, with the current peaking at the centre — Figure 4. An 868 MHz half-wave dipole, 164 mm tip to tip. The current peaks at the centre feed and falls to zero at both tips. Open this in the calculator.

Hang it vertically to match the polarisation of the whips on your other nodes, and keep it clear of metal.

Compared with a 433 MHz antenna

LoRaWAN also has an EU433 plan, and many remote-control modules use the same 433.05 to 434.79 MHz band. Half the frequency means twice the length: a 433.92 MHz whip is 164 mm, the same as an 868 MHz dipole. A 433 MHz whip on an 868 MHz module is a half wavelength long, which presents a very different impedance from the quarter-wave the module expects, so it is not a substitute.

A quarter-wave whip for 433.92 MHz: 164 mm, twice the length of the 868 MHz whip — Figure 5. A 433.92 MHz whip, 164 mm, twice the 868 MHz length. Open this in the calculator.

Power limits include the antenna

The regional parameters set the default maximum radiated power as EIRP, which includes the antenna's gain: +16 dBm for EU868 and +30 dBm for US915. A higher-gain antenna does not let you exceed those limits; it means turning the transmitter down. In Europe the default channels also carry a duty cycle under 1%.

Checklist

Cut for 868.3 MHz in Europe or 915 MHz in North America.
Quarter-wave whip: 82 mm or 78 mm. Dipole: 164 mm or 156 mm.
Start a few millimetres long and trim, if you can measure.
Give a whip a ground plane; a dipole does not need one.
Keep the antenna away from metal and batteries, and vertical on every node.

Antenna length calculator for an 868.3 MHz quarter-wave whip: 82.0 mm (3.23 in), 86.3 mm in free space, a 34.5 cm wavelength, 234 ÷ f = 0.269 ft and the EU 863 to 870 MHz band, with the working — Figure 6. The calculator for an 868.3 MHz quarter-wave whip, with the free-space length, the 234/f check, the band and the working. Open this in the calculator.

For other frequencies or antenna types, open the antenna length calculator, enter the frequency, choose a quarter-wave whip, a dipole or a 5/8-wave whip, and adjust the shortening factor for your wire.

Sources

LoRa Alliance, RP002-1.0.3 LoRaWAN Regional Parameters (EU863-870: 863 to 870 MHz, default channels 868.1, 868.3 and 868.5 MHz, duty cycle under 1%, default max EIRP +16 dBm; US902-928: uplink 902.3 to 914.9 MHz in 200 kHz steps and 903.0 to 914.2 MHz, downlink 923.3 to 927.5 MHz, max EIRP +30 dBm)
47 CFR 15.247, Operation within the bands 902-928 MHz, 2400-2483.5 MHz and 5725-5850 MHz
Department of the Army, TM 11-666, Antennas and Radio Propagation (February 1953) (end effect; L = 0.95 × 492/f = 468/f feet; thicker conductors shorten more; the ground-plane antenna and its radials)
NIST CODATA, speed of light in vacuum (299,792,458 m/s, exact)
CEPT Report 85 (non-specific short range devices in 433.05 to 434.79 MHz and 863 to 870 MHz)

Frequently asked questions

How long should a LoRa antenna be for 868 MHz?

About 82 mm (3.23 in) for a quarter-wave wire whip, using the usual 5% end-effect trim on the 86.3 mm free-space quarter wavelength at 868.3 MHz. A half-wave dipole is about 164 mm tip to tip, two 82 mm arms.

How long should a LoRa antenna be for 915 MHz?

About 78 mm (3.06 in) for a quarter-wave whip at 915 MHz, and about 156 mm for a half-wave dipole. Across the US channels it ranges from 78.9 mm at 902.3 MHz to 76.8 mm at 927.5 MHz.

Can I use a 915 MHz antenna on 868 MHz?

It will work, but not at its best. The two frequencies are about 5.4% apart, so a 915 MHz whip is about 4 mm shorter than an 868 MHz one and resonates above the 868 MHz channels. For the best range, use an antenna made or cut for your band.

Does a LoRa wire antenna need a ground plane?

A quarter-wave whip does: it is half of an antenna, and the ground plane supplies the other half. On a module that is the board’s ground copper, a metal case or a few quarter-wave radial wires. A half-wave dipole needs no ground plane.

Why is a LoRa antenna shorter than a quarter wavelength?

Because of end effect. Capacitance at the tip makes the element behave as if it were longer than it is, so it is cut about 5% short to resonate. The US Army’s TM 11-666 gives the classic half-wave form as 468 divided by the frequency in MHz, in feet, and notes that thicker conductors need more shortening.