About this calculator
An antenna works best when its physical length is a specific fraction of the wavelength it is radiating. Get that wrong and most of your transmit power reflects back down the feedline instead of leaving the antenna.
This calculator converts a frequency into a wavelength and then into cut lengths for the common antenna types, correcting for velocity factor and giving the answer in both metric and imperial units.
How it works
Wavelength is the speed of light divided by frequency: λ = c / f. At 433.92 MHz that is 69.1 cm; at 2.45 GHz, 12.2 cm.
Radio waves travel slightly slower in a conductor than in free space, so a resonant antenna is a little shorter than the free-space calculation suggests. The velocity factor accounts for it — about 0.95 for bare wire, which is why the traditional formulas use 468 rather than 492 for a dipole in feet.
A half-wave dipole is fed at its centre and each leg is a quarter wavelength. In free space it presents about 73 Ω, which is why 75 Ω coax pairs so naturally with one.
A quarter-wave monopole is only half an antenna: the ground plane or radials form the missing half by mirroring it. Over a good ground plane the feedpoint impedance is nearer 36 Ω, close enough to 50 Ω to work well. Without a ground plane it detunes badly and radiates from the feedline shield instead.
A 5/8-wave vertical concentrates more energy toward the horizon, which is useful for ground-level communication, but it is not resonant on its own and needs a matching coil at the base.
Worked example
A quarter-wave wire whip for a 433 MHz LoRa module.
- λ = 299792458 / 433.92e6 = 0.6909 m
- Velocity factor for bare wire: 0.95 → 0.6564 m
- Quarter wave: 0.6564 / 4 = 0.1641 m = 16.4 cm
- Cross-check with the shop formula: 71.5 / 433.92 = 0.1648 m — agrees
About 16.4 cm of wire. Cut it a few millimetres long and trim while watching SWR — and remember the module needs a ground plane, even just a patch of copper on the board, for the whip to work against.
Practical notes
- Cut long and trim short. Nearby metal, the enclosure, the ground plane and the feedline all pull resonance downward, so start about 5% long and trim while measuring.
- Velocity factors: 0.95 for bare wire, 0.66 for solid-polyethylene coax, 0.82 for foam coax, and 0.6–0.7 for a trace on FR4. Use the coax figure only when the coax itself is the radiating element.
- A monopole without a ground plane is not a working antenna. Radials, a metal chassis, or a copper pour all serve; without one the coax shield radiates and the pattern and impedance are unpredictable.
- Antennas are reciprocal — whatever is true for transmitting is equally true for receiving. A badly cut antenna hurts range in both directions.
- Transmitting into a badly matched antenna reflects power back into the output stage. Low-power modules usually survive it; higher-power amplifiers may not.
- Check your local regulations before transmitting. Frequency allocations and power limits differ by country, and 433 MHz in particular is licensed differently in different regions.
Frequently asked questions
How long should a 433 MHz antenna be?
A quarter-wave whip is about 16.4 cm of wire, allowing for velocity factor. A half-wave dipole is about 32.8 cm in total, 16.4 cm per leg.
What is velocity factor?
The ratio of the speed of a wave in a medium to its speed in free space. For bare wire it is roughly 0.95, so a resonant antenna is about 5% shorter than the free-space wavelength calculation gives.
Why does my antenna need a ground plane?
A quarter-wave monopole is electrically half a dipole; the ground plane provides the mirror image that completes it. Without one the feedpoint impedance is wrong and the coax shield ends up radiating.
Dipole or quarter-wave whip?
A dipole needs no ground plane and is easy to make from two wires, so it suits fixed installations. A whip is half the size and works well on a device that already has a ground plane — a PCB or a metal chassis.
What happens if the antenna is the wrong length?
It presents a poor match, so much of the power reflects back down the feedline rather than radiating. Range falls in both directions, and at higher powers the reflected energy can stress the transmitter.