What is the antenna length formula?
A half-wave dipole is L = k × c ÷ (2f) tip to tip, and a quarter-wave monopole is L = k × c ÷ (4f), with c = 299,792,458 m/s and k the shortening factor. With k = 0.95, a dipole at 433.92 MHz is 32.82 cm.
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Antenna length calculator
Half-wave dipole or quarter-wave monopole, this antenna length calculator gives the length for any frequency with an adjustable shortening factor, or works back from a length to its resonant frequency. Results are in metric and imperial units.
Find
Examples
Antenna
Hz
Accepts prefixes: 433.92M, 2.45G.
0.95 is the 468 / f wire rule. 1 means no correction.
Half-wave dipole, tip to tip
32.82 cm
12.92 in
- Each dipole leg
- 16.41 cm 6.46 in
- Quarter-wave monopole
- 16.41 cm 6.46 in
- Free-space wavelength λ
- 69.09 cm 27.2 in
- Free-space λ/2
- 34.54 cm 13.6 in
- Free-space λ/4
- 17.27 cm 6.8 in
k = 0.95 makes the element 95 % of its free-space electrical length. Treat this as a starting point: cut long, then trim while measuring S11 or VSWR at the frequency you need.
0.95 comes from wire antennas with end insulators, and the cited 1965 article applies it up to about 30 MHz. University antenna notes give 0.94 to 0.96 for a resonant dipole. At 433.9 MHz it is only a first guess, so enter your own k if you have measured one.
Half-wave dipoleQuarter-wave monopole
Lengths at 433.9 MHz for different shortening factors
| k | Dipole, tip to tip | Each dipole leg | Monopole |
|---|---|---|---|
| 1.00 | 34.54 cm | 17.27 cm | 17.27 cm |
| 0.98 | 33.85 cm | 16.93 cm | 16.93 cm |
| 0.95 | 32.82 cm | 16.41 cm | 16.41 cm |
How to calculate antenna length from frequency
Divide the speed of light by the frequency to get the wavelength, then take half of it for a dipole or a quarter for a monopole and multiply by a shortening factor k. At 433.92 MHz the wavelength is 69.09 cm, so with k = 0.95 a half-wave dipole is 32.82 cm tip to tip and a quarter-wave monopole is 16.41 cm.
Antenna length formula for dipoles and monopoles
A straight antenna is resonant when it is close to a half wavelength long, or a quarter wavelength over a ground plane. The electrical length comes from the free-space wavelength; the shortening factor converts it to a length you can cut.
λ = c ÷ f
- λ
- free-space wavelength in m
- c
- speed of light, 299,792,458 m/s (exact)
- f
- frequency in Hz
- k
- shortening factor: physical length ÷ electrical length
- L
- physical length in m
The dipole length formula takes half of that wavelength and the quarter-wave antenna length is a quarter of it, each scaled by k:
L(dipole) = k × λ ÷ 2 L(monopole) = k × λ ÷ 4
Rearranged to find the frequency a given length resonates at:
f(dipole) = k × c ÷ (2L) f(monopole) = k × c ÷ (4L)
The traditional wire-antenna rule in feet is the same equation with k near 0.95. A free-space half wave is 491.8 ÷ f(MHz) feet, and the usual shortcut is:
L(ft) ≈ 468 ÷ f(MHz)
Worked examples
Example 1: a half-wave dipole at 433.92 MHz
λ = 299,792,458 ÷ 433,920,000 = 69.09 cm. With k = 0.95, L = 0.95 × 69.09 cm ÷ 2 = 32.82 cm (12.92 in) tip to tip, which is 16.41 cm per leg. Cut each leg a little long and trim both equally.
Example 2: a quarter-wave whip at 2.45 GHz
The free-space quarter wave is 3.059 cm. With k = 0.95 the element is 2.906 cm (1.144 in). The difference between the two is 1.53 mm, so the shortening factor is worth a real measurement at this frequency.
Example 3: a 14.1 MHz wire dipole against the 468 / f rule
With k = 0.95 the dipole is 33.13 ft. The 468 ÷ 14.1 rule gives 33.19 ft. They differ by 0.17 %, because 468 ÷ f corresponds to k = 0.9516 with the exact speed of light.
Antenna lengths for common frequencies
Computed with k = 0.95, a wire-antenna factor stated for up to about 30 MHz, so treat the higher rows as starting lengths. The free-space wavelength has no correction applied.
| Frequency | Wavelength | Dipole, tip to tip | Each dipole leg | Monopole | Monopole (imperial) |
|---|---|---|---|---|---|
| 27 MHz | 11.1 m | 5.274 m | 2.637 m | 2.637 m | 8.652 ft |
| 146 MHz | 2.053 m | 97.54 cm | 48.77 cm | 48.77 cm | 19.2 in |
| 169 MHz | 1.774 m | 84.26 cm | 42.13 cm | 42.13 cm | 16.59 in |
| 433 MHz | 69.24 cm | 32.89 cm | 16.44 cm | 16.44 cm | 6.474 in |
| 440 MHz | 68.13 cm | 32.36 cm | 16.18 cm | 16.18 cm | 6.371 in |
| 868 MHz | 34.54 cm | 16.41 cm | 8.203 cm | 8.203 cm | 3.229 in |
| 915 MHz | 32.76 cm | 15.56 cm | 7.781 cm | 7.781 cm | 3.064 in |
| 2.4 GHz | 12.49 cm | 5.933 cm | 2.967 cm | 2.967 cm | 1.168 in |
| 2.45 GHz | 12.24 cm | 5.812 cm | 2.906 cm | 2.906 cm | 1.144 in |
| 5.8 GHz | 5.169 cm | 2.455 cm | 1.228 cm | 1.228 cm | 0.4833 in |
What the shortening factor changes
Lengths at 146 MHz for the factors cited on this page.
| k | Dipole, tip to tip | Monopole | What it represents |
|---|---|---|---|
| 1.00 | 1.027 m | 51.33 cm | No correction: the free-space fraction of a wavelength |
| 0.98 | 1.006 m | 50.31 cm | Thin wire, length/diameter of 1,000 to 10,000, before insulator end effect |
| 0.96 | 98.56 cm | 49.28 cm | Thin resonant dipole, 0.48 λ long |
| 0.95 | 97.54 cm | 48.77 cm | Wire with end insulators: the factor behind 468 / f |
| 0.94 | 96.51 cm | 48.25 cm | Thick resonant dipole, 0.47 λ long |
What moves the resonance in practice
The factor k in any dipole calculator is an estimate, not a property of the frequency. Conductor diameter, end insulators, nearby metal and height above ground all move the resonance, so the usual method is to cut the element slightly long and trim it while measuring S11 or VSWR at the frequency you need. The 0.95 default comes from wire antennas held by end insulators, and the article it is taken from applies it up to about 30 MHz. McMaster University’s antenna notes put a resonant dipole at 0.47 λ to 0.48 λ depending on thickness, which is k = 0.94 to 0.96 and brackets the default. Those notes describe a dipole, so for a whip or rod with no end insulator it is still only a first guess.
A monopole also depends on what it is fed against: the ground plane acts as the other half of the antenna, so a small board, a short counterpoise or a plastic case with a battery beside the element will all shift it. These formulas describe straight conductors in air. Meandered, helical, loaded and printed antennas are outside the model and need vendor data or an electromagnetic simulation.
Glossary
- Wavelength (λ)
- The distance a wave travels in one cycle: c ÷ f in free space.
- Half-wave dipole
- A center-fed straight antenna about half a wavelength long from tip to tip.
- Quarter-wave monopole
- A single element about a quarter wavelength long, fed against a ground plane that acts as its other half.
- Shortening factor (k)
- Physical length divided by free-space electrical length, usually a little below 1.
- End effect
- The lowering of an antenna’s resonant frequency caused by the conductor ends and whatever supports them.
- Length-to-diameter ratio
- Element length divided by conductor diameter. Thinner elements need less shortening.
Related guides
- Frequency to wavelength calculator: wavelength in free space, cable or PCB.
- VSWR calculator: check the match while you trim the element.
- Free space path loss calculator: what the link loses once the antenna radiates.
Frequently asked questions
How do I use this as a dipole length calculator?
Choose Half-wave dipole and enter the frequency. You get the half-wave dipole length tip to tip and the length of each leg: at 433.92 MHz with k = 0.95, that is 32.82 cm and 16.41 cm.
How long should a 433 MHz antenna be?
A quarter wave at 433 MHz is 17.31 cm in free space (6.815 in), or 16.44 cm with k = 0.95. A half-wave dipole is twice that: 32.89 cm tip to tip with k = 0.95.
How long is a 2.4 GHz quarter-wave antenna?
3.123 cm in free space (1.229 in), or 2.967 cm with k = 0.95. At this size 1 mm is 3.4 % of the element, so plan to measure it.
Why is a real antenna shorter than half a wavelength?
An exact half-wave dipole has about +j42.5 Ω of input reactance, and shortening it removes that. McMaster University’s antenna notes give 0.47 λ for a thick dipole and 0.48 λ for a thin one, which is k = 0.94 to 0.96. Practical Wireless (1965) gives about 0.98 for length/diameter ratios of 1,000 to 10,000 and adds the detuning from end insulators, for roughly 5 % in total.
Where does the 468 / f rule come from?
A free-space half wave is 491.8 ÷ f(MHz) feet. The traditional figure multiplies 492 by 0.95 to get 468. With the exact speed of light, 468 ÷ f works out to k = 0.9516. Practical Wireless applies its general end-effect factor up to about 30 MHz.
Does wire thickness change the antenna length?
Yes. The resonant length depends on the length-to-diameter ratio. The factor is fairly flat for ordinary wire (about 0.98 between ratios of 1,000 and 10,000), and thick rods or tubing need a measured or modeled value that this dipole antenna calculator cannot supply, so enter your own k.
Does a quarter-wave monopole need a ground plane?
Yes. The element is one quarter wave and the ground plane acts as the other, which is why TI’s AN058 says monopole performance depends on the ground size. A board that is small compared with the wavelength shifts the resonance and changes the pattern.
Can I use this antenna calculator for a PCB trace antenna?
Only as a rough starting point. These formulas are for a straight conductor in air. A printed antenna has dielectric on one side and copper nearby, which changes the resonance, so follow the chip or antenna vendor’s reference design and tune it on the real board.
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Sources
- Texas Instruments AN058 (SWRA161B), Antenna Selection Guide: λ/2 and λ/4 definitions and Table 1
- NIST CODATA: speed of light in vacuum (exact)
- Practical Wireless, December 1965, Aerial Design Data: length/diameter factor and the 468 / f rule
- N. Nikolova, McMaster University, Lecture 9: Linear Wire Antennas (resonant dipole lengths, 0.47 λ thick and 0.48 λ thin)
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