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Antenna length calculator

An antenna works best when its length suits the signal's wavelength. Type a frequency to get the wavelength, the quarter-wave whip and the half-wave dipole, full length and trimmed, and the loading coil a too-short whip needs.

M = MHz, G = GHz.

A real rod or wire is cut about 95% of the full length. 100 for the textbook length.

Quarter-wave whip, λ ÷ 4

2.78 m
Wavelength, λ = c ÷ f
11.1 m
Cut the whip to (95%)
2.64 m
Half-wave dipole, λ ÷ 2
5.55 m
Dipole cut to (95%)
5.27 m

A short whip and its loading coil

A whip well under λ ÷ 4 acts like a small capacitor: about 10 pF for a 1 m car whip.

Loading coil in series, L = 1 ÷ (4π² f² C)

3.47 µH
The whip's reactance it cancels
589 Ω

The formula

λ = c over f = 300 over f in MHz metres

c is the speed of light, about 300,000,000 m/s: a radio wave covers one wavelength each cycle. A quarter-wave whip over a ground plane, like a car roof or a board's ground copper, is λ ÷ 4. A half-wave dipole is two quarter-wave arms fed in the middle, λ ÷ 2 end to end. Along a real rod the wave runs a little slower and the ends add a little, so cut about 95% of the full length, then trim for the best match.

FrequencyWavelengthQuarter-waveCut to (95%)
27 MHz (CB)11.1 m2.78 m2.64 m
100 MHz (FM)3 m74.9 cm71.2 cm
433 MHz69.2 cm17.3 cm16.4 cm
2.4 GHz (Wi-Fi)12.5 cm3.12 cm2.97 cm

A worked example

A CB radio at 27 MHz:

λ = 300 over 27 ≈ 11.1 m, so λ ÷ 4 ≈ 2.78 m

Cut to 95%, that's about 2.64 m: too tall for most cars. A 1 m whip is too short to resonate. Electrically it's about 10 pF in series with about 10 Ω of radiation resistance, the part that sends the power into the air. At 27 MHz the 10 pF is 590 Ω standing in the way, so a loading coil in series cancels it:

L = 1 over 4π² f² C = 1 over 4π² × (27 MHz)² × 10 pF ≈ 3.5 µH

That coil is the fat bit at the base of a CB whip.

Free lesson

Now build it yourself

Each lesson comes in three short parts: see the idea, try it on a live board, then build it yourself, with quick checks as you go.

Try it yourself: free lesson

“A short antenna” is lesson 5 of 6 in Carrier Cove, Signals & Wireless (RF) World 1. Free with an account. Lessons unlock in order, so you’ll do the 4 before it first.

Or start from the very first lesson, no account needed

The ideas behind it

Questions people ask

How do I calculate the length of a quarter-wave antenna?

Divide 300 by the frequency in MHz to get the wavelength in metres, take a quarter, and cut about 95% of that. At 433 MHz the wavelength is 69.2 cm, a quarter is 17.3 cm, and you'd cut about 16.4 cm.

Why cut an antenna shorter than the formula says?

Along a real rod or wire the wave runs a little slower than in free space, and the ends add a little. So the antenna resonates at about 95% of the textbook length. Cut it slightly long, then trim for the best match.

How long is a 2.4 GHz antenna?

The wavelength at 2.4 GHz is 12.5 cm, so a quarter-wave is 3.12 cm, or about 3 cm once trimmed. That's why Wi-Fi and Bluetooth antennas fit inside phones and on small boards.

What is a loading coil?

A coil in series with a whip that's shorter than a quarter wave. The short whip acts like a small capacitor, and the coil's reactance cancels it at one frequency, making the antenna resonant. For a 10 pF whip at 27 MHz it's about 3.5 µH.

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