Yagi Antenna Calculator – Yagi-Uda Design Tool

Step 1

Design

Pick the band, the number of elements or the boom length, and the element tubing. The calculator places the elements on a DL6WU or uniform spacing, then tunes the reflector, the director taper and the driven element with the wire solver for gain and front-to-back across your design band.

Display units

Band & size

Band preset

Centre frequency

MHz

Design bandwidth

Size by

Elements

Element spacing

Front-to-back aim

Elements, boom & feed

Element material

Element diameter

Driven element diameter

Boom and mounting

Feed and match

Hairpin wire spacing

Hairpin wire diameter

Line velocity factor

Fold spacing, centre to centre

Fed conductor diameter

Unfed conductor diameter

System impedance

Solver accuracy

Band, size and element changes need a new run. Feed, boom and display-unit changes apply straight away.

Layout top view, to scale; beam to the right

ElementsBoomFeed point and match

Feed

Feed & match

A Yagi with closely coupled directors has a low feed resistance, typically 12–35 Ω. The feed network above brings it to the coax impedance. Changing the feed type or its dimensions redesigns the match at f₀ straight away, retuning the driven element where the network needs it; the elements stay as they are.

Schematic between the element and the coax

Values

Cut list

Step 2

Analyze

Each frequency point is a full method-of-moments solve of every element. S11 is at the coax, after the feed and match chosen in step 1. The shaded band is your design band; the dashed vertical line marks f₀ and dashed horizontal lines are your goals.

Sweep span

Points

Input return loss S11 at the coax, dB

Impedance element terminals and coax port, Ω

Gain against frequency forward, dBi

Front-to-back and front-to-rear dB

At f₀

Radiation pattern and currents

The E-plane contains the elements and the boom; for a horizontally mounted Yagi it is the azimuth pattern. The H-plane is at right angles to the elements, the elevation pattern of a horizontal Yagi. Free space, no ground reflection.

3D radiation pattern at f₀

Radiation pattern at f₀ gain, dBi; forward is up

Smith chart S11 at the coax, design band in accent

Element currents at f₀ centre current, relative to the driven element

Bars show the magnitude; the line shows the phase lag behind the driven element. A good director row carries a steadily lagging, slowly falling current: the travelling wave that forms the beam.

Pattern cuts at f₀

Touchstone export

One-port S11 at the coax over the sweep in Touchstone 1.1 format (MHz, magnitude/angle, referenced to the system impedance). Paste into a .s1p file for a circuit simulator or scikit-rf.

Model. Galerkin method of moments with piecewise-sinusoidal basis and test functions on each thin wire (Richmond). The field of each basis is the closed-form near field of a sinusoidal current filament, taken on the wire surface; a delta-gap source drives the centre of the driven element. Conductor loss comes from the skin-effect surface impedance of the tubing. Gain is the IEEE gain (radiation over accepted power, so it includes conductor loss); realized gain also subtracts the mismatch at the coax. The model has no boom, mounting hardware or ground: it describes the electrical elements, and the cut list adds the boom correction.

About this Yagi antenna calculator

Updated November 8, 2026 · NextAntennas

This free Yagi antenna calculator designs a Yagi-Uda antenna for any frequency from 1 MHz to 20 GHz, including the 6 m, 2 m, 70 cm and 23 cm amateur bands, FM broadcast, UHF TV, LoRa, ADS-B and 2.4 GHz Wi-Fi. Enter the frequency, the number of elements or the boom length and the element tubing. It places the elements on the DL6WU spacing used by most long VHF and UHF Yagis, or on a uniform spacing, and tunes every element length with a method-of-moments wire solver, the same class of solver as NEC. You get the element lengths and spacings, a cut list with boom correction, the matching network, an NEC deck for 4nec2 or EZNEC, and the gain, front-to-back ratio, beamwidth and SWR to expect.

How to use it

Design: choose a band, the number of elements or the boom length, the tubing diameter and the boom mounting. The calculator returns the element lengths, spacings and cut lengths, and designs the feed: a hairpin (beta) match, a quarter-wave coax transformer or a folded dipole with a 4:1 balun, with the component values and the hairpin or line lengths.
Analyze: S11 and SWR at the coax, input impedance, forward gain in dBi and dBd, front-to-back and front-to-rear ratio, E- and H-plane beamwidth, polar and 3D radiation patterns and the element currents.
Optimize: set goals for gain, front-to-back, front-to-rear and return loss over the band, and let Nelder–Mead or differential evolution adjust element lengths, positions and the match.

Example: 7-element 2 m Yagi at 144.3 MHz

Designed by this calculator with 6 mm aluminium elements on a non-metallic boom and otherwise default settings: DL6WU spacing, 7 elements and a hairpin match to 50 Ω. Forward gain 12.1 dBi (9.9 dBd), front-to-back 31 dB at 144.3 MHz, beamwidth 45° × 52°. The driven element shows 31 − j24 Ω, matched with a 72 nH hairpin (63 mm long in 3 mm wire at 25 mm spacing). Boom length 2493 mm.

Element positions and lengths, 7-element 2 m Yagi
Element	Position from reflector (mm)	Length (mm)	Each half (mm)	Length / λ
Reflector	0	1008	504	0.485
Driven element	416	960	480	0.462
Director 1	571	944	472	0.454
Director 2	945	927	463	0.446
Director 3	1392	916	458	0.441
Director 4	1911	909	455	0.438
Director 5	2493	904	452	0.435

Lengths are tip to tip for a non-metallic boom. For elements through a metal boom, add the boom correction shown in the cut list. Build it at a different frequency or with different tubing by changing the inputs above.

Example: 12-element 70 cm Yagi at 432.1 MHz

Designed by this calculator with 4 mm aluminium elements on a non-metallic boom and otherwise default settings: DL6WU spacing, 12 elements and a hairpin match to 50 Ω. Forward gain 14.9 dBi (12.7 dBd), front-to-back 23 dB at 432.1 MHz, beamwidth 33° × 36°. The driven element shows 14 − j22 Ω, matched with a 11 nH hairpin (12 mm long in 2 mm wire at 10 mm spacing). Boom length 1977 mm.

Element positions and lengths, 12-element 70 cm Yagi
Element	Position from reflector (mm)	Length (mm)	Each half (mm)	Length / λ
Reflector	0	367	183	0.528
Driven element	139	323	161	0.465
Director 1	191	323	162	0.466
Director 2	316	312	156	0.449
Director 3	465	305	153	0.440
Director 4	638	300	150	0.433
Director 5	833	297	148	0.428
Director 6	1041	294	147	0.423
Director 7	1259	291	146	0.420
Director 8	1488	289	145	0.417
Director 9	1728	287	144	0.414
Director 10	1977	285	143	0.411

Yagi gain against boom length

Gain grows with boom length rather than with element count. These are the forward gains of DL6WU Yagis designed by this calculator with its default settings (6 mm aluminium elements at 144.3 MHz, 2% design band, front-to-back aim 20 dB). Other frequencies scale with the wavelength.

Yagi gain against number of elements and boom length
Elements	Boom length (λ)	Gain (dBi)	Gain (dBd)
3	0.28	7.2	5.1
4	0.46	8.7	6.6
5	0.67	10.1	7.9
6	0.92	10.8	8.7
7	1.20	12.1	9.9
8	1.50	12.7	10.5
10	2.15	14.0	11.9
12	2.85	14.9	12.7
14	3.62	15.8	13.6
16	4.42	16.6	14.5
20	6.02	17.8	15.7
25	8.02	18.9	16.8
30	10.02	19.8	17.6

Yagi design rules of thumb

The reflector is about 5% longer than a resonant half-wave dipole of the same tubing and sits about 0.2 λ behind the driven element. Directors are 5–10% shorter than resonance and get shorter along the boom. Thicker elements must be cut shorter for the same tuning, and elements that pass through a metal boom must be cut longer. A close first director (0.075 λ in the DL6WU layout) lowers the feed impedance to 20–35 Ω, which is why most Yagis need a matching network.

Frequently asked questions

How long should the elements of a Yagi antenna be?

Close to half a wavelength, adjusted by position. In the 7-element 2 m example on this page (6 mm tubing), the reflector is 0.485 λ, the driven element 0.462 λ and the directors run from 0.454 λ down to 0.435 λ. Thicker tubing needs shorter elements and a metal boom needs longer ones, so let the calculator work out the lengths for your tubing and boom.

How much gain does a Yagi antenna have?

Gain depends mainly on boom length. Designs from this calculator give about 7 dBi for 3 elements, 12 dBi for 7 elements on a 1.2 λ boom, 15 dBi for 12 elements on 2.9 λ and 18 dBi for 20 elements on 6.0 λ. Subtract 2.15 dB for gain in dBd.

How do you match a Yagi to 50 ohms?

The driven element of a Yagi usually shows 12 to 35 Ω. A hairpin (beta) match shortens the driven element and adds a shunt inductance across the feed point; a quarter-wave transformer of impedance √(R × 50 Ω) works with a resonant element; a folded dipole with a 4:1 balun raises the impedance. The calculator sizes all three, including the hairpin length and the conductor sizes a folded dipole needs.

What is the difference between front-to-back and front-to-rear ratio?

Front-to-back compares the forward gain with the gain exactly behind the antenna. Front-to-rear compares it with the strongest lobe anywhere in the rear half, so it is never larger than the front-to-back ratio and describes rejection of signals from behind more realistically.

What is the difference between dBi and dBd?

dBi is gain over an isotropic radiator; dBd is gain over a half-wave dipole, which itself has 2.15 dBi. Subtract 2.15 dB from a figure in dBi to get dBd.

How accurate is this Yagi calculator?

The method-of-moments solver was checked against an independent solver on 3- to 16-element designs: forward gain agreed within about 0.1 dB and feed resistance within about 7% at the default accuracy. Build accuracy usually matters more: at 432 MHz and above, a millimetre on a director is a noticeable part of its tuning range, so cut carefully and check the SWR with an antenna analyzer.

Related calculators

Dipole & Monopole Antenna Calculator: size a half-wave dipole or a ground-plane antenna, the starting point for a Yagi's driven element.
RF Exposure Calculator: a Yagi concentrates power in its beam, so check the safe distance in front of it.
dBm to Watts Converter: convert transmitter power and add the Yagi's gain to get the effective radiated power.
Microstrip Patch Antenna Calculator: a flat printed antenna for 900 MHz and up.
Microstrip Patch Array Calculator: high gain from a flat panel instead of a boom.
Skin Depth Calculator: conductor loss and plating depth for element tubing.

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Engineering Theory

Theory Behind the Equations

How the calculator works: a method-of-moments solve of the wires for the currents, the far field and the gain, a DL6WU or uniform layout tuned by that solver, and closed-form feed networks matched at the design frequency.

1. What Is a Yagi-Uda Antenna?

A Yagi-Uda antenna is a row of parallel half-wave elements on a boom. Only one, the driven element, is connected to the feed line. Behind it is a slightly longer reflector, and in front of it a row of shorter directors. The parasitic elements are excited by mutual coupling, and their lengths and spacings set the phase of their currents so that the fields add in the forward direction and cancel behind the antenna.

A long director row behaves like a slow-wave structure: the currents form a travelling wave along the boom slightly slower than light, which is why gain grows with boom length rather than with element count. Typical results are 7 dBi for three elements, 11 dBi on a one-wavelength boom and about 3 dB more for each doubling of the boom beyond that.

2. Mutual Coupling and the Method of Moments

Every element current induces a voltage on every other element, so the antenna is a set of coupled thin wires. The calculator solves Pocklington's integral equation for the currents by the method of moments. Each element is divided into segments, and the current is expanded in overlapping piecewise-sinusoidal (PWS) functions, one centred on each interior node:

Piecewise-sinusoidal basis

f_{n} (z) = \frac{\sin (k (Δ - | z - z_{n} |))}{\sin (k Δ)}, | z - z_{n} | \leq Δ

Δ is the segment length and k = 2π/λ. A sinusoid is the natural current shape on a thin wire, so few segments are needed.

Testing with the same functions (Galerkin's method) turns the integral equation into a matrix equation for the basis amplitudes I_n:

Moment equations

\sum_{n} Z_{mn} I_{n} = V_{m}, Z_{mn} = - \int f_{m} (z) E_{z}^{(n)} (ρ, z) d z

V_m is 1 V at the driven element's centre node (delta-gap source) and zero elsewhere. ρ is the wire radius a on the same element and the element spacing between elements.

The field of a sinusoidal current filament has an exact closed form (Schelkunoff), so each matrix entry needs only a one-dimensional integral over the test function:

Near field of one PWS basis

E_{z}^{(n)} = - \frac{j η}{4 π \sin (k Δ)} [\frac{e^{- j k R_{1}}}{R_{1}} + \frac{e^{- j k R_{2}}}{R_{2}} - 2 \cos (k Δ) \frac{e^{- j k R_{0}}}{R_{0}}]

R₁, R₂ and R₀ are the distances from the observation point to the two ends and the centre of the basis. The 1/R peaks at the nodes are integrated with a sinh mapping, so even very thin elements are handled accurately.

The currents are symmetric about the boom, so only half of each element is unknown, which halves the matrix. A 20-element Yagi solves in well under a second, so a full frequency sweep takes a few seconds.

3. Input Impedance and Conductor Loss

With 1 V across the feed gap, the input impedance is the inverse of the solved feed current. The skin-effect resistance of the tubing adds a surface-impedance term to the matrix, so the solved currents already include conductor loss:

Input impedance and surface impedance

Z_{in} = \frac{1}{I_{feed}}

Δ Z_{mn} = \frac{Z_{s}}{2 π a} \int f_{m} f_{n} d z, Z_{s} = (1 + j) \sqrt{\frac{ω μ_{0}}{2 σ}}

Aluminium or copper tubing loses well under 0.1 dB on most VHF and UHF Yagis. Thin stainless-steel rod or very low feed resistances can lose noticeably more, because the large director currents flow through a resistive surface.

4. Far Field, Gain and Front-to-Back Ratio

Each PWS basis radiates like a short sinusoidal dipole, so the far field is a closed-form sum over all bases on all elements, with the element along z and the boom along x:

Far field

E_{θ} = j 60 \frac{e^{- j k r}}{r} \sum_{n} I_{n} e^{j k (x_{n} \sin θ \cos φ + z_{n} \cos θ)} \frac{\cos (k Δ \cos θ) - \cos (k Δ)}{\sin θ \sin (k Δ)}

Gain, realized gain and front-to-back

G = \frac{4 π U}{P_{in}}, G_{r} = G (1 - {| Γ |}^{2})

F / B = G_{dB} (0 °) - G_{dB} (180 °)

U = r²|E|²/2η is the radiation intensity and P_in = ½Re(V I*) the accepted power. The radiated power from integrating U over the sphere matches P_in minus the conductor loss to better than 0.1%, a built-in check on the solve.

Front-to-back compares the forward lobe with the single direction straight behind. Front-to-rear compares it with the strongest lobe anywhere in the rear half of the E- and H-plane cuts, which is the stricter figure and the one that decides how well the antenna rejects interference from behind. Beamwidths are the −3 dB widths of the two principal cuts.

5. Element Spacing: DL6WU and Uniform

Günter Hoch, DL6WU, published a spacing schedule that gives wideband, well-behaved long Yagis: reflector to driven element 0.2 λ, driven element to the first director 0.075 λ, then director spacings of 0.18, 0.215, 0.25, 0.28, 0.30, 0.315, 0.33, 0.345, 0.36, 0.375 and 0.39 λ, and 0.40 λ for every director after that. The close first director lowers the feed impedance; the widening spacings keep the travelling wave in step along the boom.

The calculator takes those positions, or a uniform spacing of your choice, and tunes three shape parameters with the wire solver: the reflector length, the first director length and a logarithmic director taper, L_n = L_D1 − s·ln n. The objective is the average forward gain at the band edges and f₀, with penalties when the front-to-back falls below your aim or the feed resistance below 12 Ω. The driven element is then resonated at f₀ and the match designed.

6. Boom Correction

The solver models the elements in free space. A metal boom that the elements pass through shortens them electrically, so they must be cut longer. The cut list adds a correction of k times the boom diameter or width, with k about 0.7 for elements bonded through a thin round boom and roughly half that for elements insulated through it. Elements mounted on insulators well above the boom, or on a non-metallic boom, need no correction.

These factors are rules of thumb from the DL6WU and G3SEK boom-correction curves; the correction shrinks as the boom gets thicker in wavelengths, and square booms differ from round ones. If you have a measured value for your hardware, enter it as the correction factor.

7. Matching the Feed

The hairpin (beta) match is an L-network. The driven element is shortened until its reactance is capacitive, and a shorted two-wire stub across the feed point provides the shunt inductance:

Hairpin match

X_{DE} = - \sqrt{R (Z_{0} - R)}, X_{L} = \frac{R Z_{0}}{\sqrt{R (Z_{0} - R)}}

ℓ = \frac{λ}{2 π} \arctan \frac{X_{L}}{Z_{h}}, Z_{h} = 120 arccosh \frac{s}{d}

R is the element resistance, Z₀ the coax impedance, s and d the hairpin wire spacing and diameter. It needs R < Z₀ and a 1:1 current balun.

The quarter-wave transformer keeps the driven element resonant and inserts a line of impedance Z_t = √(R·Z₀), a quarter wavelength long times the velocity factor; two 75 Ω cables in parallel make 37.5 Ω, which matches about 28 Ω to 50 Ω. The folded dipole raises the element impedance by its step-up ratio, which a 4:1 half-wave coax balun then divides by four:

Folded dipole step-up ratio

r = {(1 + \frac{\ln (2 s / d_{1})}{\ln (2 s / d_{2})})}^{2}

d₁ is the fed conductor, d₂ the unfed one and s their centre spacing. Equal conductors give r = 4; a thicker unfed conductor raises r. A perfect match needs r = 4Z₀/R.

8. Validity and Limitations

The thin-wire method of moments is accurate for element diameters below about 0.02 λ and segments longer than a few diameters, which covers practical Yagis from HF to the low gigahertz. As a check, the solver was compared with an independent mixed-potential (MININEC-type) solver on 3-, 5-, 7- and 16-element designs: the forward gain agreed within about 0.1 dB and the feed resistance within about 7% at the default 16 segments per element. The feed reactance depends on how the gap at the feed point is modelled and can differ by a few ohms; the hairpin or the driven-element length trims that out on the bench. The solver runs in free space and models straight, parallel, centre-fed elements:

No ground: real elevation patterns over ground add reflection lobes, and the gain over ground is up to 6 dB higher at low angles.
No boom, mast, clamps or feed cable: the boom correction handles the first; keep the coax perpendicular to the elements and use a balun.
The folded dipole is modelled through its step-up ratio and a single equivalent element; tune its length on the bench.
Boom-correction factors are rules of thumb.

Treat the results as a strong starting point, and check the built antenna with an antenna analyzer before final assembly.

References

Balanis, C.A., Antenna Theory: Analysis and Design, 4th ed., Wiley, 2016, ch. 8 and 10.
Richmond, J.H., "Radiation and scattering by thin-wire structures in the complex frequency domain", NASA CR-2396, 1974.
Viezbicke, P.P., "Yagi Antenna Design", NBS Technical Note 688, 1976.
Hoch, G., DL6WU, "More Gain with Yagi Antennas", VHF Communications, 1977; and Reed, D., G3SEK, DL6WU design notes.
Lawson, J.L., W2PV, Yagi Antenna Design, ARRL, 1986.
Stutzman, W.L. and Thiele, G.A., Antenna Theory and Design, 3rd ed., Wiley, 2012.
Burke, G.J. and Poggio, A.J., Numerical Electromagnetics Code (NEC) — Method of Moments, LLNL, 1981.