Delta Loop & Full-Wave Loop Antenna Calculator

A full-wave loop antenna has a conductor perimeter close to one wavelength at the design frequency. The exact resonant physical length is not determined by wavelength alone, so the calculator uses a practical starting formula and allows correction during tuning.

Wavelength Formula

The free-space wavelength is:

λ = c / f

For convenient HF and VHF calculations:

λ (m) ≈ 300 / f (MHz)

where:

• λ = wavelength in meters;
• f = operating frequency in MHz;
• c = speed of light.

This is the electromagnetic wavelength in free space. It is not automatically the final wire length of a resonant full-wave loop.

Full-Wave Loop Perimeter Formula

A commonly used practical starting formula is:

L (m) ≈ 306 / f (MHz)

or:

L (ft) ≈ 1005 / f (MHz)

where L is the total loop perimeter.

The 306/f and 1005/f formulas provide an approximate construction length rather than a universal resonant dimension. Actual full-wave loop dimensions vary with geometry, conductor characteristics, height, and surroundings. (66Pacific)

Calculator option: Correction factor K: [ 306 ]

For a custom practical formula:

L = K / f

This lets the user apply a known correction factor from modeling, previous measurements, or a specific antenna design.

Delta Loop Side Length Formula

For an equilateral delta loop:

Side = L / 3

If the calculated perimeter is 43.10 m:

Side = 43.10 / 3 = 14.37 m

For an isosceles or custom triangular loop, the three sides must add up to the calculated perimeter:

A + B + C = L

Changing the shape can also change feed-point impedance and resonance, so equal perimeter does not guarantee identical electrical behavior.

Triangle Height Formula

For an equilateral triangle:

H = Side × √3 / 2

or approximately:

H = Side × 0.866

This value is useful for estimating the required mast or support height before allowing for ground clearance.

Square and Rectangle Formulas

For a square full-wave loop:

Side = L / 4

For a rectangle:

2 × (Width + Height) = L

If the user specifies an aspect ratio:

r = Width / Height

then:

Height = L / [2(r + 1)]

Width = r × Height

Different width-to-height ratios can significantly change feed-point impedance, which is why rectangle dimensions should not be treated as purely cosmetic. (Practical Antennas)

Quarter-Wave Matching Section Formula

A quarter-wave matching section has an electrical length of λ/4. Its physical length is shortened according to the velocity factor of the transmission line.

For a coaxial matching section:

Lmatch (m) ≈ 75 × VF / f (MHz)

Lmatch (ft) ≈ 246 × VF / f (MHz)

where VF is the coax velocity factor.

For example, a solid-polyethylene cable may use a velocity factor around 0.66, while some foam-dielectric cables are closer to 0.80. Always use the manufacturer’s value for the actual cable when available. (66Pacific)

The table below uses the practical starting formula 306 / frequency in MHz and assumes an equilateral delta loop. These are initial dimensions for calculation and planning, not guaranteed finished resonant lengths.

The frequencies above are calculation examples rather than a statement of permitted operating frequencies in every country. Enter the exact design frequency you intend to use.

160 Meter Delta Loop

At 1.85 MHz, a simple 160 meter delta loop calculation gives about 165.41 m (542.7 ft) of total wire. An equilateral version would require sides of about 55.14 m (180.9 ft) and nearly 47.75 m (156.7 ft) of vertical triangle height.

At this scale, available supports and installation height usually determine the practical geometry.

Load 160m Settings

80 Meter Delta Loop

At 3.60 MHz, the calculated 80m loop perimeter is approximately 85.00 m (278.9 ft). An equilateral delta has sides of about 28.33 m (93.0 ft).

Because an 80 meter loop is physically large, a flattened delta, rectangle, or horizontal loop may fit a property better than a perfect equilateral triangle.

Load 80m Settings

40 Meter Delta Loop

At 7.10 MHz, the starting wire length is approximately 43.10 m (141.4 ft). Each side of an equilateral 40 meter delta loop is about 14.37 m (47.1 ft), with a geometric height near 12.44 m (40.8 ft).

This is a useful starting calculation, but modeled 40m delta loops designed for specific feed impedances can require noticeably different dimensions. (Practical Antennas)

Load 40m Settings

30 Meter Delta Loop

At 10.10 MHz, the calculated perimeter is approximately 30.30 m (99.4 ft). Equilateral sides are about 10.10 m (33.1 ft).

Choose the exact design frequency before cutting the wire if a particular part of the band is most important.

Load 30m Settings

20 Meter Delta Loop

At 14.10 MHz, a full-wave loop starting length is approximately 21.70 m (71.2 ft). An equilateral 20m delta loop has sides of about 7.23 m (23.7 ft).

Its smaller size makes it easier to experiment with apex-up, apex-down, and different feed-point positions.

Load 20m Settings

17 Meter Delta Loop

At 18.10 MHz, the starting perimeter is about 16.91 m (55.5 ft), with equilateral sides around 5.64 m (18.5 ft).

Load 17m Settings

11 Meter / 27 MHz Delta Loop

At 27.20 MHz, an 11 meter delta loop requires approximately 11.25 m (36.9 ft) of wire using the 306/f starting formula. Each equilateral side is about 3.75 m (12.3 ft) and the triangle height about 3.25 m (10.7 ft).

For an 11m delta loop antenna, enter the exact operating frequency rather than relying on a generic “27 MHz” value when precise resonance matters.

Load 11m / 27 MHz Settings

10 Meter Delta Loop

At 28.40 MHz, the calculated perimeter is approximately 10.77 m (35.3 ft). Each side of an equilateral 10m delta loop is about 3.59 m (11.8 ft).

Load 10m Settings

6 Meter Delta Loop

At 50.50 MHz, the starting full-wave perimeter is approximately 6.06 m (19.9 ft), with equilateral sides near 2.02 m (6.6 ft).

At higher frequencies, small physical changes represent a larger fraction of a wavelength, so measure and trim carefully.

Load 6m Settings

2 Meter Delta Loop

At 145 MHz, the simple full-wave calculation gives approximately 2.11 m (6.9 ft) of total conductor and sides near 0.70 m (2.3 ft).

Construction details become increasingly important at VHF, including conductor size, feed arrangement, connectors, and nearby conductive material.

Load 2m Settings

1. Choose the design frequency. Use the actual frequency around which you want the antenna to be optimized rather than only selecting a band name.
2. Calculate the initial perimeter. Use the loop antenna calculator to determine total wire length and the dimensions of the selected geometry.
3. Choose the physical shape. An equilateral delta is simple to calculate, but available supports may make an isosceles triangle, rectangle, square, or horizontal loop more practical.
4. Cut the wire slightly long. Leave enough conductor for attachment, feed-point hardware, and final trimming.
5. Install the loop in its intended position. Resonance and impedance can change when the antenna is raised, lowered, or moved near buildings, trees, metal objects, and the ground.
6. Connect the feedline and matching system. Use direct coax feed only when the antenna impedance is suitable, or add the required transformer, matching section, balanced line, or balun.
7. Measure and tune. Check resonance and SWR with the antenna in its final installation. Trim in small, equal increments where appropriate and remeasure after each adjustment.

Keep antenna conductors, supports, and feedlines safely clear of overhead power lines and locations where people could contact RF-active parts of the system.

Feed-point position changes more than the convenience of connecting coax. On a full-wave loop, it affects current distribution, input impedance, polarization, and the resulting radiation pattern.

Apex-Up — Vertical Polarization

For an apex-up equilateral delta, a common feed position for predominantly vertical polarization is approximately one-quarter of the total loop length down one sloping side from the top apex. This places the feed point somewhat above the lower corner. (Practical Antennas)

Diagram label: Feed point ≈ L / 4 from apex

This arrangement is useful when vertical polarization and lower-angle radiation are desired.

Apex-Up — Horizontal Polarization

Feeding a vertically oriented loop at the top or bottom, where current is predominantly horizontal, favors horizontal polarization. The exact result still depends on geometry and feed-point location. (Practical Antennas)

Diagram label: Feed at center of horizontal section

Apex-Down

An apex-down delta can be convenient when two high supports are available and the lowest point can serve as the feed location. Depending on the chosen feed point, this configuration is commonly used for predominantly horizontal polarization. (Портативные антенны)

Horizontal Loop

A horizontal full-wave loop has its entire plane parallel or nearly parallel to the ground. Its elevation pattern is strongly affected by height above ground: a relatively low horizontal loop can favor high-angle radiation, while greater electrical height changes the pattern and lowers major radiation angles.

Calculator control: Feed point → Show expected polarization and radiation direction

Diagram labels: Horizontal polarization Vertical polarization Broadside direction Feed point Current maximum / minimum

There is no single correct impedance for every full-wave loop antenna. Input impedance depends on loop geometry, feed point, conductor dimensions, installation height, ground, and nearby objects.

Feed-Point Impedance

Antenna input impedance is written as:

Z = R + jX

where:

• R is the resistive component;
• X is the reactive component;
• at resonance, X is ideally close to zero.

A simple full-wave loop is often described as having a feed-point impedance around 100 Ω, which explains the traditional use of a 75 Ω quarter-wave matching section. However, this is only an approximation. By changing loop geometry and installation conditions, practical full-wave loops can be designed around 50 Ω, 75 Ω, approximately 112 Ω, 200 Ω, or other values. (66Pacific)

For this reason, a loop antenna impedance calculator should distinguish between:

Geometry-based estimate: useful for planning. Modeled impedance: calculated using an electromagnetic model. Measured impedance: the value obtained from the installed antenna.

Quarter-Wave Coax Matching

For a quarter-wave transformer, the ideal characteristic impedance is:

Zt = √(Zin × Z0)

where:

• Zin = antenna feed-point resistance at resonance;
• Z0 = target feedline impedance;
• Zt = transformer impedance.

For an antenna near 100 Ω connected to 50 Ω coax:

Zt ≈ √(100 × 50) ≈ 70.7 Ω

That is why a practical 75 Ω coaxial quarter-wave section is often used.

Its physical length is:

Lmatch = λ/4 × VF

or, in meters:

Lmatch ≈ 75 × VF / f (MHz)

A matching section transforms impedance only near the frequency for which its electrical length was designed. Its behavior changes as frequency moves away from that point.

Baluns and Feedlines

A closed wire loop is a balanced antenna, while ordinary coaxial cable is an unbalanced transmission line. A suitable current balun or common-mode choke can help keep unwanted RF current off the outside of the coax shield.

Do not choose a 4:1 balun simply because the antenna is a delta loop. A 4:1 transformation is appropriate only when the actual antenna and feed arrangement require that impedance ratio. Practical loop designs around 200 Ω may use a 4:1 transformer, while loops nearer 50–75 Ω may be fed differently. (Practical Antennas)

Matching options:

Direct 50/75 Ω coax Suitable when the installed feed-point impedance is already close enough to the feedline and transmitter requirements.

75 Ω quarter-wave transformer Useful for a design near approximately 112 Ω into a 50 Ω system, or as a traditional approximate match for loops near 100 Ω.

Balun / impedance transformer Use the ratio required by the actual feed-point impedance.

Balanced line + tuner Useful when multiband operation and a wide range of impedances are expected.

Radiation resistance and feed-point impedance are related concepts, but they are not interchangeable.

Radiation resistance is the equivalent resistance representing power converted into electromagnetic radiation.

Input impedance is what the feedline sees at the antenna terminals. It includes the resistive and reactive behavior at that particular feed point and is affected by current distribution, losses, geometry, and the surrounding environment.

For electrically small single-turn loops with nearly uniform current, the familiar approximation is:

Rr ≈ 31,200 × (A / λ²)² Ω

where A is loop area.

That formula is for a small loop antenna, not for a resonant full-wave delta loop. A full-wave loop has a non-uniform standing-wave current distribution, so applying the small-loop radiation-resistance equation to a 1λ loop gives misleading results.

For a full-wave loop, radiation resistance and input impedance are better determined from a geometry-specific electromagnetic model or from measurement of the installed antenna. Shape alone can shift the feed impedance across a very wide range. (Practical Antennas)

Calculator note: Radiation resistance is not calculated from frequency alone. Use modeling or measured impedance for a specific installation.

A resonant full-wave loop normally radiates most strongly broadside to the plane of the loop around its fundamental full-wave resonance. This is the opposite of the classic electrically small loop, which has a null broadside to its plane. (Practical Antennas)

Loop Antenna Gain

There is no universal delta loop gain value.

Gain depends on:

• loop geometry;
• orientation;
• polarization;
• current distribution;
• antenna height;
• elevation angle;
• ground conductivity and dielectric properties;
• conductor loss;
• nearby objects.

In free-space modeling, a full-wave loop can show a modest broadside gain advantage over a half-wave dipole, but real installed performance depends heavily on height and ground. (Practical Antennas)

For this reason, avoid interpreting a generic “loop antenna gain” figure as a guaranteed on-air result.

Broadside Radiation

For a vertically mounted delta loop, the principal directions are generally perpendicular to the plane of the triangle near the fundamental resonance.

Diagram: Loop plane ↔ Maximum broadside radiation

If the antenna is rotated around its vertical axis, its azimuth pattern rotates with it.

Height Above Ground

Pattern selector: 0.10λ | 0.25λ | 0.50λ | 1.00λ

Height above ground can substantially change the elevation pattern, feed impedance, and resonant dimensions. Ground conductivity and dielectric constant also affect modeled results, especially when significant portions of the loop are electrically close to the ground. (Practical Antennas)

Advanced result labels: Azimuth pattern Elevation pattern Estimated beamwidth Broadside gain Polarization Take-off angle

Only display numerical pattern or gain results when they come from an actual antenna model rather than a generic formula.

A horizontal and a vertical full-wave loop may use similar amounts of wire, but they can behave very differently after installation.

A horizontal loop antenna calculator therefore needs more than perimeter alone if radiation pattern or impedance is being predicted. Antenna height is a critical input.

All three are closed full-wave wire antennas, but geometry changes their mechanical requirements and electrical behavior.

A circular loop encloses the largest possible area for a given perimeter, but practical wire antennas are usually built as triangles, squares, diamonds, or rectangles because those shapes are easier to support.

The best geometry is therefore not automatically the one with the highest theoretical performance. Available support points, feedline routing, target polarization, desired impedance, and installation height can matter more.

Yes, a delta loop designed as a full-wave antenna on one band can operate on higher frequencies, especially when used with a suitable feed system and tuner. However, it does not behave like the same fundamental-mode antenna on every band.

As frequency rises:

• the loop becomes several wavelengths in circumference;
• additional current maxima and minima appear;
• the radiation pattern develops more lobes;
• broadside behavior changes;
• feed-point impedance may vary widely;
• SWR on coax can increase loss.

A loop designed near 7 MHz, for example, can be used on higher-frequency bands, but its radiation pattern will not remain the same as its 40m fundamental pattern. (66Pacific)

For multiband operation, balanced feedline and an antenna tuner can be attractive because the system is not dependent on maintaining a low SWR on a long run of 50 Ω coax.

If coax is used with high SWR, remember that cable loss can make the SWR measured at the transmitter appear better than the actual mismatch at the antenna. A lower indicated SWR caused by feedline attenuation does not mean that antenna-system efficiency has improved. (Портативные антенны)

Multiband calculator outputs: Electrical loop length on selected band Approximate harmonic relationship Feedline warning Expected multi-lobe pattern warning Tuner / matching note

The calculated dimensions are the beginning of the antenna design process. The resonant frequency of the completed loop can differ from the mathematical estimate.

Wire Diameter

Changing conductor diameter changes the electrical behavior and bandwidth of the antenna. A calculation based only on frequency cannot account for every conductor size.

Wire Insulation

Insulation introduces dielectric loading around the conductor and can change its effective electrical length. Two loops with the same physical dimensions may therefore resonate differently if one uses bare wire and the other heavily insulated wire.

Height Above Ground

Ground affects both resonant frequency and input impedance. A loop modeled in free space can require adjustment when installed close to real ground. (Practical Antennas)

Ground Conditions

Conductivity and dielectric constant influence current image effects and radiation pattern. This becomes particularly important for vertically polarized loops with lower sections close to the ground.

Nearby Objects

Metal roofs, gutters, towers, fences, utility wiring, reinforced concrete, other antennas, and nearby structures can detune the loop or distort its pattern.

Trees and Supports

Trees can move in the wind and their electrical effect changes with moisture. Insulators, ropes, and the way the conductor is attached can also slightly alter the final geometry.

Wire Sag

A loop that was calculated as a perfect equilateral triangle may become a curved, irregular triangle once suspended. That changes enclosed area and side geometry.

Feed Point

Moving the feed point changes polarization and feed impedance even when total wire length remains unchanged.

Matching Line

A quarter-wave transformer must be cut according to the actual velocity factor of the coax, not simply to one-quarter of the free-space wavelength.

Recommended tuning process:

Install the antenna in its intended final position. Measure the impedance or SWR around the target frequency. If resonance is too low, shorten the loop gradually. If resonance is too high, additional conductor length is required. Recheck after each change rather than making one large correction.

Calculator message: Calculated dimensions are a starting point. Final resonance must be verified on the installed antenna.

Example 1 — 40m Delta Loop

Design frequency: 7.10 MHz

Free-space wavelength: 300 / 7.10 ≈ 42.25 m

Practical starting perimeter: 306 / 7.10 ≈ 43.10 m / 141.4 ft

Equilateral side: 43.10 / 3 ≈ 14.37 m / 47.1 ft

Triangle height: 14.37 × 0.866 ≈ 12.44 m / 40.8 ft

75 Ω quarter-wave section, VF 0.66: 75 × 0.66 / 7.10 ≈ 6.97 m / 22.9 ft

75 Ω quarter-wave section, VF 0.80: 75 × 0.80 / 7.10 ≈ 8.45 m / 27.7 ft

The matching-section values are physical cable lengths based on the selected velocity factor. Verify the actual cable specification before cutting.

Calculate a 40m Delta Loop

Example 2 — 20m Delta Loop

Design frequency: 14.10 MHz Starting perimeter: 21.70 m / 71.2 ft Each equilateral side: 7.23 m / 23.7 ft Triangle height: 6.26 m / 20.6 ft

A 20 meter delta loop is compact enough that changing the feed point or orientation is often practical without rebuilding the entire support system.

Calculate a 20m Delta Loop

Example 3 — 11m / 27 MHz Delta Loop

Design frequency: 27.20 MHz Starting perimeter: 11.25 m / 36.9 ft Each equilateral side: 3.75 m / 12.3 ft Triangle height: 3.25 m / 10.7 ft

For a 27 MHz delta loop antenna, even a small frequency change affects the required dimensions. Enter the intended design frequency into the calculator for a more useful starting value.

Calculate an 11m Delta Loop

Example 4 — 80m Delta Loop

Design frequency: 3.60 MHz Starting perimeter: 85.00 m / 278.9 ft Each equilateral side: 28.33 m / 93.0 ft Triangle height: 24.54 m / 80.5 ft

If an equilateral 80m delta will not fit the available supports, changing to a flatter triangle or rectangle can make installation possible. Recalculate or model the resulting impedance rather than assuming it remains unchanged.

Calculate an 80m Delta Loop

The calculator should clearly separate simple dimensional estimates from modeled antenna performance.

Default dimensional assumption: Full-wave loop starting perimeter = 306 / f (MHz) meters or 1005 / f (MHz) feet. These formulas are practical approximations and should be followed by real-world tuning. (66Pacific)

Geometry assumption: Equilateral delta calculations use L/3 for each side and Side × √3/2 for triangle height.

Matching-section assumption: Quarter-wave coax length = 75 × VF / f (MHz) in meters. (66Pacific)

Impedance assumption: Do not infer a precise feed-point impedance from frequency alone. Full-wave loop impedance changes with geometry, feed point, height, conductor, and ground. Geometry-specific designs can be created for substantially different impedance levels. (Practical Antennas)

Radiation-pattern assumption: Any numerical gain, beamwidth, azimuth, elevation, Smith chart, current distribution, or VSWR-over-frequency result should come from an electromagnetic model using the selected geometry and installation parameters rather than from the basic wire-length formula. Advanced delta-loop design tools demonstrate how ground, feed-point position, coax loss, and geometry alter these results. (Портативные антенны)

Important: Calculated dimensions are construction starting points. Install the antenna in its final position, measure resonance and impedance, and tune the physical length and matching system as required.

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