Calculate helical antenna dimensions from frequency and number of turns: helix diameter, turn spacing and wire length, plus estimated gain and beamwidth.
Related Calculators
- Electrical Length Calculator
- 1/4 Wave Resonator Calculator
- Angle Of Arrival Calculator
- 3 dB Rule Calculator
- All Physics Calculators
Helical Antenna Formula
The helical antenna calculator uses the operating frequency to find wavelength, then scales the helix dimensions from the circumference ratio and turn spacing ratio you enter.
- ฮป = wavelength
- c = speed of light, 299,792,458 m/s
- f = frequency in Hz
- C = helix circumference
- RC = circumference ratio, C/ฮป
- D = helix diameter
- S = spacing between turns
- RS = turn spacing ratio, S/ฮป
- N = number of turns
- H = total antenna height
- L = approximate wire length
- ฮฑ = pitch angle
- Zin = approximate input impedance in ohms
- DdBi = empirical idealized directivity estimate in dBi, not realized gain
- B = beamwidth factor used for HPBW and FNBW estimates
The frequency unit selector first converts your frequency to Hz. The length output selector only changes the displayed units, not the underlying calculation. The circumference ratio sets the helix circumference relative to wavelength, while the spacing ratio sets the distance between turns relative to wavelength. From those values, the calculator finds geometric size, conductor length and pitch. Input resistance, idealized directivity and beamwidth use simplified axial-mode approximations, shown here only for 4 to below 15 turns, C/ฮป from 0.8 to 1.15 and pitch from 12ยฐ to 14ยฐ. The upper turn limit is a conservative software bound. Outside that range, geometry remains available and RF estimates are marked unavailable. The default ratios 1 and 0.25 give a 14.04ยฐ pitch, just beyond this strict model interval.
Typical Axial-Mode Helical Antenna Starting Values
These values are common starting points for an axial-mode helical antenna. Final dimensions may need adjustment for conductor diameter, ground plane size, matching method, and nearby materials.
| Parameter | Common starting range | Calculator input or result |
|---|---|---|
| Circumference ratio | 0.8 to 1.2 ฮป | C/ฮป |
| Turn spacing ratio | 0.2 to 0.3 ฮป | S/ฮป |
| Pitch angle | About 12ยฐ to 14ยฐ | Pitch angle result |
| Number of turns | 3 to 15 turns | Number of turns |
| Input impedance | Often near 140 ฮฉ when C/ฮป = 1 | Approx. input impedance |
Example Calculations
Example 1: 2.4 GHz helix with 8 turns
Suppose you enter a frequency of 2400 MHz, 8 turns, C/ฮป = 1.0, and S/ฮป = 0.25.
- Wavelength: about 12.491 cm
- Helix circumference: about 12.491 cm
- Helix diameter: about 3.976 cm
- Turn spacing: about 3.123 cm
- Total antenna height: about 24.983 cm
- Approximate wire length: about 103.006 cm
- Pitch angle: about 14.04ยฐ
- Input resistance: not estimated here because the 14.04ยฐ pitch exceeds the declared 14ยฐ model limit
Example 2: 915 MHz helix with 6 turns
Suppose you enter a frequency of 915 MHz, 6 turns, C/ฮป = 1.0, and S/ฮป = 0.25.
- Wavelength: about 32.764 cm
- Helix circumference: about 32.764 cm
- Helix diameter: about 10.430 cm
- Turn spacing: about 8.191 cm
- Total antenna height: about 49.146 cm
- Approximate wire length: about 202.635 cm
- Pitch angle: about 14.04ยฐ
- Input resistance: not estimated here because the 14.04ยฐ pitch exceeds the declared 14ยฐ model limit
FAQ
What does C/ฮป mean for a helical antenna?
C/ฮป is the helix circumference divided by wavelength. A value of 1 means the circumference is one wavelength at the operating frequency. For many axial-mode helical antenna designs, C/ฮป near 1.0 is a common starting point.
What does S/ฮป mean?
S/ฮป is the spacing between adjacent turns divided by wavelength. A value of 0.25 means each turn is spaced one-quarter wavelength from the next turn. With C/ฮป = 1 and S/ฮป = 0.25, the pitch angle is about 14 degrees.
Why are gain and beamwidth labeled approximate?
The directivity, HPBW and FNBW formulas are empirical idealized axial-mode estimates, not guaranteed realized gain. Published models use different directivity coefficients; this calculator names the coefficient-12 variant and restricts its range. Actual performance depends on conductor diameter, ground plane, feed matching, materials, losses and nearby objects, and can differ substantially. Use simulation and measurement for a finished design.
