Ham Radio Calculators: Antennas, Feedline, Power and RF Safety

Antenna length, feedline loss and RF exposure distance are arithmetic rather than opinion, and getting them approximately right before you buy anything saves more money than any purchasing decision on this site. These are the eighteen calculations that come up most, each with the formula, the band chart behind it, and an honest note about what the number does not tell you.

Antenna dimensions

Cut the wire once. Every tool here gives the formula, the band chart and the trimming margin, and every one of them is arithmetic that has not changed in ninety years.

• Dipole length 468 / f(MHz) feet, tip to tip The first calculation nearly every new HF operator runs. Total length, each leg, trimming allowance and a full band chart.
• Quarter-wave vertical 234 / f(MHz) feet of radiator Radiator length plus the radial field that is the other half of the antenna. Includes 5/8 wave and half-wave options.
• End fed half wave Same length, one support Wire length, the 49:1 transformer ratio, counterpoise length and the choke position that stops the coax joining the antenna.
• Full-wave loop 1005 / f(MHz) feet of circumference Square, delta and circular loops, with the receive noise advantage explained and the 75 ohm matching section length.
• J-pole and Slim Jim Three quarter waves plus a stub Radiator, stub, tap position and spacing for VHF and UHF, with copper pipe and roll-up ladder line construction.
• Wavelength and frequency 300 / f(MHz) metres The conversion underneath every other antenna calculation, with half, quarter, eighth and 5/8 wave dimensions.

Where the antenna goes

Length sets the frequency. Height, radials and orientation decide whether anyone hears you.

• Antenna height and takeoff angle Half a wavelength up is about 30 degrees Height in wavelengths, main lobe elevation, and the honest verdict that rope beats watts on a DX path.
• Radial field planner 32 or more on the ground, 4 elevated How many, how long, how much wire, and what four radials actually costs you in decibels.
• VHF and UHF range 1.415 x sqrt(height in feet), miles Radio horizon for both stations, why a repeater reaches fifty miles, and why power barely helps above 50 MHz.

Feedline and matching

The quietest way to throw away a station is a feedline nobody measured. These four tools cover everything between the radio and the antenna.

• Coax loss 3 dB means half your power Loss by cable type, length and frequency, power delivered at the antenna, and the extra loss a mismatch causes on a lossy line.
• SWR and reflected power 2:1 reflects 11 percent Reflected power, return loss, mismatch loss and an honest account of when the number actually matters.
• Impedance matching sqrt(Zsource x Zload) Quarter-wave transformer impedance, stub lengths corrected for velocity factor, and coaxial baluns from measured cable.
• Balun and choke selector 12 turns on an FT-240-31 Which ratio for which antenna, turn counts by band, and the symptoms that mean your feedline has joined the antenna.

Power and safety

One of these is required by federal rule. The other three decide whether the station stays on the air.

• RF exposure evaluation Required of every amateur station Compliance distance for controlled and uncontrolled environments, with mode duty cycle and transmit fraction applied.
• Power supply sizing 100 W HF needs about 30 A Station current totals, headroom, and the DC wire gauge that stops a radio browning out on transmit peaks.
• Battery runtime 20 Ah runs 100 W for about 4 hours Usable capacity by chemistry, receive versus transmit contribution, and the fuse and wire that go with each.
• ERP and EIRP Power minus loss plus gain Effective radiated power, the 2.15 dB between the two references, and the 60 metre limit that is specified this way.
• Decibels and power ratios 3 dB doubles, 10 dB is ten times Conversions, dBm, dBi versus dBd, and what every common upgrade is really worth in S units.

The three numbers worth knowing without a calculator

If you remember nothing else from this section, remember these. They answer most of the questions that come up on the air and they are all mental arithmetic.

Where the numbers come from

Every constant on this site is traceable rather than estimated, which matters because a wrong antenna dimension wastes an afternoon and a wrong exposure figure is a compliance problem.

• Antenna dimensions come from the speed of light and the standard end-effect correction. A full wavelength is 984 divided by frequency in feet; a half-wave dipole in real wire is about five percent shorter than half that, which gives 468.
• Coax attenuation figures are manufacturer datasheet values at the standard test frequencies, interpolated logarithmically between them because attenuation behaves that way rather than linearly.
• RF exposure limits come directly from 47 CFR 1.1310, and the duty cycle figures are the standard ones used in the FCC OET Bulletin 65 Supplement B worksheets. The regulation itself is published at ecfr.gov and the safety guidance at fcc.gov.
• Band plans and privileges come from 47 CFR 97.301 and 97.305.
• Battery and current figures are typical published equipment specifications at 13.8 volts, which is what every amateur radio manual quotes.

What no calculator can tell you

Every tool here is closed-form arithmetic, and arithmetic has limits that are worth being explicit about.

• Nearby objects. Gutters, chain-link fences, aluminium siding and other antennas within a fraction of a wavelength detune an antenna and absorb power. If an antenna measures strangely, look at what is next to it before you look at the wire.
• Ground quality. Soil conductivity varies by more than an order of magnitude between wet clay and dry sand, and it affects vertical efficiency and horizontal takeoff angle. The tables here assume average ground.
• Real patterns. A calculator gives a main lobe angle; modelling software gives the whole three-dimensional pattern over your specific ground with your specific supports. For a wire antenna the arithmetic is enough, and for a beam on a tower the modelling earns its time.
• Whether the antenna is a good idea. Dimensions do not tell you whether a vertical or a dipole suits your lot, which is a judgement covered on choosing a first HF antenna and vertical versus dipole.
• What is actually wrong. A high SWR reading has half a dozen possible causes and the calculator cannot distinguish them. The diagnostic sequence is on reading SWR and fixing a bad match.

Measuring, rather than calculating

The instrument that turns all of this from theory into a working antenna is an analyser. A NanoVNA H4 vector network analyzer$89.90 sweeps 9 kHz to 1.5 GHz, shows resistance and reactance separately, plots a Smith chart, and finds a bad connector by time-domain reflectometry, for under a hundred dollars. It is the single most useful purchase for anyone who intends to build antennas rather than buy them.

For permanent monitoring rather than diagnosis, a Daiwa CN-501H cross-needle SWR and power meter$151.99 shows forward, reflected and SWR on a cross-needle display, which reveals a changing match faster than any digital readout. And every diagnosis should start with a XRDS-RF 100 W dummy load, 50 ohm$45.49, because verifying that the radio and the meter are both honest takes thirty seconds and saves an afternoon of blaming the antenna. All three are compared on antenna analyzers and SWR and power meters.