Why formulas matter
Amateur radio uses a modest amount of math. Most of it falls into a handful of formulas, useful for exam preparation and for everyday jobs like cutting an antenna or estimating power. The results are approximations; real-world antennas and components deviate from textbook values.
Ohm’s law and power
For a direct-current circuit:
- V = I x R (volts = amps x ohms)
- P = V x I (watts = volts x amps)
- P = I^2 x R
- P = V^2 / R
Example: 12 V across a 6 ohm load gives I = 12 / 6 = 2 A and P = 12 x 2 = 24 W.
For schematic parts like these, see ham radio schematic symbols.
Frequency and wavelength
Radio waves travel at about 300,000,000 meters per second (about 299,792,458 m/s precisely). The relation between frequency and wavelength is:
- Wavelength (m) = 300 / frequency (MHz) (approximate)
- Frequency (MHz) = 300 / wavelength (m)
Example: 146 MHz gives about 300 / 146 = 2.05 m, which is why that band is called “2 meters.” (See VHF and UHF compared.)
Antenna length
A common rule of thumb for a half-wave dipole in free space:
- Length (feet) = 468 / frequency (MHz)
- Length (meters) = 142.6 / frequency (MHz) (approximately)
Example: at 7.1 MHz, 468 / 7.1 is roughly 66 feet total. The factor accounts for end effects and velocity; real antennas usually need trimming for height, nearby objects and wire type. A quarter-wave vertical is about half this length. Always measure with an antenna analyzer or SWR meter. For build details, see ham radio antenna designs you can build at home.
Decibels
- Power ratio in dB = 10 x log10(P2 / P1)
- Voltage ratio in dB = 20 x log10(V2 / V1)
Useful reference points:
- 3 dB is about double the power (or half).
- 10 dB is ten times the power.
- 6 dB is about four times the power (and double the voltage).
An S-unit on a receiver is commonly taken as 6 dB, though meters vary in accuracy.
Reactance and resonance
- Inductive reactance: XL = 2 x pi x f x L
- Capacitive reactance: XC = 1 / (2 x pi x f x C)
- Resonant frequency: f = 1 / (2 x pi x sqrt(L x C))
With f in hertz, L in henries and C in farads. At resonance, XL equals XC. This is the basis of tuned circuits, filters and many antenna matching networks.
Resistors and capacitors in combination
- Resistors in series: R = R1 + R2 + …
- Resistors in parallel: 1/R = 1/R1 + 1/R2 + … (for two: R = R1 x R2 / (R1 + R2))
- Capacitors in parallel: C = C1 + C2 + …
- Capacitors in series: 1/C = 1/C1 + 1/C2 + …
Capacitors behave opposite to resistors.
SWR
SWR (standing wave ratio) indicates how well the antenna matches the feedline:
- Reflection coefficient = (ZL - Z0) / (ZL + Z0)
- SWR = (1 + |reflection|) / (1 - |reflection|)
For a purely resistive load, SWR is simply the larger of ZL/Z0 or Z0/ZL. A 100 ohm load on 50 ohm line gives SWR 2:1. A lower SWR is generally better, but SWR alone does not tell you antenna efficiency. See the diagram of a radio transmitter for where the match fits in the chain.
Other common calculations
- Period = 1 / frequency
- PEP (peak envelope power) and average power differ in SSB voice; check your local power limit’s definition.
- Effective radiated power takes transmitter power, line loss (see the coax cable loss chart) and antenna gain into account.
Tips for using formulas
- Keep units consistent: MHz with meters, hertz with farads and henries.
- Use a calculator with log and square root functions.
- Check results for plausibility.
Frequently asked questions
What are all the formulas for frequency?
The core ones are wavelength = speed of light / frequency and the resonance formula above. Period is 1 / frequency.
What is the 3-3-3 rule for ham radio?
Sources use the phrase in different ways, so it has no single formal meaning in amateur radio; check the context in which you saw it.
What does 72 mean in ham radio?
Hams use number codes for greetings (see the ham radio terms glossary); “73” means best regards and “72” is sometimes used among low-power (QRP) operators, but usage is informal.