Ham Radio Math Toolkit

Note: This page is unrelated to my law practice.

AI-Assisted Disclosure: I used AI tools to build these pages and pull data/specifications from various public sources (such as manufacturer's websites, datasheets, internet forums, etc...). I do my best to review everything, but I can't review specifications for every underlying item because: (1) it can be wrong; (2) it change over time; and (3) these pages are just in support of my hobbies - I don't have the time to verify every single thing. I used AI to create these pages and aggregate the data because I wanted these tools and reference material for myself, and I thought it would be useful to share with others. Always confirm details directly with the manufacturer or original sources. Use this information at your own risk. Please note that if you use AI to verify this information it will likely come back as "accurate" citing my website as the source. You will need to verify the actual source of the data, not my aggregation of the data.

Antenna, RF, and utility calculators in one place. All computations run locally in your browser. Cards are collapsed by default—click a title or use the left sidebar to open a tool.

Antenna lengths

Common “starting point” wire lengths. Use the shortening factor to account for end-effect / insulation / environment.

Frequency (MHz)

Shortening factor

Formulas

Uses classic ham constants in feet:

Half-wave dipole (total) ≈ 468 / f(MHz)

Quarter-wave ≈ 234 / f(MHz)

Full-wave loop circumference ≈ 1005 / f(MHz)

Then multiplies by the shortening factor.

Coax electrical length

Compute physical length for a desired electrical length (degrees or wavelength fraction) using velocity factor (VF).

Mode Degrees Fraction of wavelength

Coax type (sets VF)

Velocity factor (VF)

Frequency (MHz)

Electrical length (degrees)

Show units

Formulas

λ (in coax) = (c / f) · VF

Length = λ · (degrees/360) or λ · fraction

c = 299,792,458 m/s

Coax loss

Uses embedded attenuation tables (typical) from manufacturer datasheets. Interpolates between points.

Coax type

Frequency (MHz)

Length

Length units

Input power (W)

Connectors (count)

Loss per connector (dB)

Note

Free-space path loss (FSPL)

Quick sanity check for links (real-world paths also include polarization, terrain, clutter, antenna patterns, fade margin, etc.).

Frequency (MHz)

Distance

Distance units

Formula

Power & dB

Convert W ↔ dBm/dBW, compare two power levels, and convert dBd ↔ dBi.

Power conversion

Power (W)

Power (dBm)

Power (dBW)

For voltage conversions: Z (Ω)

Voltage (V RMS)

Voltage (Vpp)

dB difference ΔdB = 10·log10(P2/P1)

P1 (W)

P2 (W)

Antenna gain (dBd)

Antenna gain (dBi)

Formulas

dBm = 10·log10(P(W)·1000)

dBW = 10·log10(P(W))

P(W) = 10^(dBm/10) / 1000

V_RMS = √(P·Z)

V_pp = 2·√2·V_RMS

dBi = dBd + 2.15

Quick band picker

Pick a common ham band center frequency, then push it into the calculators.

Band

Frequency (MHz)

You can still override any field per-tool.

Reactance & resonance

Handy for LC networks, traps, and “why is my tuner doing that?” moments.

Frequency (MHz)

Capacitance (pF)

Inductance (µH)

Sign convention

Formulas

X_L = 2πfL

X_C = -1/(2πfC)

f₀ = 1/(2π√(LC))

(Use f in Hz, L in H, C in F.)

SWR / Return loss

Two ways: (1) forward/reflected power (wattmeter), or (2) load impedance vs Z0.

Mode Forward/Reflected Impedance (R+jX)

Forward power (W)

Reflected power (W)

Formulas

|Γ| = √(P_ref/P_fwd)

SWR = (1+|Γ|)/(1-|Γ|)

Return Loss (dB) = -20·log10(|Γ|)

Mismatch Loss (dB) = -10·log10(1-|Γ|²)

Γ = (Z_L - Z₀)/(Z_L + Z₀)

Sources

Coax loss/VF values embedded on this page are pulled from these public datasheets (typical values; always verify your exact part / revision):

General formulas (SWR, dB conversions, FSPL, reactance) are standard RF engineering relationships commonly found in ARRL handbooks and basic EM references.

Here are some of my other amateur/ham radio pages:

Antenna Height Restriction Legal Reference Checker