Ham Radio Math Toolkit

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

lambda (in coax) = (c / f) * VF

Length = lambda * (degrees/360) or lambda * 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 (Ohms)

Voltage (V RMS)

Voltage (Vpp)

dB difference DeltadB = 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 = sqrt(P*Z)

V_pp = 2*sqrt2*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 (uH)

Sign convention

Formulas

X_L = 2pifL

X_C = -1/(2pifC)

f₀ = 1/(2pisqrt(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

|Gamma| = sqrt(P_ref/P_fwd)

SWR = (1+|Gamma|)/(1-|Gamma|)

Return Loss (dB) = -20*log10(|Gamma|)

Mismatch Loss (dB) = -10*log10(1-|Gamma|^2)

Gamma = (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.