# Formulas on the General Exam

This page contains all the formulas needed for the General class ham radio license exam.  You might want to print out these formulas and review them just before entering the exam room, but leave this sheet in the car!  Do not bring it into the exam room with you!

 Prefix Symbol Value International System of Units (SI) giga- G 109 1,000,000,000 one billion mega- M 106 1,000,000 one million kilo- k 103 1,000 one thousand (none) (none) 100 1 one centi- c 10−2 .01 one one-hundredth milli- m 10−3 .001 one one-thousandth micro- µ 10−6 .000001 one one-millionth nano- n 10−9 .000000001 one one-billionth pico- p 10−12 .000000000001 one one-trillionth

Standing wave ratio:

$$SW\!R = \frac{highest\text{-}impedance}{lowest\text{-}impedance}$$

Length of 1/2 wavelength antenna:

$$Length~ \text{(in feet)} = \frac{468}{Frequency~ \text{(in MHz)}}$$

Length of 1/4 wavelength antenna:

$$Length~ \text{(in feet)} = \frac{234}{Frequency~ \text{(in MHz)}}$$

International System of Units (SI):

$$1~ \text{nF} = 10^{-3}~ \text{µF}$$

$$1~ \text{pF} = 10^{-3}~ \text{nF}$$

Equal-value resistors in series:

$$R_i = \frac{R_t}{n}$$

Equal-value resistors in parallel:

$$R_t = \frac{R_i}{n}$$

Resistors in parallel:

$$\frac{1}{R_t} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}$$

Inductors in series:

$$L_t = L_1 + L_2$$

Equal-value inductors in parallel:

$$L_t = \frac {L_i}{n}$$

Capacitors in parallel:

$$C_t = C_1 + C_2 + C_3$$

Equal-value capacitors in series:

$$C_t = \frac {C_i}{n}$$

Capacitors in series:

$$\frac {1}{C_t} = \frac {1}{C_1} + \frac {1}{C_2}$$

Transformers:

$$E_s = E_p \times \left(\frac {N_s}{N_p} \right)$$

$$\frac {N_P}{N_S} = \sqrt{\frac {Z_P}{Z_S}}$$

RMS voltage:

$$V_P = \frac{V_{RMS}}{0.707}$$

$$V_{PP} = V_P \times 2$$

$$V_{RMS} = V_P \times 0.707$$

Power:

$$P = E \times I$$

$$P = \frac {E^2}{R}$$

$$P = I^2 \times R$$

$$E = \sqrt{P \times R}$$

Peak envelope power:

$$V_P = \frac{V_{PP}}{2}$$

$$V_{RMS} = V_P \times 0.707$$

$$PEP = \frac{{V_{RMS}}^2}{R}$$

Decibel math:

$$loss\text{-}\!factor = 10 ^ \left( \large \frac{-loss \text{-} in \text{-} db}{10} \right)$$

$$percent \text{-}loss = ( 1 - loss\text{-}\!factor ) \times 100\%$$

Frequency modulation:

$$bandwidth = 2 \times \left(D_{MAX} + M_{MAX}\right)$$

Upconverter:

$$multiplier = \frac {transmitted \text{-}frequency}{lower \text{-}frequency}$$

$$lower \text{-}frequency \text{-}maximum \text{-}deviation = \frac {transmitted \text{-}frequency \text{-}maximum \text{-}deviation}{multiplier}$$