Reference · Quick Recall

Formula Cheat Sheet

Every key formula on the site, on one page — organized for fast recall and built to print cleanly onto a couple of sheets for the bench or last-minute Associate CET review.

Ohm's Law & Power

Voltage

V = I × R

volts = amps × ohms

Current

I = V / R

Resistance

R = V / I

Power

P = V × I

Power (current)

P = I² × R

Power (voltage)

P = V² / R

Series & Parallel

Series resistance

R_T = R1 + R2 + R3 …

Parallel resistance

1/R_T = 1/R1 + 1/R2 …

Two in parallel

R_T = (R1×R2)/(R1+R2)

product over sum

Series capacitance

1/C_T = 1/C1 + 1/C2 …

opposite of resistors

Parallel capacitance

C_T = C1 + C2 …

Series inductance

L_T = L1 + L2 …

Parallel inductance

1/L_T = 1/L1 + 1/L2 …

Voltage divider

V_out = V_in × R2/(R1+R2)

Current divider

I_x = I_T × (R_T/R_x)

AC, Reactance & Resonance

Capacitive reactance

X_C = 1 / (2πfC)

ohms

Inductive reactance

X_L = 2πfL

ohms

Impedance (series RLC)

Z = √(R² + (X_L−X_C)²)

Resonant frequency

f_r = 1 / (2π√(LC))

Period / frequency

f = 1/T ; T = 1/f

RC time constant

τ = R × C

63% in 1τ

RL time constant

τ = L / R

RMS (sine)

V_rms = 0.707 × V_peak

Peak (sine)

V_peak = 1.414 × V_rms

Peak-to-peak

V_pp = 2 × V_peak

Average (sine)

V_avg = 0.637 × V_peak

full-wave rectified

RMS from average (sine)

V_rms = 1.11 × V_avg

Peak from average (sine)

V_peak = 1.57 × V_avg

Average from RMS (sine)

V_avg = 0.9 × V_rms

average over one half cycle

Impedance (R and X in parallel)

Z = (R × X) / √(R² + X²)

one resistance in parallel with one reactance

Resonance (practical units)

f(kHz) = 159.2 / √(LC)

L in µH, C in µF

Charge, Energy & Batteries

Capacitor charge

Q = C × V

coulombs = farads × volts

Energy in a capacitor

W = ½ × C × V²

joules

Capacitor current

I = C × (dV/dt)

d = change (Δ); t in seconds

Inductor voltage

V = L × (di/dt)

henries × amps per second

Energy in an inductor

W = ½ × L × I²

joules

Battery internal resistance

V_out = EMF − (R_int × I_out)

terminal voltage sags as load current rises

Semiconductors & Amplifiers

BJT current gain

β = I_C / I_B

Emitter current

I_E = I_C + I_B

Alpha

α = β / (β+1)

CE voltage gain

A_v = −R_C / r′e

r′e = 26mV/I_E

Op-amp inverting

A_v = −R_f / R_in

Op-amp non-inverting

A_v = 1 + R_f / R_in

Diode drop (Si)

≈ 0.7 V

Ge ≈ 0.3 V

LED resistor

R = (V_s − V_f) / I_f

Decibels

Power ratio

dB = 10·log₁₀(P2/P1)

Voltage ratio

dB = 20·log₁₀(V2/V1)

dBm

dBm = 10·log₁₀(P / 1mW)

0 dBm = 1 mW

Double power

+3 dB

×2 power

Double voltage

+6 dB

×2 voltage

RF & Antennas

Wavelength

λ(m) = 300 / f(MHz)

free space

Wavelength in feet

λ(ft) = 984 / f(MHz)

ETA sheet form

Frequency from feet

f(MHz) = 984 / λ(ft)

ETA sheet form

Speed of light

c = f × λ

c ≈ 3 × 10⁸ m/s

Wavelength in degrees

0.5λ = 180° ; 0.25λ = 90°

half wave and quarter wave

Half-wave dipole

L(m) ≈ 142.5 / f(MHz)

468 / f(MHz) in feet. The ~5% end effect is already in the constant; never multiply by the coax velocity factor (that belongs to the feedline). Cut long and trim.

Quarter-wave vertical

L(m) ≈ 71.25 / f(MHz)

234 / f(MHz) in feet; end effect already included, as for the dipole.

Gain conversion

dBi = dBd + 2.15

VSWR

VSWR = (1+|Γ|)/(1−|Γ|)

|Γ| = size of the reflection coefficient

Digital & Counters

Counter division

f_out = f_in / 2ⁿ

n flip-flops

Max count

2ⁿ states

n bits

BCD

each decimal digit → 4 bits

Two's complement

invert bits, add 1

to negate

555 Timer

Astable frequency

f = 1.44 / ((R1+2R2)·C)

Astable duty cycle

D = (R1+R2)/(R1+2R2)

Monostable pulse

t = 1.1 × R × C

Constants & Conversions

Pi (ETA value)

π = 3.14

Two pi (ETA value)

2π = 6.28

Log of pi

log π = 0.497

Meters to feet

1 m = 3.28 ft

Inches to centimeters

1 in = 2.54 cm

Radians to degrees

1 rad = 57.3°

Order of operations

PEMDAS

Parentheses, Exponents, Multiplication, Division, Add, Subtract

SI Prefixes

Prefix	Symbol	Multiplier	Power of ten
tera	T	trillion	10¹²
giga	G	billion	10⁹
mega	M	million	10⁶
kilo	k	thousand	10³
none	none	1	10⁰
milli	m	1/thousandth	10⁻³
micro	µ	1/millionth	10⁻⁶
nano	n	1/billionth	10⁻⁹
pico	p	1/trillionth	10⁻¹²

Resistor Color Code

Color	Digit	Multiplier	Tolerance	Temp. coeff. (ppm)
Black	0	1 Ω	–	250
Brown	1	10 Ω	±1%	100
Red	2	100 Ω	±2%	50
Orange	3	1 kΩ	–	15
Yellow	4	10 kΩ	–	25
Green	5	100 kΩ	±0.5%	20
Blue	6	1 MΩ	±0.25%	10
Violet	7	10 MΩ	±0.10%	5
Gray	8	100 MΩ	±0.05%	1
White	9	1 GΩ	–	–
Gold	–	0.1 Ω	±5%	–
Silver	–	0.01 Ω	±10%	–
No color	–	–	±20%	–

Same values as ETA's chart. The multiplier is the band's power of ten (gold ×0.1, silver ×0.01); the temperature coefficient band appears on some precision 6-band resistors.

Study tip: Print this, then cover the formula column and try to recall each one from its name. The formulas you stumble on are exactly the ones to drill in the Circuits Lab and Algebra Solver.