Reference chart
Electronics formulas cheat sheet
Print it: Ohm's law and power cheat sheet (PDF: A4 · US Letter)
Print it: Electronics formulas cheat sheet (PDF: A4 · US Letter)
Every formula the lessons teach, on one page. Each one says what it gives you and links to the guide that explains it, plus a calculator where there's one to do the sum for you.
The basics
| Formula | What it gives | Learn it |
|---|---|---|
| V = I × R | The voltage across a resistor (Ohm's law) | guide · calculator |
| I = V ÷ R | The current a voltage pushes through a resistance | guide · calculator |
| R = V ÷ I | The resistance that sets a current | guide · calculator |
| V = mA × kΩ | Ohm's law in milliamps and kilohms, with no conversions | guide |
| P = V × I | Power, in watts | guide · calculator |
| P = I² × R | Power from current and resistance | guide · calculator |
| P = V² ÷ R | Power from voltage and resistance | guide · calculator |
| 1 A = 1 coulomb per second | What one amp means | guide |
| 1 V = 1 joule per coulomb | What one volt means | guide |
| R = (Vsupply − VLED) ÷ I | The series resistor for an LED | guide · calculator |
| R = (Vsupply − n × VLED) ÷ I | One resistor for n LEDs in series | guide · calculator |
Series and parallel
| Formula | What it gives | Learn it |
|---|---|---|
| Rtotal = R1 + R2 + R3 | Resistors in series | guide · calculator |
| 1 ÷ Rtotal = 1 ÷ R1 + 1 ÷ R2 + … | Resistors in parallel | guide · calculator |
| R = (R1 × R2) ÷ (R1 + R2) | Two resistors in parallel: product over sum | guide · calculator |
| ΣIin = ΣIout | Kirchhoff's current law: what flows into a junction flows out | guide |
| ΣVrises = ΣVdrops | Kirchhoff's voltage law: the drops round a loop add up to the rise | guide |
| Vout = Vin × R2 ÷ (R1 + R2) | A voltage divider's output | guide · calculator |
| I1 = I × R2 ÷ (R1 + R2) | How current splits between two parallel resistors | guide |
| Rth = R1 ∥ R2 | A divider's Thevenin resistance, seen from its output | guide |
| VL = Vth × RL ÷ (Rth + RL) | The voltage a load gets from a Thevenin equivalent | guide |
| IN = Vth ÷ Rth | The Norton current of the same network | guide |
| Vpack = V1 + V2 + … | Cells in series add their voltages | guide |
Capacitors and inductors
| Formula | What it gives | Learn it |
|---|---|---|
| Q = C × V | The charge on a capacitor | guide |
| E = ½ × C × V² | The energy stored in a capacitor | guide · calculator |
| τ = R × C | The RC time constant: 63% charged after one τ | guide · calculator |
| V(t) = Vs × (1 − e−t/τ) | A capacitor's voltage as it charges | guide · calculator |
| V = V0 × e−t/τ | A capacitor's voltage as it discharges: 37% left after one τ | guide · calculator |
| V = L × ΔI ÷ Δt | The voltage a coil makes when its current changes | guide |
| τ = L ÷ R | The RL time constant | guide · calculator |
| Ifinal = V ÷ R | The current an RL circuit settles at | guide · calculator |
| E = ½ × L × I² | The energy stored in a coil's magnetic field | guide |
AC, reactance and filters
| Formula | What it gives | Learn it |
|---|---|---|
| f = 1 ÷ T | Frequency from the period | guide |
| Vrms = Vpeak ÷ √2 ≈ 0.707 × Vpeak | The RMS value of a sine wave | guide |
| P = Vrms² ÷ R | AC power in a resistor | guide |
| XC = 1 ÷ (2π f C) | A capacitor's reactance | guide · calculator |
| XL = 2π f L | A coil's reactance | guide · calculator |
| |Z| = √(R² + X²) | Impedance: resistance and reactance combined | guide · calculator |
| fc = 1 ÷ (2π R C) | The cutoff of an RC low-pass or high-pass filter | guide · calculator |
| lag = tan⁻¹(f ÷ fc) | The phase lag of an RC low-pass | guide |
| f₀ = 1 ÷ (2π√(LC)) | An LC circuit's resonant frequency | guide · calculator |
| C = 1 ÷ (4π² × f² × L) | The capacitor that tunes a coil to f | guide |
| Q = centre frequency ÷ bandwidth | The Q factor of a tuned circuit | guide |
| bandwidth ≈ R ÷ (2π × L) | How wide a band a series RLC circuit passes | guide |
| L = R ÷ (2π f) and C = 1 ÷ (2π f R) | A speaker crossover's coil and capacitor | guide |
| dB = 10 × log₁₀(Pout ÷ Pin) | A power ratio in decibels | guide · calculator |
| dB = 20 × log₁₀(Vout ÷ Vin) | A voltage ratio in decibels | guide · calculator |
| square = (4 ÷ π) × (sin x + sin 3x ÷ 3 + sin 5x ÷ 5 + …) | A square wave as odd harmonics | guide |
Diodes and transistors
| Formula | What it gives | Learn it |
|---|---|---|
| Vload = Vsupply − VD | What's left after a diode's forward drop | guide |
| Vpeak out ≈ Vpeak in − 1.4 V | A bridge rectifier's output peak | guide |
| ΔV ≈ I ÷ (fr × C) | The ripple on a rectifier's smoothing capacitor | guide |
| R = (Vin − VZ) ÷ (Iload + IZ,min) | The series resistor for a Zener regulator | guide · calculator |
| P = VZ × I | The power in a Zener diode | guide · calculator |
| Vout = V × RLDR ÷ (Rfixed + RLDR) | A light sensor (LDR) divider's output | guide |
| Rfixed ≈ √(Rdark × Rlight) | The fixed resistor that gives an LDR divider the widest swing | guide |
| IC = β × IB | A transistor's collector current in its active region | guide |
| RB = (Vcontrol − 0.7 V) ÷ IB | The base resistor for a transistor switch | guide |
| P = I² × RDS(on) | The heat in a MOSFET switched fully on | guide |
Op-amps
| Formula | What it gives | Learn it |
|---|---|---|
| Vout = A × (V+ − V−) | An op-amp with no feedback: a comparator | guide |
| V+ = V− | The golden rule, with negative feedback | guide |
| Vout = Vin | A voltage follower (buffer) | guide |
| G = 1 + Rf ÷ Rg | A non-inverting amplifier's gain | guide · calculator |
| G = −Rf ÷ Rin | An inverting amplifier's gain | guide · calculator |
| Vout = −Rf × (V1 ÷ R1 + V2 ÷ R2) | A summing amplifier (mixer) | guide |
| ΔV ≈ Vswing × Rth ÷ (Rth + Rf) | The gap between a Schmitt trigger's thresholds | guide |
| fcorner ≈ GBW ÷ noise gain | Where an amplifier's gain starts to fall | guide |
| fmax = SR ÷ (2π × Vpeak) | The fastest full-size sine before slew rate distorts it | guide |
| f ≈ 1 ÷ (2.2 × R × C) | A relaxation oscillator's frequency, with its feedback divider at a half | guide |
Digital logic
| Formula | What it gives | Learn it |
|---|---|---|
| n bits → 2ⁿ patterns, 0 to 2ⁿ − 1 | How far n bits can count | guide · calculator |
| 1011 = 1 × 8 + 0 × 4 + 1 × 2 + 1 × 1 = 11 | Binary to decimal: add the place values | guide · calculator |
| A ⊕ B = Ā · B + A · B̄ | XOR from AND, OR and NOT | guide |
| NOT (A · B) = Ā + B̄ | De Morgan's first law | guide |
| NOT (A + B) = Ā · B̄ | De Morgan's second law | guide |
| NAND(A, A) = NOT A | A NOT gate from a NAND | guide |
| SUM = A ⊕ B, CARRY = A · B | A half adder | guide |
| SUM = A ⊕ B ⊕ CIN | A full adder's sum bit | guide |
| VOTE = (A AND B) OR (B AND C) OR (A AND C) | A 2-out-of-3 majority voter | guide |
| P = D2 ⊕ D1 ⊕ D0 | An even parity bit | guide |
| Gi = Bi ⊕ Bi+1 | Binary to Gray code | guide |
| ones' complement of x = (2ⁿ − 1) − x | Flipping every bit of an n-bit number | guide |
| D = (IN AND LOAD) OR (Q AND NOT LOAD) | A register bit with load enable | guide |
| fout = fclock ÷ 2 | Each flip-flop in a counter halves the frequency | guide |
| states = 2 × number of flip-flops | How many states a Johnson counter has | guide |
Microcontrollers
| Formula | What it gives | Learn it |
|---|---|---|
| duty = value ÷ 255 | The PWM duty cycle from analogWrite | guide |
| average = duty × VHIGH | A PWM pin's average voltage | guide |
| Iavg ≈ duty × Ion | The average current through a PWM load | guide |
| V ≈ reading × 5 V ÷ 1024 | Volts from an analogRead value | guide |
| out = (x − fromLow) × (toHigh − toLow) ÷ (fromHigh − fromLow) + toLow | What map() works out | guide |
| I = (5 − VLED) ÷ (R + 25 Ω) | LED current from a 5 V pin, with the pin's own resistance | guide |
| elapsed = now − start | Timing with millis() instead of delay() | guide |
Sensor signals
| Formula | What it gives | Learn it |
|---|---|---|
| filtered = filtered + α × (reading − filtered) | An exponential moving average | guide |
| falias = | f − n × fs | | The false frequency an undersampled signal shows | guide |
| fs > 2 × highest frequency | The Nyquist rule for a true capture | guide |
| error ∝ 1 ÷ √N | How averaging N readings shrinks the noise | guide |
| value = (reading − offset) ÷ gain | A two-point calibration | guide |
| cutoff ≈ alpha × sample rate ÷ 2π | The corner of a one-line filter in code | guide |
Control and PID
| Formula | What it gives | Learn it |
|---|---|---|
| error = setpoint − measurement | What a closed loop works on | guide |
| output = bias + Kp × error | A proportional (P) controller | guide |
| error = missing push ÷ Kp | The steady-state error that P control leaves | guide |
| integral = integral + error × Δt | The I term's running total | guide |
| output = Kp × error + Kd × (error − prev) ÷ Δt | A PD controller: the D term damps overshoot | guide |
| Kp = 0.6 Ku, Ki = 1.2 Ku ÷ Tu, Kd = 0.075 Ku × Tu | Ziegler-Nichols starting gains for PID | guide |
| phase lag = 360° × f × T | The lag a dead time T adds at frequency f | guide |
| angle = 0.98 × (angle + gyro × Δt) + 0.02 × accelAngle | A complementary filter for a tilt angle | guide |
Robots and motion
| Formula | What it gives | Learn it |
|---|---|---|
| distance = ticks × π × diameter ÷ ticks per turn | Distance from a wheel encoder | guide |
| radius = (track ÷ 2) × (L + R) ÷ (L − R) | The turn radius of a two-wheeled robot | guide |
| heading = heading + rate × dt | Heading from a gyro | guide |
| x = x + d × cos(heading), y = y + d × sin(heading) | Position by dead reckoning | guide |
| stopping distance = v² ÷ 2a | How far a robot needs to brake | guide |
Power and batteries
| Formula | What it gives | Learn it |
|---|---|---|
| runtime = mAh ÷ mA | Battery life, in hours | guide · calculator |
| Wh = Ah × V | A battery's stored energy | guide · calculator |
| efficiency = Pout ÷ Pin | How much power arrives where you want it | guide |
| P = VF × I | The power lost in a diode | guide |
| Pheat = (Vin − Vout) × I | The heat in a linear regulator | guide · calculator |
| Vout ≈ Vin × D | A buck converter's output | guide · calculator |
| Vout ≈ Vin ÷ (1 − D) | A boost converter's output | guide |
| ΔI = (Vin − Vout) × D ÷ (f × L) | A buck converter's ripple current | guide · calculator |
| ΔV ≈ ΔI ÷ (8 × f × C) | A buck converter's output ripple | guide · calculator |
| Vout ≈ Vpp − 2 × 0.7 V | A diode charge pump's output | guide |
Wires, PCBs and heat
| Formula | What it gives | Learn it |
|---|---|---|
| R = ρ × L ÷ A | A wire's resistance from its length and area | guide · calculator |
| Vdrop = I × R | The volts lost along a wire | guide · calculator |
| R = (length ÷ width) × 0.5 mΩ | A 1 oz copper trace's resistance, counted in squares | guide · calculator |
| I = k × ΔT0.44 × A0.725 | The IPC-2221 current a trace can carry | calculator |
| Imax = √(P ÷ R) | The current one via can carry | guide |
| ΔV = I × t ÷ C | How far a rail dips before the decoupling capacitor runs out | guide |
| R = √(L ÷ C) | The termination resistor that stops ringing | guide |
| ΔT = P × θ | Temperature rise through a thermal resistance | guide · calculator |
| Tj = Ta + P × (θJC + θCS + θSA) | A chip's junction temperature on a heatsink | guide · calculator |
Radio
| Formula | What it gives | Learn it |
|---|---|---|
| λ = c ÷ f = 300 ÷ f in MHz | Wavelength, in metres | guide · calculator |
| L ≈ 0.95 × λ ÷ 4 | A quarter-wave antenna, trimmed about 5% | guide · calculator |
| m = (max − min) ÷ (max + min) | AM modulation depth | guide |
| fc − fm and fc + fm | Where AM's sidebands sit | guide |
| sin a × sin b = ½ cos(a − b) − ½ cos(a + b) | Why a mixer gives the sum and difference | guide |
| 1 ÷ fcarrier ≪ R × C ≪ 1 ÷ faudio | The RC for an envelope detector | guide |
| Pmax = V² ÷ (4 × RS) when RL = RS | Maximum power transfer | guide |
| loss ≈ 20 log₁₀(d in km) + 20 log₁₀(f in MHz) + 32.4 dB | Free-space path loss in a link budget | guide |
Free lesson
Now build it yourself
Each lesson comes in three short parts: see the idea, try it on a live board, then build it yourself, with quick checks as you go.
Try it yourself: free lesson
“Ohm's law” is lesson 5 of 6 in Copper Flats, Electronics World 1. Free with an account. Lessons unlock in order, so you’ll do the 4 before it first.
Or start from the very first lesson, no account neededWork it out
The ideas behind it
- Ohm's law explainedV = I × R: set any two of voltage, current and resistance and the third follows.
- Electrical power explained: P = V × IP = V × I: how fast energy turns into heat, and why a resistor has a power rating.
- Kirchhoff's laws explained: KCL and KVLWhat flows into a junction flows out, and the drops round a loop add up to the rise.
- Voltage divider explainedTwo resistors that split a voltage: the formula, potentiometers, and why a load drags the output down.
Questions people ask
What are the most important electronics formulas?
Ohm's law, V = I × R, and power, P = V × I. Between them they size almost every resistor in a beginner circuit: the current it sets, and the watts it has to shed as heat. Most of the other formulas build on these two.
How do I remember the three forms of Ohm's law?
Learn V = I × R and rearrange it. Divide both sides by R to get I = V ÷ R, or by I to get R = V ÷ I. Work in volts, amps and ohms, or in volts, milliamps and kilohms, which give the same answer.
Why doesn't my circuit match the formula exactly?
Formulas assume ideal parts. Real resistors sit anywhere in their tolerance band, batteries sag under load, and diodes drop a little more or less than the round number. Expect a few percent of difference, and check with a multimeter.
More charts
- Standard resistor values chartThe E12, E24 and E96 series, decade by decade, and which one to reach for.
- SMD resistor code chartTurn 472, 4702, 4R7 or 01C on a tiny resistor into ohms.
- LED forward voltage by colourEach colour's forward voltage, and how many LEDs fit in series on 5 V, 9 V or 12 V.
- Electronics unit prefixes and conversionsp, n, µ, m, k, M and G, conversion tables, and what 4k7 or 2n2 means.
- Capacitor code chartTurn 104, 473J or 2A into a value, a tolerance and a voltage rating.
- Common diodes chart1N4148, 1N4007, 1N5819 and the 1N47xx Zeners compared, and which one to use.
- Common transistors chartRatings, gain and pinouts for the BJTs and MOSFETs in every parts kit.
- Logic gate truth tablesAll seven gates' truth tables, how to write each one, and the chip numbers to buy.
- Arduino Uno pins and limitsWhich Uno pin does what, and how much current each pin and the whole board can give.
- Binary, decimal and hex table0 to 15 in all three bases, the powers of two, common bytes, and converting four bits at a time.
- AWG wire gauge chartAWG and mm² side by side, ohms per metre, and roughly how many amps each size takes.
- Battery voltage and capacity chartFull, nominal and flat voltages, typical mAh, and how full a lithium cell is from its voltage.
- Electronics glossaryFrom AC to Zener diode: the words of electronics, each in a sentence or two.