Reference
Volts, amps, ohms, watts — the four quantities that govern every circuit you'll ever build. This page collects the formulas, calculators, component charts, and design rules of thumb that turn those four quantities into working hardware, in one searchable cheat sheet.
This reference is for educational and hobbyist purposes only. Working with electricity carries real risks — shock, burns, fire, and damage to equipment. Mains voltage (110 V / 230 V AC) and stored energy in capacitors and inductors can be lethal even after a circuit is unpowered. Always verify component ratings, follow local electrical codes, and consult a qualified electrician for anything connected to mains. The site owner is not liable for any injury, damage, or loss arising from the use of this reference.
How to use: jump to a section from the quick-reference wheel, plug numbers into the interactive calculators, or scroll the component charts and reference tables for at-a-glance values. Every formula links back to the underlying law so you can derive the rest yourself.
Click any term to see a beginner-friendly explanation. Cross-references inside an explanation open in a stacked modal — Escape closes them one at a time.
Type any two of the four quantities — voltage V, current I, resistance R, or power P — and the wheel solves for the rest in real time. Click a quadrant to jump to its input, or load an example to see the math in action.
Quantity Magnitudes · V · I · R · P (log₁₀)
The algebra behind every circuit on this page. Click Try it on any card to load that formula’s example into the Quick Wheel above.
The foundational DC relationship — voltage, current, and resistance lock each other in. Every other formula on this page builds on it.
Example A 9 V battery across 100 Ω drives 90 mA through the wire.
How fast a circuit converts electrical energy into heat, light, or motion. One watt is one joule per second.
Example A USB port at 5 V supplying 2 A delivers 10 W — enough to warm a small heater.
Charge can’t accumulate at a node, so all the current entering must leave it. The accounting trick that lets you solve any branched circuit.
Example A node fed by 100 mA from one branch and 50 mA from another has 150 mA flowing out the third leg.
Walk a closed loop and the voltage rises must equal the voltage drops. Pick a direction, sum the signs — the loop closes back on itself.
Example In a 9 V battery + 6 Ω + 3 Ω series loop, the resistors drop 6 V and 3 V respectively, summing to the 9 V supply.
Resistors in series share the same current; their resistances add. Voltages divide proportionally to each resistance.
Example 100 Ω + 200 Ω in series with a 12 V supply equals 300 Ω total → 40 mA through the chain.
Resistors in parallel share the same voltage; reciprocals add. Currents split inversely with each resistance — the smaller resistor carries more.
Example 100 Ω ‖ 200 Ω = 66.7 Ω. At 5 V the parallel pair draws 75 mA total.
Series caps store the same charge but split the voltage; their reciprocals add. Useful for raising the working voltage when you only have low-V parts.
Example Two 100 µF caps in series ≈ 50 µF. Charging through 10 kΩ from 12 V draws 1.2 mA at t=0.
Parallel caps share the voltage and accumulate capacitance — the canonical decoupling stack on every PCB power rail.
Example 10 µF + 100 nF + 1 nF in parallel covers low- to high-frequency noise on a single 5 V supply.
Pavg = Vrms · Irms · cos φ.
The cos φ term is the power factor — reactive loads
(motors, transformers, LED drivers) need it explicitly.
Plug in any two values and the rest follow. The first calculator is a deeper dive on Ohm’s law — with sliders, V–I curves, and a power-vs-resistance plot — so you can see why the numbers move, not just what they are. More calculators (LED current-limiting, voltage divider, RC time constant…) land in later batches.
Enter or drag any two of V, I, R, or P and the rest are computed live. The chart on the left plots your operating point against a family of resistance lines; the chart on the right shows how power scales with resistance at the current voltage.
V–I Characteristic Curves
Power vs Resistance
Pick a supply voltage, an LED color, and the desired forward current. The calculator returns the series resistor you need, snapped to the nearest standard E-series value, and shows the operating point on the LED’s I–V curve.
LED I–V Curve · operating point · power shading
Two resistors in series across a supply pull a fraction of the input voltage out at their midpoint. Set Vin, R1, and R2 to see the unloaded Vout; add an optional load to see how the output sags under real-world current draw.
Vout vs R2 · load overlay when Rload > 0
Combine two or more resistors or capacitors and read the equivalent value. Resistors and capacitors follow opposite rules: resistors add in series and reciprocate in parallel; capacitors do the reverse.
Individual values vs equivalent total
A resistor charging a capacitor follows V(t)=V·(1−e−t/τ), where τ = R·C. After 5τ the cap is essentially full (99.3 %). Drag the sliders, hit Play, and watch the curve fill in.
V(t) · markers at τ (63.2 %) and 5τ (99.3 %)
Real-world battery math: charge time, runtime, capacity from a discharge test, and a voltage → SOC estimator. Linear approximation (skips the CC/CV taper above ~80 %); use the efficiency knob to fold in switching / heat losses.
Discharge a charged cell at a known constant load and time how long it
lasts to its cutoff voltage. capacity_mAh = current_mA × time_h
gives the actual usable capacity at that current — measured capacity falls at
higher discharge currents (Peukert effect).
Estimate state of charge from a per-cell voltage reading. Accuracy depends on chemistry — Li-ion's flat middle-of-curve gives ±10 % under no load; lead-acid is ±5 %. For multi-cell packs, divide pack voltage by cell count first.
A hands-on bench: pick colors on a live resistor preview, scan an E-series value cloud sized by popularity, and toggle the tolerance chart on demand. Every panel stays in sync with the dark/light theme and feeds the Quick Wheel above when you find a value worth playing with.
Pick the color of each band — the value, tolerance, and tolerance bar update live. The mini-chart below compares this nominal value across every common tolerance grade so you can see how much tighter each step gets.
Manufacturers don’t make every possible resistor — they ship preferred values from the IEC 60063 E-series. Each step doubles the previous: E6 for ±20% parts, E12 for ±10%, E24 for ±5%, E96 for ±1%. Type a target value to find the closest preferred match in the active series.
No values match your filter.
Decoupling, pull-ups vs. pull-downs, choosing the right transistor, protecting inputs — the practical rules of thumb that aren’t in a textbook. Filter by tier, or search for a specific topic.
Place a 100 nF ceramic + 10 µF bulk
capacitor as close as possible to every IC’s power pin. The
100 nF handles fast transients; the 10 µF holds the rail
steady during current spikes. Skipping decoupling is the #1 cause
of mysterious “random” bugs that vanish when you press a
finger on the board.
Example An ATmega328P needs decoupling within 10 mm of VCC; otherwise EMI couples into the ADC and you’ll see noisy readings.
Floating MCU inputs read random values — you must define a
default. Pull-up: input idles high, switch pulls
it low. Pull-down: input idles low, switch pulls
it high. Use 10 kΩ for general logic,
4.7 kΩ for I²C / 1-Wire (datasheet-specified),
100 kΩ when you need ultra-low quiescent current.
Example AVR / ESP32 / RP2040 all expose internal pull-ups (~30–50 kΩ). Toggle them in software instead of soldering external resistors when the value isn’t critical.
Some ICs (FPGAs, DDR memory, mixed-signal chips) require core / IO rails to come up in a specific order — typically core before IO. Wrong order can latch up the chip permanently. Read the Power Sequencing section of every datasheet before you design the supply rails.
Example Xilinx 7-series FPGAs require VCCINT before VCCAUX before VCCO. Violating that order is silent until you ship 100 units that all fail in the field.
Anything connected to a connector or human-touchable surface
(USB, audio jacks, switches, buttons) needs ESD protection. A
25 kV finger-zap into a bare GPIO will kill the IC every
time. Use TVS diodes (e.g. PESD5V0S2UT,
USBLC6-2SC6) inline with each exposed signal —
5 V / 8 V / 12 V variants per logic level.
Example USB ports without ESD diodes blow MCUs the first time someone shuffles across carpet and plugs in a cable.
BJTs (2N3904, BC547) are
current-controlled — drive the base with a few mA via
a series resistor. MOSFETs (IRLZ44N, AO3401)
are voltage-controlled — drive the gate above
VGS(th). For switching loads above ~500 mA, prefer
MOSFETs: lower RDS(on) means less heat. For analog gain
stages, BJTs still rule.
Example Switching a 12 V relay at 50 mA:
a 2N7000 logic-level MOSFET works at a 3.3 V gate.
A 2N3904 BJT needs ~1 mA base current via a
1 kΩ resistor.
If your circuit might be plugged in backwards (battery clips, screw terminals, barrel jacks), add reverse protection or risk magic smoke. Schottky in series: simple, ~0.3 V drop, fine for low-current loads. P-channel MOSFET (gate to ground via a Zener): near-zero drop, perfect for battery-powered designs.
Example A barrel-jack 12 V supply reversed
across an LM7805 instantly cooks the regulator unless you have a
1N5819 or P-FET in the path.
Mechanical contacts bounce 5–20 ms when toggled,
generating dozens of false edges per press. Two clean fixes:
RC filter — 10 kΩ + 100 nF
gives a ~1 ms time constant, smooth in hardware.
Software debounce — track the last edge
time, ignore changes within 20 ms. SPDT switches with a
cross-coupled NAND latch produce a perfect bounce-free signal.
Example An Arduino “count button presses” sketch without debouncing will register 5–15 counts for one physical press.
Power dissipated in a part raises its junction temperature:
TJ = TA + (P × θJA).
For a TO-220 package, θJA ≈ 50 °C/W
without a heatsink. Drop 2 W into one and the
junction hits 100 °C above ambient — over TJ(max)=150 °C
if your room is over 50 °C. Use heatsinks, copper pours, or
larger packages above ~1 W.
Example An LM317 dropping 5 V
at 1 A dissipates 5 W. Without a heatsink it would hit
250 °C above ambient — instant smoke. Add a TO-220
heatsink (θHS≈10 °C/W) and it stabilises at
50–60 °C above ambient.
PCB traces aren’t superconductors. IPC-2221 rule of thumb
(1 oz copper, 10 °C rise): 1 A → 10 mil,
3 A → 30 mil,
5 A → 60 mil,
10 A → 200 mil. For internal layers, double
the width. KiCad’s Calculator Tools has IPC-2221 built
in.
Example Routing a 5 A motor supply on a 10 mil trace: temperature-rise calc says 60 °C — trace warms enough to melt solder mask near connectors.
GPIOs typically tolerate VCC + 0.3 V
max. Connecting them to higher-voltage signals or noisy
real-world inputs (sensors, motor encoders, automotive busses)
requires clamping. Standard recipe: 1 kΩ series
resistor + Schottky diodes to VCC and GND. The diodes
shunt over- and under-shoots; the resistor limits current
through them to safe values (typically ≤ 1 mA into
the ESD structure).
Example Reading a 12 V automotive signal directly into a 3.3 V GPIO blows the input the first time the alternator spikes to 18 V.
Each digital interface has its own gotchas. I²C is
open-drain — both SDA and SCL must have pull-ups (typically
2.2 kΩ–10 kΩ; smaller for fast-mode
+ long buses, larger for low-power); without them the bus floats
and reads garbage. SPI is push-pull, so no
pull-ups, but keep CLK runs short (< 15 cm at
4 MHz+) and route MISO/MOSI as a balanced pair; for noisy
environments add a 22 Ω series resistor near the
driver to round the edges. UART tolerates long
wires but breaks if the two endpoints don’t share a common
ground; a return-current path through chassis or USB shield
counts.
Example An I²C bus that works on the bench but
flakes once you add a third sensor needs the pull-ups dropped
from 10 kΩ to 4.7 kΩ — the
extra device capacitance has slowed the rise time below spec.
Pick a linear regulator (LDO) when the input
voltage is only a little above the output, the load current is
modest (< 500 mA), and you need clean low-noise rails
(analog, RF, audio). Efficiency is just
Vout / Vin — drop 12 V to
3.3 V at 1 A and you dissipate 8.7 W as heat. Pick a
switching regulator (buck for step-down, boost for
step-up) when the conversion ratio is large, current is high, or
battery life matters; expect 85–95 % efficiency but more
switching-noise hygiene (input/output caps, layout, inductor
choice).
Example A 5 V → 3.3 V rail at 100 mA is fine on an LDO (170 mW dissipated). A 12 V → 3.3 V rail at 500 mA on the same LDO would dissipate 4.35 W — switch to a buck converter.
When current through any inductor (relay coil, solenoid, motor,
transformer) is suddenly interrupted, the collapsing magnetic
field generates a high-voltage spike of opposite polarity
to the supply — easily hundreds of volts from a 12 V coil.
That spike will instantly destroy the switching transistor or MCU
pin that turned the load off. The fix is a flyback diode (e.g.
1N4148 for small coils, 1N4007 for
relays) reverse-biased across the inductor — anode to the
load’s low side, cathode to the supply rail. For PWM motor
drive add an RC snubber across the switch as well.
Example Driving a 12 V automotive relay coil from an MCU through a 2N7000 MOSFET requires a diode across the coil; without it the MOSFET fails on the first switch-off and takes the GPIO with it.
An LDO needs a minimum
Vin − Vout headroom (the
“dropout” spec) to regulate; below that, the output
just follows the input minus the dropout. Classic 7805 needs
~2 V; modern LDOs (e.g. AMS1117 ~1.1 V, MCP1700
~178 mV at 250 mA) are far better for battery use.
Watch quiescent current (Iq) for always-on
battery designs — an LDO drawing 5 mA Iq drains a coin cell
dead in days, while a low-Iq part (1 µA Iq) lasts years.
Always-confirm output capacitor type; many low-quiescent LDOs
specifically require a low-ESR ceramic cap to stay stable.
Example Powering an MCU sleeping at 5 µA from a 7805 (Iq = 5 mA) means the regulator wastes 1000× more current than the load. Replace with a low-Iq LDO (e.g. TPS7A02) and battery life jumps from days to years.
A crystal’s rated frequency is only achieved at its
specified load capacitance (CL,
typically 8–22 pF). The MCU oscillator pins see two caps to
ground (C1, C2) plus stray board
capacitance (Cstray, ~3–5 pF for a clean
two-layer board). Standard formula:
CL = (C1·C2) / (C1+C2) + Cstray.
Pick C1 = C2 = 2·(CL − Cstray)
as a starting point. Wrong CL shifts the actual
frequency tens of ppm — fine for blinking an LED, fatal for
precision timing or radio.
Example A 16 MHz crystal spec’d for CL = 18 pF on a board with Cstray ≈ 3 pF needs C1 = C2 = 2 × (18 − 3) = 30 pF. Using the wrong 22 pF caps from another design pulls the frequency off by ~30 ppm and your USB serial drifts.
No design guides match your filter.
SI prefixes, resistor and capacitor markings, wire-gauge ratings, logic thresholds, and battery-cell voltages — the lookup tables that round out the cheat sheet. Switch tables with the tabs, or filter rows live with the search box.
| Prefix | Symbol | Factor | Hobby example |
|---|---|---|---|
| yotta | Y | 1024 | (astrophysics scale) |
| zetta | Z | 1021 | — |
| exa | E | 1018 | — |
| peta | P | 1015 | — |
| tera | T | 1012 | 1 TΩ insulation resistance |
| giga | G | 109 | 5 GHz Wi-Fi, 1 GHz scope |
| mega | M | 106 | 16 MHz crystal, 10 MΩ multimeter input |
| kilo | k | 103 | 1 kΩ pull-up, 1 kV insulation tester |
| (none) | — | 100 | 1 V, 1 A, 1 Ω — the base units |
| milli | m | 10−3 | 1 mA LED current, 100 mV ripple |
| micro | µ | 10−6 | 100 µF bulk cap, 10 µA leakage |
| nano | n | 10−9 | 100 nF decoupling, ns timing |
| pico | p | 10−12 | 22 pF crystal load cap |
| femto | f | 10−15 | fs laser pulses |
| atto | a | 10−18 | — |
| zepto | z | 10−21 | — |
| yocto | y | 10−24 | — |
| Color | Digit | Multiplier | Tolerance |
|---|---|---|---|
| Black | 0 | ×1 | — |
| Brown | 1 | ×10 | ±1% |
| Red | 2 | ×100 | ±2% |
| Orange | 3 | ×1k | — |
| Yellow | 4 | ×10k | — |
| Green | 5 | ×100k | ±0.5% |
| Blue | 6 | ×1M | ±0.25% |
| Violet | 7 | ×10M | ±0.1% |
| Gray | 8 | — | ±0.05% |
| White | 9 | — | — |
| Gold | — | ×0.1 | ±5% |
| Silver | — | ×0.01 | ±10% |
| Code | Picofarads | Conventional | Common use |
|---|---|---|---|
| 100 | 10 pF | 10 pF | RF tuning, crystal load |
| 220 | 22 pF | 22 pF | Crystal load cap |
| 471 | 470 pF | 470 pF | RF coupling |
| 102 | 1,000 pF | 1 nF | EMI filter |
| 222 | 2,200 pF | 2.2 nF | Audio coupling |
| 472 | 4,700 pF | 4.7 nF | Snubber, audio |
| 103 | 10,000 pF | 10 nF | Local bypass |
| 223 | 22,000 pF | 22 nF | Audio |
| 473 | 47,000 pF | 47 nF | Mid-frequency bypass |
| 104 | 100,000 pF | 100 nF (0.1 µF) | Decoupling — the workhorse |
| 224 | 220,000 pF | 220 nF (0.22 µF) | Decoupling, audio |
| 474 | 470,000 pF | 470 nF (0.47 µF) | Bulk decoupling |
| 105 | 1,000,000 pF | 1 µF | Bulk decoupling, audio |
| 106 | 10,000,000 pF | 10 µF | Bulk filtering, MLCC |
| AWG | Diameter | Cross-section | Resistance | Max current | Common use |
|---|---|---|---|---|---|
| 30 | 0.255 mm | 0.0507 mm² | 339 mΩ/m | ~0.86 A | Wire-wrap, fine signal |
| 26 | 0.405 mm | 0.129 mm² | 134 mΩ/m | ~2.2 A | Ribbon cable, sensor leads |
| 24 | 0.511 mm | 0.205 mm² | 84.2 mΩ/m | ~3.5 A | USB power, hookup wire |
| 22 | 0.644 mm | 0.326 mm² | 53.0 mΩ/m | ~7 A | General hobby, breadboard |
| 20 | 0.812 mm | 0.518 mm² | 33.3 mΩ/m | ~11 A | Speaker wire, low-power motors |
| 18 | 1.024 mm | 0.823 mm² | 21.0 mΩ/m | ~16 A | Power leads, DC supplies |
| 16 | 1.291 mm | 1.31 mm² | 13.2 mΩ/m | ~22 A | Small battery cables |
| 14 | 1.628 mm | 2.08 mm² | 8.28 mΩ/m | ~32 A | Mains household wiring (1.5–2.5 mm² typical EU) |
| 12 | 2.053 mm | 3.31 mm² | 5.21 mΩ/m | ~41 A | High-current power |
| 10 | 2.588 mm | 5.26 mm² | 3.28 mΩ/m | ~55 A | Battery banks, EVs (4–6 mm² typical EU) |
| 8 | 3.264 mm | 8.37 mm² | 2.06 mΩ/m | ~73 A | Inverter feeds, 50 A circuits |
| Family | VCC | VIL,max | VIH,min | VOL,max | VOH,min | Notes |
|---|---|---|---|---|---|---|
| 5 V TTL (74xx, 74LSxx) | 5.0 V | 0.8 V | 2.0 V | 0.4 V | 2.4 V | Tolerates 5 V inputs into 5 V chips |
| 5 V CMOS (74HCxx) | 5.0 V | 1.5 V | 3.5 V | 0.05 V | 4.95 V | Higher noise margin than TTL |
| 3.3 V LVTTL | 3.3 V | 0.8 V | 2.0 V | 0.4 V | 2.4 V | Compatible with 5 V TTL inputs |
| 3.3 V CMOS (74LVCxx) | 3.3 V | 0.99 V | 2.31 V | 0.1 V | 3.2 V | Common on Arduino, ESP32, RPi |
| 1.8 V CMOS | 1.8 V | 0.54 V | 1.26 V | 0.1 V | 1.7 V | Modern SoCs, FPGAs core IO |
| RS-232 | ±5 to ±15 V | +3 V | −3 V | +5 V | −5 V | Inverted; mark/space at ±voltages |
| Cell type | Nominal | Fully charged | Discharged (cutoff) | Typical capacity | Rechargeable | Notes |
|---|---|---|---|---|---|---|
| Alkaline AA | 1.5 V | 1.6 V | 0.9 V | ~2500 mAh | No | High internal resistance; sags hard at high current |
| Alkaline AAA | 1.5 V | 1.6 V | 0.9 V | ~1200 mAh | No | Same chemistry as AA, smaller cell |
| NiMH AA | 1.2 V | 1.4 V | 1.0 V | 2000–2500 mAh | Yes | Low-self-discharge (LSD) variants hold charge for years |
| NiMH AAA | 1.2 V | 1.4 V | 1.0 V | 800–1000 mAh | Yes | Same chemistry as NiMH AA |
| Lead-acid (per cell) | 2.0 V | 2.1 V | 1.75 V | 7 Ah – 200 Ah | Yes | 6 cells = 12 V SLA / car battery |
| LiFePO4 (18650) | 3.2 V | 3.65 V | 2.5 V | ~1500 mAh | Yes | Safer Li chemistry; flat discharge curve; long cycle life |
| Li-ion (LiCoO2, 18650) | 3.7 V | 4.2 V | 3.0 V | 2500–3500 mAh | Yes | Phones, laptops, e-bikes; needs BMS |
| Li-Po (pouch) | 3.7 V | 4.2 V | 3.0 V | 100–10000 mAh | Yes | Drones, RC; identical chemistry to Li-ion in pouch form |
| CR2032 coin | 3.0 V | 3.3 V | 2.0 V | 220–240 mAh | No | RTC backup, remote controls, key fobs |
| 9 V (PP3, alkaline) | 9.0 V | 9.6 V | 5.4 V | ~600 mAh | No | Six 1.5 V cells in series internally |
| Color | VF typical | VF range | IF typical | Wavelength | Notes |
|---|---|---|---|---|---|
| Infrared (IR) | 1.4 V | 1.2 – 1.6 V | 20 – 100 mA | 850 – 940 nm | Remote controls, IR proximity sensors |
| Red | 2.0 V | 1.8 – 2.2 V | 10 – 20 mA | 620 – 660 nm | Indicator LEDs, classic 5 mm |
| Orange | 2.1 V | 2.0 – 2.2 V | 10 – 20 mA | 600 – 620 nm | Status indicators |
| Yellow / Amber | 2.1 V | 2.0 – 2.3 V | 10 – 20 mA | 580 – 600 nm | Indicator, automotive |
| Green (standard) | 2.2 V | 2.0 – 2.4 V | 10 – 20 mA | 555 – 570 nm | Older AlGaInP green |
| Green (pure / high-brightness) | 3.2 V | 3.0 – 3.5 V | 10 – 20 mA | ~525 nm | InGaN green; brighter, higher VF |
| Blue | 3.2 V | 3.0 – 3.5 V | 10 – 20 mA | 460 – 475 nm | Backlights, accents |
| White | 3.4 V | 3.0 – 3.6 V | 10 – 20 mA | broadband | Blue die + yellow phosphor — drives like a blue LED |
| Ultraviolet (UV) | 3.5 V | 3.2 – 4.0 V | 20 mA | 380 – 410 nm | Blacklight, curing, counterfeit detection |
| RGB (per channel) | — | see R / G / B above | 10 – 20 mA / ch | per channel | Three independent dies; each needs its own resistor |
| Imperial | Metric | L × W | Power (R) | Hand-solder | Notes |
|---|---|---|---|---|---|
| 0201 | 0603 | 0.6 × 0.3 mm | ⅒ W (50 mW) | Very hard | Phone-grade density; needs microscope + paste |
| 0402 | 1005 | 1.0 × 0.5 mm | ⅒ W (62 mW) | Hard | Common on dense hobby boards; tweezers + flux + practice |
| 0603 | 1608 | 1.6 × 0.8 mm | ⅒ W (100 mW) | Medium | Sweet spot for hobby SMD; visible without magnification |
| 0805 | 2012 | 2.0 × 1.25 mm | ⅛ W (125 mW) | Easy | Beginner-friendly SMD entry size |
| 1206 | 3216 | 3.2 × 1.6 mm | ¼ W (250 mW) | Easy | Common for higher-power resistors and bulk caps |
| 1210 | 3225 | 3.2 × 2.5 mm | ½ W (500 mW) | Easy | Wider variant of 1206; bulk MLCCs (10 µF+) |
| 2010 | 5025 | 5.0 × 2.5 mm | ¾ W (750 mW) | Very easy | Power resistors, current-sense |
| 2512 | 6432 | 6.4 × 3.2 mm | 1 W | Very easy | Power resistors; high-current sense |
No rows match your filter.