Five calculators for the bench, each giving every derived value at once:
- Ohm's law: pick the two quantities you know among voltage, current, resistance and power, and get the other two.
- Resistors and LEDs: series and parallel totals of any list, an unloaded voltage divider (and the R2 for a wanted output), and the series resistor for one or more LEDs with the next standard value from the E6, E12, E24, E48 or E96 series, the real current, the power in the resistor and a suggested power rating.
- Colour code: read 4, 5 or 6 bands into a value, tolerance and temperature coefficient, or turn a value into its bands, with a drawing of the resistor.
- RC, LC and 555: RC time constant and filter cut-off, capacitive and inductive reactance, LC resonance, and 555 timer astable frequency and duty cycle or monostable pulse length.
- Wire and battery: AWG diameter, cross-section, copper resistance and voltage drop, and a battery life estimate for a duty-cycled load.
Values accept engineering notation: 4k7 or 4.7k for 4,700 Ω, 100n for 100 nF, 2.2µ, 1M. Results come back with the right prefix.
Ohm's law and power
V = I × R and P = V × I, so P = I²R = V²/R as well. 12 V across 220 Ω drives 54.5 mA and turns 0.65 W into heat, which is more than a common 1/4 W resistor can take. That is the most frequent use of the first tab: checking that a resistor will not overheat.
LED resistors, step by step
An LED needs its current limited, and the simplest way is a series resistor: R = (V_supply − n × V_forward) / I. For a red LED (about 2.0 V) on 5 V at 20 mA, R = 3 V / 0.02 A = 150 Ω, which is a standard value. On a 9 V battery at 15 mA the exact value is 466.7 Ω; the tool picks the next value up in the chosen series, 470 Ω, so the current is 14.9 mA rather than slightly too much. The resistor dissipates I²R = 0.10 W, so a 1/4 W part gives the usual 2× margin. Forward voltage varies between LEDs and with temperature; use the datasheet value, and avoid supplies only a few tenths of a volt above V_forward, where small variations swing the current a lot.
Colour codes and E series
Bands follow IEC 60062: black 0, brown 1, red 2, orange 3, yellow 4, green 5, blue 6, violet 7, grey 8, white 9; gold and silver multiply by 0.1 and 0.01 (pink by 0.001); gold is ±5 %, silver ±10 %, brown ±1 %, red ±2 %, and the 6th band gives the temperature coefficient (brown 100 ppm/K, red 50, and so on). Yellow, violet, red, gold is 47 × 100 = 4.7 kΩ ±5 %. A 4-band code holds two significant digits, so 47.5 kΩ (an E96 value) only exists as a 5-band code: yellow, violet, green, red, brown.
Standard values come from IEC 60063: E12 (10, 12, 15, 18, 22, 27, 33, 39, 47, 56, 68, 82) for ±10 % parts, E24 for ±5 %, E96 for ±1 %. Each value is about one tolerance step from the next, so any resistance is within reach of one standard part.
Timing, wires and batteries
An RC network reaches 63.2 % of its final voltage after one time constant τ = RC and 99.3 % after 5τ; as a first-order filter its −3 dB cut-off is 1/(2πRC). The 555 astable high time is ln 2 × (R1 + R2) × C and its low time ln 2 × R2 × C: with 1 kΩ, 10 kΩ and 10 µF that is 6.87 Hz at a 52.4 % duty cycle. The monostable pulse is ln 3 × R × C, about 1.1 RC.
Wire sizes use the AWG definition d = 0.127 mm × 92^((36 − n)/39) and annealed copper's resistivity. The current column is a guide only, computed from 3 to 10 A per mm²; real limits depend on insulation, bundling and temperature, and building wiring must follow the local code. Battery life divides the usable capacity by the average current; a sensor drawing 50 mA for 1 % of the time and 50 µA otherwise averages 0.55 mA. For a worked LED example read Ohm's law and LED resistors step by step; the scientific calculator handles anything else.
