Enter any two of voltage, current, resistance or power and the calculator returns the other two, along with conductance and energy consumed per hour. Enter three or four and it cross-checks them against each other. Series and parallel resistor networks can be solved at the same time.
| Known | Voltage V | Current I | Resistance R | Power P |
|---|---|---|---|---|
| V and I | — | — | V / I | V · I |
| V and R | — | V / R | — | V² / R |
| V and P | — | P / V | V² / P | — |
| I and R | I · R | — | — | I² · R |
| I and P | P / I | — | P / I² | — |
| R and P | √(P · R) | √(P / R) | — | — |
| Symbol | Quantity | SI unit | Unit symbol |
|---|---|---|---|
| V | Voltage, potential difference | volt | V |
| I | Current | ampere | A |
| R | Resistance | ohm | Ω |
| P | Power | watt | W |
| G | Conductance | siemens | S |
| E | Energy per hour | kilowatt-hour | kWh |
A single-phase 230 V supply feeds a purely resistive load drawing 10 A. Two separate resistor groups of 10 Ω, 22 Ω and 47 Ω are also evaluated, once wired in series and once in parallel.
| Input | Unit | Accepted range | Required |
|---|---|---|---|
| Voltage V | V | ≥ 0 | Any two of the four |
| Current I | A | ≥ 0 | Any two of the four |
| Resistance R | Ω | ≥ 0 | Any two of the four |
| Power P | W | ≥ 0 | Any two of the four |
| Series resistors | Ω | Comma separated, each ≥ 0 | Optional |
| Parallel resistors | Ω | Comma separated, each ≥ 0 | Optional |
| Circuit | Voltage | Current | Resistance | Power |
|---|---|---|---|---|
| LED with series resistor | 5 V | 0.02 A | 250 Ω | 0.1 W |
| USB charger output | 5 V | 2 A | 2.5 Ω | 10 W |
| Car headlamp | 12 V | 4.58 A | 2.62 Ω | 55 W |
| Domestic light bulb | 230 V | 0.26 A | 882 Ω | 60 W |
| Electric kettle | 230 V | 9.13 A | 25.2 Ω | 2100 W |
| 13 A ring final circuit | 230 V | 13 A | 17.7 Ω | 2990 W |
| Immersion heater | 230 V | 13 A | 17.7 Ω | 3000 W |
Ohm's law states that the current through a conductor between two points is directly proportional to the voltage across those points, written as V = I × R. Georg Ohm published it in 1827. The constant of proportionality is resistance, measured in ohms. The law holds for ohmic materials such as metals at constant temperature. It does not hold for semiconductors, diodes, filament lamps or electrolytes, whose resistance changes with voltage, current or temperature.
Power equals voltage multiplied by current, P = V × I, giving watts when volts are multiplied by amperes. Substituting Ohm's law gives two more forms: P = I² × R when you know current and resistance, and P = V² / R when you know voltage and resistance. All three give the same answer for a purely resistive DC circuit. For AC circuits with reactance you must also account for power factor.
Resistors in series add directly: Rtotal = R₁ + R₂ + R₃ and so on, so the total is always larger than the largest individual resistor. Resistors in parallel add as reciprocals: 1/Rtotal = 1/R₁ + 1/R₂ and so on, so the total is always smaller than the smallest individual resistor. For two resistors in parallel the shortcut is the product over the sum. A single zero-ohm path in parallel short-circuits the network and the total becomes zero.
Voltage, current, resistance and power form a system with two degrees of freedom, so any two known quantities determine the other two. One value alone leaves the circuit underdetermined. If you enter three or four values the calculator cross-checks them against each other within a two percent tolerance and reports which relationship fails, because an inconsistent set usually means a measurement or unit error rather than a real circuit.
Conductance is the reciprocal of resistance, G = 1 / R, measured in siemens and formerly in mhos. It expresses how readily a circuit passes current rather than how strongly it opposes it. Conductance is convenient for parallel networks because conductances add directly, in the same way resistances add in series. A zero resistance gives infinite conductance, so the calculator reports conductance only when resistance is greater than zero.
Results are for estimation and preliminary design. Ohm's law applies to ohmic conductors at constant temperature; verify against measured values and a qualified engineer before relying on them.
multicalci.com — free engineering calculators