Ohm's Law Calculator
Calculate electrical resistance from voltage and current using Ohm's Law: R = V / I. Use it for circuit analysis, troubleshooting electronic circuits, or sizing resistors and conductors in DC and AC (resistive) systems.
Last updated: May 2026
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About this calculator
Ohm's Law states that the current through a conductor between two points is directly proportional to the voltage across them, with resistance as the proportionality constant: V = I × R, or equivalently R = V / I and I = V / R. Variables: Voltage (V) is electrical potential difference in volts; Current (I) is the flow of charge in amperes (amps, A); Resistance (R) is in ohms (Ω). Edge cases: zero current with non-zero voltage gives infinite resistance (an open circuit); zero voltage with non-zero current is impossible in a purely resistive element (could occur transiently with stored energy in inductors or capacitors). Ohm's Law applies to PURELY RESISTIVE elements — resistors, heating elements, incandescent bulbs at steady-state, and most metal conductors. It does NOT apply directly to capacitors and inductors (which require differential equations involving dV/dt and dI/dt), nor to semiconductor devices (diodes, transistors) which have non-linear V-I curves where R is voltage-dependent. For AC circuits, replace resistance with impedance (Z), which combines resistance and reactance: V = I × Z. The companion power formula P = V × I = I² × R = V²/R is essential for sizing components — a 100Ω resistor carrying 1A dissipates 100W of heat, far beyond a typical 1/4W resistor's rating. The combination V = IR + P = VI is the foundation of every electrical circuit calculation from simple LED dropping resistors to high-voltage transmission line analysis.
How to use
Example 1 — LED current-limiting resistor. A 5V supply driving an LED that drops 2.1V and needs 20mA (0.02A) of current requires a series resistor with the remaining 2.9V dropped across it. Voltage across resistor = 5.0 − 2.1 = 2.9V. Current = 0.020A. Step 1: R = 2.9 / 0.020 = 145Ω. Use the next standard value: 150Ω. Verify ✓. Power dissipated in resistor = V × I = 2.9 × 0.020 = 0.058W = 58mW — a standard 1/4W (250mW) resistor handles this with plenty of margin. Example 2 — Wire sizing for a heater. A 240V resistive heater draws 12.5A. Step 1: R = 240 / 12.5 = 19.2Ω. The heating element has 19.2Ω resistance. Verify ✓. Power = V × I = 240 × 12.5 = 3,000W = 3kW. The supply wiring must be sized for 12.5A continuous; in the US that requires 14 AWG copper minimum (15A circuit, but for continuous loads NEC requires 80% derating, so 14 AWG handles 12A continuous — 12 AWG is the safer choice for sustained operation at 12.5A).
Frequently asked questions
What is the difference between AC and DC for Ohm's Law?
For purely resistive loads, Ohm's Law applies identically to both AC and DC — the resistance value is the same in both cases. The complication in AC circuits is that capacitive and inductive elements have impedance that varies with frequency: capacitor impedance is 1/(2πfC) and inductor impedance is 2πfL. These reactive impedances combine with resistance to form total impedance Z = √(R² + X²) for a series circuit, and current and voltage are out of phase. For most practical AC applications involving heaters, incandescent lights, and resistive elements, treating it as pure resistance gives accurate results. For motors, transformers, and electronic equipment with reactive components, you need to calculate real power (W), apparent power (VA), and reactive power (VAR) separately. Power factor (cosφ) relates these: a power factor of 0.8 means 80% of the volt-amps drawn is real (useful) power and 20% is reactive. Utilities charge industrial customers based on apparent power and often penalize low power factor.
How does resistance change with temperature?
Almost all materials change resistance with temperature, governed by the temperature coefficient (α). For metals (copper, aluminum, tungsten), resistance INCREASES with temperature at roughly 0.4% per °C — a copper wire at 100°C has about 40% higher resistance than at 0°C. This matters for power lines (resistance increases as they heat up, increasing losses), light bulbs (filament resistance increases dramatically when lit), and high-current circuits. For carbon and most semiconductors, resistance DECREASES with temperature. For specialized alloys like manganin and constantan, the temperature coefficient is nearly zero — these are used in precision resistors that must hold their value across temperature. The general formula is R(T) = R₀(1 + α(T - T₀)), where R₀ is resistance at reference temperature T₀. For an LED's current-limiting resistor, this temperature dependence usually does not matter; for power resistors at high temperature, you may need to oversize because resistance drift changes the actual current.
What are the most common mistakes when applying Ohm's Law?
The biggest is applying it to non-ohmic devices — diodes, transistors, and most semiconductor junctions have nonlinear V-I curves where 'resistance' is not constant and Ohm's Law doesn't give a meaningful single resistance value. The second is confusing voltage drop across an element with the supply voltage; in a series circuit, Ohm's Law applies to each element using THAT element's voltage drop, not the total supply. The third is forgetting to add resistor power-dissipation calculations: a 100Ω resistor at 12V dissipates 1.44W (V²/R) — a standard 1/4W resistor would burn out. Always check P = V²/R or I²R against the resistor's wattage rating. The fourth is mixing up amps and milliamps in low-current circuits — 20mA is 0.020A, not 20A; many beginners crash circuits this way. The fifth is treating wire resistance as zero — long runs (50m+) of small-gauge wire at high current have meaningful resistance that drops voltage and dissipates power, requiring proper voltage-drop calculations.
When should I NOT use Ohm's Law?
Skip Ohm's Law for non-linear devices: diodes (use the diode equation I = Is(e^(V/nVT) − 1)), transistors (use the transistor model — Ebers-Moll, hybrid-π, etc.), LEDs (treat as constant-voltage drop with current set by external resistor), and varistors. Avoid it for capacitors and inductors in transient analysis — these store energy and require differential equations or Laplace-domain analysis (i = C·dV/dt, V = L·dI/dt). Do not use Ohm's Law in AC analysis without converting to impedance and accounting for phase relationships. Skip it for high-frequency RF circuits where skin effect changes effective resistance and stray capacitance/inductance dominates. Do not use it for plasma discharges, gas discharge lamps, electrochemical cells, or thermistors operating in their non-linear range. Finally, do not apply Ohm's Law to extremely high voltages or currents where field effects (corona discharge, electromigration, fusing) dominate beyond simple resistive behaviour.
How are voltage, current, resistance, and power all related?
The power triangle: P = V × I (universal), combined with Ohm's Law V = I × R gives P = I² × R and P = V² / R. These three forms (P=VI, P=I²R, P=V²/R) are interchangeable but used differently in practice. P = V × I is best when you know both V and I directly (motor nameplate ratings, power supply specs). P = I² × R is best for transmission losses where current flows through known wire resistance — doubling current quadruples loss, which is why power transmission uses very high voltage (low current) to minimize line losses. P = V² / R is best for heating elements where you know supply voltage and element resistance — doubling voltage quadruples power output, which is why a 240V appliance produces 4× the heat of a 120V version with the same element resistance. Memorize all four (V=IR, P=VI, P=I²R, P=V²/R) and you can solve any single-element resistive circuit instantly.