Solve for voltage, current, resistance, or power using V = IR. Also calculate watts to amps, amps to volts, RMS voltage, peak voltage, and power factor — all 5 modes covering every Ohm's Law formula combination. Verified formulas, instant results.
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Ohm's Law, formulated by Georg Simon Ohm in 1827, is the foundational relationship of electrical engineering: Voltage equals Current multiplied by Resistance (V = I × R). It describes how voltage, current, and resistance are always related in any ohmic (linear) conductor — increase the voltage and current rises proportionally; increase the resistance and current falls proportionally.
Ohm's Law applies to DC circuits, AC resistive loads, and the resistive component of AC circuits with inductance or capacitance. It does not directly apply to non-linear components such as diodes, transistors, and LEDs, which have non-constant resistance depending on operating conditions.
V = I × R (Voltage = Current × Resistance)
I = V / R (Current = Voltage / Resistance)
R = V / I (Resistance = Voltage / Current)
Combining Ohm's Law (V = IR) with the power formula (P = VI) gives twelve interrelated equations. Knowing any two of the four quantities (V, I, R, P) lets you solve for all others:
The most common Ohm's Law calculation in home and commercial electrical work is converting watts to amps to size breakers and wires. Since P = V × I, you can rearrange to get I = P / V. For a 1,200-watt microwave on a 120V circuit: I = 1,200 / 120 = 10 amps. Add a safety margin: this needs a 15-amp or 20-amp circuit (never load above 80% continuously per NEC 210.19).
For AC circuits with reactive loads (motors, HVAC compressors), include the power factor: I = P / (V × PF). A 1-horsepower motor (746W) at 120V with 0.85 PF draws I = 746 / (120 × 0.85) = 7.3 amps. Ignoring power factor would undersize the wire and breaker dangerously.
DC / Resistive AC: I = P / V
AC with Power Factor: I = P / (V × PF)
3-phase AC: I = P / (V × 1.732 × PF)
Example (DC): 500W at 12V = 500/12 = 41.7 A
Example (AC): 2,000W at 240V, PF=0.9 = 2000/(240×0.9) = 9.26 A
AC voltage alternates as a sine wave, so its instantaneous value is always changing. RMS (Root Mean Square) voltage is the mathematically equivalent DC value that would deliver the same average power to a resistive load. This is why the US "120V" standard is an RMS value — its peak voltage is actually 169.7 volts, and its peak-to-peak voltage is 339.4 volts.
RMS matters for: selecting component voltage ratings (capacitors must be rated above peak voltage, not RMS), transformer design, oscilloscope measurements (which show peak-to-peak), and understanding why a 230V European appliance should not be plugged directly into a 120V outlet without a transformer.
V_rms = V_peak × 0.7071 (= V_peak / √2)
V_peak = V_rms × 1.4142 (= V_rms × √2)
V_peak-to-peak = 2 × V_peak = V_rms × 2.8284
V_avg = V_peak × 0.6366 (= V_peak × 2/π)
Form factor = V_rms / V_avg = 1.1107 (sine wave only)
US 120V example: Peak = 169.7V, Peak-to-peak = 339.4V
Power factor (PF = cosφ) describes how efficiently a circuit converts apparent power (VA) to real useful work (watts). A purely resistive load (incandescent bulb, resistive heater) has PF = 1.0 — 100% of drawn current does work. An inductive load (motor, transformer) stores energy in its magnetic field each cycle and returns it, creating a lagging phase angle between voltage and current. This reactive current increases I²R losses without contributing to output power.
Power triangle: Apparent Power VA² = Real Power W² + Reactive Power VAR². PF = W/VA. Phase angle φ = arccos(PF). A motor drawing 10A at 240V with PF = 0.8 has apparent power 2,400 VA, real power 1,920W, and reactive power VAR = sqrt(2400² − 1920²) = 1,440 VAR.
PF = Real Power (W) / Apparent Power (VA)
PF = cos(φ) where φ = phase angle between V and I
Real Power W = VA × PF = V × I × PF
Apparent Power VA = W / PF = V × I
Reactive Power VAR = VA × sin(φ) = √(VA² − W²)
KVA to KW: KW = KVA × PF
Voltage drop is the direct application of Ohm's Law (V = I × R) to wire resistance. Every wire has non-zero resistance; current through that resistance drops voltage before it reaches the load. The NEC recommends keeping total voltage drop below 3% for branch circuits (Section 210.19 Informational Note No. 4). Excessive voltage drop causes motors to overheat, lights to dim, and appliances to malfunction.
The NEC voltage drop formula uses circular mils (CM) — the traditional US measurement of wire cross-sectional area: VD = 2 × K × I × L / CM, where K = 12.9 for copper at 75°C, I = amperes, L = one-way length in feet, and CM = circular mils of the wire gauge selected.
| Scenario | Known | Find | Formula | Answer |
|---|---|---|---|---|
| LED resistor sizing | V=5V, I=20mA | R | R = V/I | 250 Ω |
| Motor current draw | P=1,500W, V=120V | I | I = P/V | 12.5 A |
| Heater power output | V=240V, R=57.6Ω | P | P = V²/R | 1,000 W |
| Battery voltage needed | I=5A, R=24Ω | V | V = I×R | 120 V |
| Wire I²R heat loss | I=20A, R=0.198Ω | P | P = I²×R | 79.2 W |
| Fuse rating for circuit | P=800W, V=120V | I | I = P/V × 1.25 | 8.33A → 15A fuse |
In DC circuits, Ohm's Law is straightforward — resistance is constant and V = IR always holds. In AC circuits, capacitors and inductors introduce reactance (X, in ohms), which opposes AC current flow without dissipating power. The total opposition is impedance Z = √(R² + X²). The AC version of Ohm's Law becomes V = I × Z.
For purely resistive AC loads (heaters, incandescent lamps, resistive stoves), impedance equals resistance and standard Ohm's Law applies directly using RMS values. For inductive loads (motors, transformers, ballasts), you must use impedance and account for power factor to avoid undersizing conductors and protective devices.
In electronics: calculating resistor values for LEDs, voltage dividers, and current-limiting circuits. In residential electrical: sizing breakers and wires for appliances, EV chargers, and HVAC equipment. In industrial: motor starter sizing, power factor correction capacitor banks, transformer kVA ratings. In automotive: calculating fuse ratings, battery internal resistance, and alternator output. In telecommunications: impedance matching for maximum power transfer (load impedance = source impedance for max transfer).