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Select the quantity you want to find, then enter any two known values below.

V
Voltage
Volts
I
Current
Amps
R
Resistance
Ohms (Ω)
P
Power
Watts
Solving for: Voltage (V) — enter current and resistance, or power and current, or power and resistance below.
Leave blank if solving for V Enter a valid voltage.
Leave blank if solving for I Enter a valid current.
Leave blank if solving for R Enter a valid resistance.
Leave blank if solving for P Enter a valid power value.
Choose what to calculate Select an option.
Include power factor for AC motors Select circuit type.
Enter the first known value Enter a valid value.
Enter the second known value Enter a valid value.
Select conversion direction Select a mode.
Enter the voltage to convert Enter a valid voltage.
50 Hz (Europe) or 60 Hz (US/Canada) Enter a valid frequency.
What to calculate Select option.
First known value Enter a valid value.
Second known value Enter a valid value.
Current the wire carries Enter a valid current.
Distance from panel to load Enter a valid length.
Wire cross-sectional area in circular mils Select wire gauge.
Supply voltage at the source Select voltage.
Conductor material affects resistance Select material.
Result
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⚠️ Disclaimer: Results are based on standard electrical engineering formulas for educational and design estimation. Always consult a licensed electrician for code-compliance decisions. Ohm's Law applies to linear, resistive components under steady-state DC or RMS AC conditions.

📚 Sources & Methodology

All formulas on this calculator are verified against the following authoritative references:

Complete Ohm's Law Guide — All Formulas Explained

What Is Ohm's Law? (V = IR)

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.

Ohm's Law — Three Forms
V = I × R (Voltage = Current × Resistance) I = V / R (Current = Voltage / Resistance) R = V / I (Resistance = Voltage / Current)

The 12-Formula Ohm's Law Wheel

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:

Find
From V & ?
From I & ?
From P & ?
V
already known
I × RV = I×R
P / IV = P/I
I
V / RI = V/R
already known
P / VI = P/V
R
V / IR = V/I
V² / PR = V²/P
V²/P or P/I²both valid
P
V × IP = V×I
I² × RP = I²R
V² / RP = V²/R

Watts to Amps — How to Convert

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.

Watts to Amps Formulas
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

RMS Voltage — What Your Voltmeter Reads

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.

RMS & Peak Voltage Conversions (Sine Wave)
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 — Why It Matters

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.

Power Factor Formulas (AC Circuits)
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 Using Ohm's Law

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.

Worked Examples: Ohm's Law in Practice

ScenarioKnownFindFormulaAnswer
LED resistor sizingV=5V, I=20mARR = V/I250 Ω
Motor current drawP=1,500W, V=120VII = P/V12.5 A
Heater power outputV=240V, R=57.6ΩPP = V²/R1,000 W
Battery voltage neededI=5A, R=24ΩVV = I×R120 V
Wire I²R heat lossI=20A, R=0.198ΩPP = I²×R79.2 W
Fuse rating for circuitP=800W, V=120VII = P/V × 1.258.33A → 15A fuse

Ohm's Law for DC vs. AC Circuits

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.

💡
NEC 80% rule: Per NEC 210.19, any continuous load (operating 3 or more hours) must not exceed 80% of the circuit's rated current. A 20-amp circuit should carry no more than 16 amps continuously. Size your breaker at I_actual × 1.25 to comply. Always apply this before selecting wire and breaker size.

Ohm's Law Applications by Industry

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).

❓ Frequently Asked Questions

Ohm's Law: V = I x R. Voltage equals current multiplied by resistance. Rearrange for current: I = V/R. For resistance: R = V/I. Combined with P = V x I, you get 12 equations covering all four electrical quantities. Named after Georg Simon Ohm who published it in 1827.
P = V x I (watts = volts x amps) for DC and resistive AC. For AC with reactive loads: P = V x I x PF (multiply by power factor). Example: 120V at 10A = 1,200W. A motor at 240V, 8A, PF=0.85 = 240 x 8 x 0.85 = 1,632W real power, but draws 1,920 VA apparent power.
V = I x R — you need the resistance to convert amps to volts. If you know power and current instead: V = P / I. You cannot calculate voltage from current alone without one more piece of information. Example: 5A through 24 ohms = 120V. 1,440W at 12A = 120V.
RMS (Root Mean Square) voltage is the effective DC-equivalent value. Peak voltage is the maximum instantaneous amplitude. V_rms = V_peak / sqrt(2). US 120V is RMS — its peak is 169.7V and peak-to-peak is 339.4V. Multimeters read RMS. Oscilloscopes show peak-to-peak. Component voltage ratings must exceed peak voltage, not RMS.
Power Factor = Real Power (W) / Apparent Power (VA) = cos(phase angle). PF = 1.0 for resistive loads. PF = 0.7 to 0.95 for motors and transformers. A motor drawing 10A at 240V (2,400 VA) consuming 1,920W has PF = 1,920/2,400 = 0.80. Low PF increases current draw without increasing useful output, increasing I2R losses and wire heating.
R = V / I. A component with 9V across it drawing 0.03A (30mA) has R = 9/0.03 = 300 ohms. From power: R = V^2/P or R = P/I^2. A 100W bulb at 120V has R = 120^2/100 = 144 ohms at operating temperature. Note: incandescent bulbs have much lower cold resistance because tungsten resistance increases with temperature.
Draw a triangle with V on top, I and R on the bottom. Cover the unknown: cover V to get I x R; cover I to get V/R; cover R to get V/I. The power triangle works the same with P on top: cover P to get V x I; cover V to get P/I; cover I to get P/V. Use the calculator above for instant results without memorizing the triangle.
Yes, with modifications. For resistive AC loads (heaters, incandescent lights, resistive heating elements): use RMS values directly in V = IR. For circuits with inductors or capacitors: replace R with impedance Z = sqrt(R^2 + X^2) where X is reactance. The phase angle phi = arctan(X/R). Power factor = cos(phi). For practical purposes, Ohm's Law using RMS values is accurate for all resistive loads.
Voltage drop = I x R_wire. For the NEC formula: VD = 2 x K x I x L / CM, where K=12.9 (copper, 75C), I=amps, L=one-way feet, CM=wire circular mils. 12 AWG (6,530 CM) at 15A over 80 feet: VD = 2 x 12.9 x 15 x 80 / 6,530 = 3.76V = 3.1% of 120V. NEC recommends keeping under 3%. Use the Voltage Drop tab above for instant results.
I^2R loss (copper loss) is the heat dissipated in a conductor: P = I^2 x R. A 12 AWG wire with resistance 0.00198 ohms/foot carrying 20A over 100 feet (total R = 0.396 ohms): P = 20^2 x 0.396 = 158 watts wasted as heat. This is why power transmission uses high voltage (low current) — halving current reduces I^2R losses by 75%. Transformer stations step up voltage for transmission and step down for distribution.
Resistance (R, ohms) opposes current in DC and AC, dissipating energy as heat. Impedance (Z, ohms) is the total AC opposition combining resistance and reactance: Z = sqrt(R^2 + X^2). Inductive reactance XL = 2*pi*f*L increases with frequency. Capacitive reactance XC = 1/(2*pi*f*C) decreases with frequency. At DC (f=0): capacitors = open circuit, inductors = short circuit. At resonance (XL = XC): Z = R only.
Kirchhoff's Voltage Law (KVL): sum of voltages around any closed loop = 0. Kirchhoff's Current Law (KCL): sum of currents at any node = 0. Together with Ohm's Law (V = IR), these three laws can solve any linear circuit. For a series circuit: apply KVL to find total resistance, then Ohm's Law for current, then KVL again for individual voltage drops. For parallel circuits: apply KCL for branch currents.

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