Voltage
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Calculate voltage, current, resistance, and power
Ohm's Law
Power
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Electrical Engineering Foundation
Solve for any electrical quantity using V = IR and the power equations P = IV, P = I²R, P = V²/R.
Ohm's Law
V = I × R
Power (basic)
P = I × V
Power (current)
P = I²R
Power (voltage)
P = V²/R
Reviewed by: CalculatorApp Electrical Engineering Team
Ohm\'s Law is the fundamental relationship governing resistive electrical circuits. Proposed by Georg Simon Ohm in 1827, it establishes that the current through a conductor is directly proportional to voltage and inversely proportional to resistance. Combined with Kirchhoff\'s laws and the power equations, it forms the basis for all circuit design, safety calculation, and power engineering.
Voltage
V = I × RCurrent
I = V / RResistance
R = V / IPower (3 forms)
P=IV | P=I²R | P=V²/R| Resistor Type | Ohm\'s Law Applicability | Use Case |
|---|---|---|
| Fixed resistor | Full (linear) | Voltage dividers, current limiting |
| Semiconductor (diode) | Non-linear | Rectification, signal clamping |
| Inductor (AC) | Use Z = jωL | Filters, transformers, motors |
| Capacitor (AC) | Use Z = 1/jωC | Filters, timing, power factor correction |
1827: Georg Ohm publishes the mathematical relationship V = IR in Die galvanische Kette.
1845: Kirchhoff extends circuit theory with his voltage and current laws (KVL, KCL).
1861: British Association formalizes the ohm as the unit of resistance.
1881: International Congress of Electricians standardizes volt, ampere, and ohm globally.
1960: SI system formally adopts the ohm (Ω) as the unit of electrical resistance.
Modern era: Ohm's Law remains the entry point for all electrical engineering education and practice.
Peer-reviewed electrical engineering research and standards.
International electrotechnical safety and wiring standards.
US National Electrical Code for safe wiring practice.
Workplace electrical safety regulations and guidelines.
Myth: Ohm's Law applies to all components.
Fact: Diodes, transistors, and other non-linear devices do not follow simple V = IR relationships.
Myth: Higher resistance always wastes more power.
Fact: P = V²/R — at constant voltage, higher resistance actually dissipates less power.
Myth: AC and DC obey Ohm's Law identically.
Fact: AC circuits with reactance require impedance Z; pure resistance circuits behave the same.
Myth: A circuit with low resistance is always safe.
Fact: Low resistance with high voltage = very high current = dangerous without proper protection.
Ohm's Law states V = IR: voltage equals current multiplied by resistance. It is the cornerstone of circuit analysis.
For resistive AC circuits, yes. For reactive components (inductors, capacitors), use impedance Z instead of R.
P = IV = I²R = V²/R. Power is the rate of energy dissipation in a resistor, measured in watts.
Series: R_total = R₁ + R₂. Parallel: 1/R_total = 1/R₁ + 1/R₂. Voltage divides in series; current divides in parallel.
KVL: the sum of all voltage drops around any closed loop equals the sum of voltage rises (total = 0 net).
KCL: the sum of currents entering a node equals the sum leaving. Charge is conserved.
R = ρL/A where ρ is resistivity, L is length, and A is cross-sectional area.
Non-linear components (diodes, transistors) and extreme conditions (superconductors) do not follow simple V=IR.
Near-zero resistance path causing very high current; potentially dangerous without overcurrent protection.
Infinite resistance path; no current flows. Voltage may still appear across an open circuit.
I = P / V or I = √(P/R). Use these forms when power and one other quantity are known.
NEC and IEC standards typically require conductors rated at 125% of continuous load current for safety.
Pair Ohm\'s Law with voltage divider, motor sizing, and frequency calculators for complete circuit and system analysis.
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