Ohm's Law Calculator

Ohm's Law states that the current through a conductor between two points is directly proportional to the voltage across those two points, with resistance as the constant of proportionality: V = I × R. Combined with Watt's Law (P = V × I), it gives twelve derived formulas that solve any combination of voltage, current, resistance, and power. This calculator accepts any two known values and returns the other two, with full unit conversion (mV, V, kV; mA, A, kA; mΩ, Ω, kΩ, MΩ; mW, W, kW). Used in every electrical and electronic design from LED resistor sizing to power-system fault analysis.

Reviewed: April 23, 2026 · Author: Naveen P N, Founder — AI Calculator · Verified against: Wikipedia: Ohm's Law, All About Circuits textbook, NEC (NFPA 70) circuit-protection rules.

Electrical safety notice. Mains voltage (120 V or 230 V AC) and many DC circuits above 60 V can kill on contact. Use Ohm's Law calculations for design and troubleshooting, but live-circuit work must follow your local electrical code (NEC, IEC 60364, BS 7671, AS/NZS 3000) and be performed by a licensed electrician. See our disclaimer.

What is Ohm's Law?

Ohm's Law states that the current passing through a conductor between two points is directly proportional to the voltage across the two points. It is one of the most fundamental principles in electrical engineering and physics.

Where:

• V = Voltage in Volts (V)
• I = Current in Amperes (A)
• R = Resistance in Ohms (Ω)

Ohm's Law Power Formulas

Power (P) is the rate at which electrical energy is transferred by an electric circuit. Combining Ohm's Law with Watt's Law allows us to solve for Power alongside Voltage, Current, and Resistance.

From these two fundamental equations, we can derive the famous "Ohm's Law Pie Chart" or "Ohm's Law Wheel", which provides 12 different formulas.

Worked example 1 — sizing a current-limiting resistor for an LED

Scenario: You want to drive a standard red LED (forward voltage V_F = 2.0 V, recommended forward current I_F = 20 mA) from a 9 V battery. What value of series resistor do you need?

Step 1 — the voltage across the resistor. Kirchhoff's voltage law tells us the supply voltage equals the sum of voltages across all series components:

Step 2 — apply Ohm's Law. The current through the resistor must equal the LED's recommended I_F (they are in series):

Step 3 — pick the next standard E-12 series value. 350 Ω isn't a stocked resistor value. The nearest standard E-12 values are 330 Ω (slightly higher current = slightly brighter, slightly riskier) or 390 Ω (slightly lower current = safe). For longevity, choose the higher value: 390 Ω.

Step 4 — verify the resistor's power rating. The resistor will dissipate:

A standard 1/4 W (0.25 W) resistor handles this comfortably with 60% margin. For higher-current LEDs, always check that the resistor's rated power exceeds the calculated dissipation by at least 50% to allow for ambient temperature derating.

This same calculation pattern appears in the LED resistor calculator for any combination of supply voltage, LED forward voltage, and current.

Worked example 2 — how much current does a 1500 W hair dryer draw?

Scenario: A 1500 W hair dryer is plugged into a US 120 V outlet. What current does it draw, and is a standard 15 A branch circuit sufficient? What if the same hair dryer is sold for the European 230 V market?

Step 1 — US outlet (120 V):

This draws 12.5 A on a 15 A circuit, which is 83% of capacity. The NEC allows continuous loads up to 80% of breaker rating, so this hair dryer is at the safety threshold. If anything else is on the same circuit (lighting, another receptacle), the breaker may trip. This is exactly why many US bathrooms have dedicated 20 A GFCI receptacles for hair dryers and curling irons.

Step 2 — European outlet (230 V) with the same 1500 W rating:

The European version draws roughly half the current for the same power. This is the fundamental advantage of higher distribution voltage — halving the current quarters the I²R losses in the supply wiring, which is why European homes use thinner cables for the same appliance loads.

Step 3 — what is the equivalent resistance of the heating element?

The European hair dryer uses a 3.7× higher resistance heating element. Plugging a US (low-resistance) hair dryer into a European 230 V outlet would draw catastrophic current and fail dramatically. This is why "international" appliances need explicit dual-voltage rating — you can't just plug a 120 V appliance into 230 V.

Worked example 3 — full-load current of a 3-phase motor (real engineering case)

Scenario: A 15 kW, 3-phase, 415 V induction motor with power factor 0.85 and efficiency 92%. What is the full-load current (FLC) for cable-sizing purposes?

The 3-phase power formula:

where V_LL is line-to-line voltage, I is line current, cosφ is power factor, η is motor efficiency. The factor of √3 (1.732) appears because, in a balanced 3-phase system, the three phase currents are 120° apart. Solving for I:

For cable sizing per IEC 60364, you don't use this current directly: motor circuits require derating for starting current (typically 6–8× FLC) and continuous-load factor (1.25 × FLC for branch-circuit conductors per NEC 430.22). So the cable must carry 1.25 × 26.7 = 33.4 A continuously, and the breaker must withstand the starting transient.

For full motor-circuit design including cable derating, see our cable-sizing calculator and motor starting-current calculator. The simple Ohm's Law on this page is the starting point for every motor circuit, but real installations require the additional derating layers.

Common mistakes — six errors that make Ohm's Law calculations wrong

1. Mixing units. Plugging milliamps into a formula that expects amps gives a 1000× error. Always convert all values to base SI units (volts, amps, ohms, watts) before applying the formula. The most common sign of a unit-mix error is a result that's wrong by a factor of 10, 100, or 1000.
2. Confusing series and parallel resistance. Series: R_total = R₁ + R₂. Parallel: 1/R_total = 1/R₁ + 1/R₂. Two 100 Ω resistors in series give 200 Ω; in parallel they give 50 Ω. Apply the wrong formula and your current calculation is off by a factor of 4.
3. Applying DC Ohm's Law to AC reactive circuits. In AC circuits with capacitors or inductors, replace resistance R with impedance Z, which is a complex number. The "reactance" of a capacitor or inductor varies with frequency. Pure DC Ohm's Law (V = IR) is only valid for purely resistive AC circuits.
4. Forgetting voltage drop in supply wiring. If your power supply is 12 V but the wires from supply to load have 0.5 V drop at the operating current, only 11.5 V actually reaches the load. Always measure voltage at the load, not at the supply, when troubleshooting.
5. Treating non-ohmic devices as resistors. Diodes (including LEDs), transistors, vacuum tubes, and incandescent bulbs are non-ohmic — their effective resistance changes with voltage, current, or temperature. Use the manufacturer's datasheet (forward voltage, characteristic curve), not a single resistance value.
6. Ignoring power dissipation. Solving for current with Ohm's Law is necessary but not sufficient — you also need to verify that the components can dissipate the calculated power without overheating. A resistor that's "correctly sized" by resistance value but underrated for power will burn out within seconds.

When Ohm's Law alone is not enough

• Diodes (including LEDs). Once forward-biased above the threshold voltage, current rises exponentially with voltage; below threshold, almost no current flows. Use the diode equation or the manufacturer's I-V curve, not a single R.
• Incandescent light bulbs. A cold tungsten filament has roughly 1/10 the resistance of its hot operating value. The inrush current at switch-on is 10× the steady-state current — this is why incandescent bulbs usually fail at the moment they're switched on.
• AC circuits with reactive components. Capacitors and inductors have impedance Z, not just resistance R. Power factor and phase angle matter. Use complex-number analysis or our 3-phase / power-factor calculators.
• Transmission-line problems. At high frequencies (MHz and above) or long distances, lumped-element Ohm's Law breaks down. Distributed parameters (characteristic impedance, propagation constant) take over. Used in RF, audio cable, and power-line analysis.
• Semiconductor devices in active mode. Transistors and op-amps don't have a single "resistance" — their behavior is described by transconductance, h-parameters, or small-signal models. Ohm's Law is used inside parts of these models, but the full device behavior requires more.

Reference: typical current draws for common loads

Use this table for quick mental-math estimates of expected current. All values assume the appliance is at its rated power and supplied at the nominal voltage shown. Real-world currents may vary ±10–15% depending on supply-voltage variation and operating mode (heating elements draw less as they warm up; motors draw 6–8× rated current at startup).

How to use: sum the currents of all loads on a circuit. Compare against the breaker rating × 0.80 (NEC continuous-load rule). If the sum exceeds 80%, redistribute loads or upsize the circuit.

Where Ohm's Law gets used — 8 real-world contexts

1. Electronics design — sizing current-limiting resistors for LEDs, voltage dividers, pull-up/pull-down resistors on logic inputs, base resistors for transistors.
2. Power-system analysis — calculating fault current, voltage drop along transmission lines, and protective device coordination per IEC 60909 (see our short-circuit calculator).
3. Cable sizing — determining minimum cross-section to keep voltage drop within 3% (lighting) or 5% (motor) limits per voltage-drop calculator rules.
4. Battery and UPS engineering — computing runtime from battery capacity, internal resistance, and load current; sizing fuses for battery protection.
5. Solar PV system design — matching panel string voltage to inverter input range, calculating cable loss, sizing combiner-box fuses.
6. Appliance and motor circuits — converting nameplate power to current to size cables, breakers, and contactors.
7. Test & measurement — calibrating shunt resistors for current sensing, designing voltage attenuators, computing meter loading errors.
8. Education — the first quantitative relationship every electrical engineering and physics student learns. Forms the basis for Kirchhoff's laws, network theorems, and AC circuit analysis.

Where Ohm's Law comes from — the story behind V = IR

Georg Simon Ohm published his treatise Die galvanische Kette, mathematisch bearbeitet ("The Galvanic Circuit Investigated Mathematically") in Berlin in 1827. He had spent eight years carefully measuring how current through metal wires varied with applied voltage, using an early thermocouple as a constant-voltage source and a torsion balance as an early ammeter. His key finding — that the relationship V/I was constant for any given metal at constant temperature — was initially dismissed by German academic establishment, costing him his teaching post.

Ohm's law was finally vindicated in 1841 when the Royal Society awarded him the Copley Medal. The SI unit of electrical resistance, the ohm (Ω), was named in his honor at the 1881 International Electrical Congress in Paris. Today his original copper wires — the literal "ohm standards" he used — are preserved at the Deutsches Museum in Munich.

Two related figures: André-Marie Ampère (after whom the unit of current is named) had published earlier work on the magnetic effects of current in 1820, and Alessandro Volta (volt) had built the first practical battery in 1800. Ohm's contribution was the quantitative relationship that tied them all together.

Related electrical calculators

• Voltage Drop Calculator — cable voltage loss for DC, single-phase, and 3-phase circuits per IEC 60364 / NEC.
• Cable Sizing Calculator — minimum conductor size for a given current, factoring in derating per IEC 60364-5-52.
• Short-Circuit Calculator — fault-current analysis per IEC 60909.
• Transformer Sizing Calculator — kVA rating from connected load, power factor, and diversity.
• Motor Starting Current Calculator — in-rush analysis for induction motor circuits.
• LED Resistor Calculator — series resistor sizing for any LED + supply combination.
• 3-Phase Power Calculator — line/phase voltage, real/apparent/reactive power, power factor.
• Voltage Divider Calculator — resistive divider design for sensing and reference.

Sources & further reading

• Wikipedia — Ohm's Law (history, microscopic origin, vector form for anisotropic materials).
• All About Circuits — DC textbook chapter 2 (free online textbook with interactive examples).
• NFPA — National Electrical Code (NEC, NFPA 70) (US electrical wiring rules, including continuous-load and motor-circuit derating).
• IEC 60364 — Low-voltage electrical installations (international wiring standard; the IEC counterpart to NEC).
• IEEE Standards Association (authoritative source for power-system, semiconductor, and measurement standards).
• Hayt, Kemmerly, Durbin. Engineering Circuit Analysis, 9th edition. McGraw-Hill. ISBN 978-0073545516. Chapter 2 covers Ohm's Law derivation, Kirchhoff's laws, and DC circuit analysis at university level.
• Horowitz, Hill. The Art of Electronics, 3rd edition. Cambridge University Press. ISBN 978-0521809269. The reference for practical electronic-circuit design; chapter 1 covers Ohm's Law and resistor selection.

Frequently Asked Questions