Ohm's Law Calculator

Calculate

Leave blank if solving for voltage. Accepts V; select mV or kV from the unit dropdown for other scales.

Select the voltage unit matching the entered value

Leave blank if solving for current. Select mA or µA for low-signal and electronics ranges.

Select the current unit matching the entered value

Leave blank if solving for resistance. Zero resistance (short circuit) is not accepted — enter a positive value.

Select the resistance unit matching the entered value

Leave blank if solving for power. Select mW for sub-watt signals or kW for high-power loads.

Select the power unit matching the entered value

Overview

Ohm's Law ties together voltage, current, resistance and power in a single relationship. Enter any two of the four quantities and the calculator returns the other two using V = I × R and P = V × I.

Inputs accept mV/V/kV, µA/mA/A, Ω/kΩ/MΩ, mW/W/kW — the calculator converts internally and displays each output in base SI units. A status badge places the result in practical context: LOW-SIGNAL, ELECTRONICS-LEVEL, LOW-VOLTAGE POWER, LINE-VOLTAGE, HIGH-POWER, or HIGH-VOLTAGE. It accepts all six input pairs: (V, I), (V, R), (V, P), (I, R), (I, P), and (R, P). For the (R, P) pair, positive square roots are used for both voltage and current.

The calculator applies to purely resistive DC circuits and single-phase AC circuits with resistive loads. It does not account for reactance, power factor, or non-linear components. For AC circuits with motors, transformers, or switching supplies, use a calculator that includes impedance and power factor.

Final design must be verified against component ratings, thermal constraints, and applicable electrical codes.

How to Use This Calculator

  1. Choose any two of the four inputs to fill — Voltage, Current, Resistance, Power. The other two will be calculated.

  2. Enter values with the unit prefix that matches your scale — e.g. 220 Ω, 3.3 V, 50 mA, 1.5 kW. Select the correct unit prefix from the dropdown next to each field.

  3. Leave the remaining two fields empty — the calculator detects which pair you entered and applies the correct Ohm's Law formula.

  4. Click Calculate — the four values V, I, R, P appear in the Results panel.

  5. Read the status badge — LOW-SIGNAL, ELECTRONICS-LEVEL, LOW-VOLTAGE POWER, LINE-VOLTAGE, HIGH-POWER, or HIGH-VOLTAGE places the result in practical engineering context.

  6. Check the engineering interpretation and recommended next step below the badge for design guidance.

Fill exactly two fields. Filling fewer or more than two fields shows a validation message — the calculator cannot determine which pair to use. All inputs accept positive non-zero values; zero is treated as empty.

Inputs & Outputs

Inputs

  • •Voltage (V)
  • •Voltage Unit — Options: V, mV, kV
  • •Current (A)
  • •Current Unit — Options: A, mA, µA
  • •Resistance (Ω)
  • •Resistance Unit — Options: Ω, kΩ, MΩ
  • •Power (W)
  • •Power Unit — Options: W, mW, kW

Outputs

  • •Voltage (V)
  • •Current (A)
  • •Resistance (Ω)
  • •Power (W)

Formula

Calculator Formula

The calculator identifies which two of the four quantities (V, I, R, P) are provided and applies the corresponding Ohm's Law relationship to derive the other two.

Step 1: Identify the input pair

The calculator detects which two fields contain non-zero values and selects the matching formula pair.

Step 2: Apply the pair formula

Input Pair Derived Values
V and I R = V / I, P = V × I
V and R I = V / R, P = V² / R
V and P I = P / V, R = V² / P
I and R V = I × R, P = I² × R
I and P V = P / I, R = P / I²
R and P I = √(P / R), V = √(P × R) — positive root used

Step 3: Unit conversion

All inputs are converted to base SI units before calculation (V, A, Ω, W). Outputs are shown in base units.

Step 4: Status classification

The computed V, I, and P are evaluated top-down against the following mutually exclusive conditions:

Condition Status
V > 277 V HIGH-VOLTAGE
P ≥ 1500 W and V ≤ 277 V HIGH-POWER
60 V ≤ V ≤ 277 V and P < 1500 W LINE-VOLTAGE
V < 60 V, I ≥ 5 A, P < 1500 W LOW-VOLTAGE POWER
V ≤ 5 V and I < 100 mA LOW-SIGNAL
V < 60 V, I < 5 A, P < 1500 W ELECTRONICS-LEVEL

Variables

Variable Meaning Units
V Voltage V
I Current A
R Resistance Ω
P Power W

Key Formula Drivers

  • For a fixed resistance, doubling voltage doubles current and quadruples power (P = V²/R)
  • For a fixed current, doubling resistance doubles voltage and doubles power (P = I²R)
  • For the (R, P) input pair, the calculator uses positive square roots: I = √(P/R), V = √(P×R)

What is Ohm's Law

Ohm's Law is the empirical relationship between voltage, current, and resistance in a linear conductor at constant temperature: voltage equals current multiplied by resistance (V = I × R). It was published by Georg Ohm in 1827 and remains the foundation of resistive circuit analysis. Combined with the power formula P = V × I, Ohm's Law gives the three common resistive power expressions: P = V × I, P = I² × R, and P = V² / R. From any two of the four quantities — V, I, R, P — the other two are fully determined.

The relationship holds for purely resistive elements: wires, resistors, heating elements, and incandescent filaments. It does not directly apply to circuits with significant capacitance, inductance, or non-linear behaviour such as diodes, transistors, motors, transformers, or switching power supplies. For those, Ohm's Law generalises to V = I × Z, where Z is the complex impedance, and a separate power factor calculation is needed for AC circuits.

In practical engineering, Ohm's Law provides the first-pass check for resistive circuit design. The same relationship that sizes a 220 Ω LED resistor at 5 V also governs a 38 Ω heating element at 240 V — the scale changes, but the physics does not. The classification system in this calculator maps the computed values to practical operating ranges (LOW-SIGNAL through HIGH-VOLTAGE) so users immediately understand the engineering context of their result.

The status classification is calibrated to US distribution voltages: 120 V / 208 V / 240 V / 277 V for residential and light commercial circuits, with anything above 277 V classified as HIGH-VOLTAGE because it exceeds common single-phase and light commercial line-voltage levels. European 230 V single-phase falls within the LINE-VOLTAGE range and is handled consistently.

Key Facts

  • Ohm's Law (V = I × R) was published by Georg Ohm in 1827 as an empirical relationship for linear conductors at constant temperature.
  • Voltage (V), current (A), resistance (Ω), and power (W) are SI-derived units used worldwide — there is no Imperial alternative for electrical quantities.
  • The relationship 1 Ω = 1 V/A is exact by definition in the SI system.
  • For a fixed resistance, doubling the voltage doubles the current and quadruples the power dissipated (P = V²/R).
  • For a fixed current, doubling the resistance doubles the voltage and doubles the power dissipated (P = I²R).
  • P = V × I gives real power directly only for purely resistive loads. For reactive AC loads, real power is V × I × cos(φ), where φ is the phase angle.
  • Standard resistor wattage ratings are 1/8 W, 1/4 W, 1/2 W, 1 W, 2 W, 5 W, and higher for wirewound types.
  • US line voltages are 120 V (residential outlets), 208 V (commercial three-phase L-N), 240 V (residential split-phase), 277 V (commercial lighting). Voltages above 277 V are classified as HIGH-VOLTAGE in this calculator.
  • The (R, P) input pair requires square root evaluation: I = √(P/R), V = √(P×R). Only positive roots are physically relevant in a passive resistive model.

Applications

  • Sizing current-limiting resistors for LEDs and indicator circuits from supply voltage and desired current.
  • Verifying voltage drop across a known resistance for a measured current.
  • Estimating heat dissipation in resistive loads — heaters, electric ranges, incandescent bulbs.
  • Checking whether measured voltage, current, and resistance are internally consistent during circuit troubleshooting.
  • Sanity-checking sensor and signal-level calculations during prototyping.
  • Teaching circuit fundamentals — Ohm's Law is the first relationship covered in any electronics or electrical engineering course.
  • Deriving missing nameplate values — for example, calculating internal resistance of a heating element from rated voltage and power.
  • Selecting shunt resistors for current measurement at very low resistance and significant current.
  • Estimating conductor or contact resistance effects in power distribution and connector design.

Example Calculation

Example 1: LED Current-Limiting Resistor

Given: V = 5 V, R = 220 Ω

I = 5 / 220 = 0.02273 A = 22.7 mA
P = 5² / 220 = 0.1136 W = 113.6 mW

Result:

  • Current = 22.7 mA (0.02273 A)
  • Power = 113.6 mW (0.1136 W)
  • Status: LOW-SIGNAL (V ≤ 5 V, I < 100 mA)
  • A standard 1/4 W (250 mW) resistor is above this dissipation, but thermal margin and enclosure temperature should still be verified.

Example 2: 12 V Automotive Accessory

Given: V = 12 V, I = 2 A

R = 12 / 2 = 6 Ω
P = 12 × 2 = 24 W

Result:

  • Resistance = 6 Ω
  • Power = 24 W
  • Status: ELECTRONICS-LEVEL (V < 60 V, I < 5 A)
  • Power exceeds 5 W — wirewound or aluminium-clad resistor with heatsinking is typically used at this level.

Example 3: 12 V LED Strip, High Current

Given: V = 12 V, I = 8 A

R = 12 / 8 = 1.5 Ω
P = 12 × 8 = 96 W

Result:

  • Resistance = 1.5 Ω
  • Power = 96 W
  • Status: LOW-VOLTAGE POWER (V < 60 V, I ≥ 5 A)
  • At this current level, voltage drop across cables and connector heating become critical. Verify wire gauge, connector ratings, and fuse selection.

Example 4: Household Resistive Heater

Given: V = 240 V, P = 1500 W

I = 1500 / 240 = 6.25 A
R = 240² / 1500 = 38.4 Ω

Result:

  • Current = 6.25 A
  • Resistance = 38.4 Ω
  • Status: HIGH-POWER (P ≥ 1500 W, V ≤ 277 V)
  • Verify conductor and breaker sizing for the calculated current. This load operates at line voltage — confirm the load is purely resistive before applying Ohm's Law.

Example 5: Industrial Three-Phase Line (Single-Phase Equivalent)

Given: V = 480 V, R = 100 Ω

I = 480 / 100 = 4.8 A
P = 480² / 100 = 2304 W = 2.3 kW

Result:

  • Current = 4.8 A
  • Power = 2.3 kW
  • Status: HIGH-VOLTAGE (V > 277 V)
  • Verify isolation, clearance, and PPE requirements per applicable safety standards. For three-phase loads, use the three-phase power formula with the √3 factor.

Standards & References

  • NIST — SI Units, Electric Current — authoritative US reference for the volt, ampere, and ohm definitions
  • NIST Special Publication 330 — The International System of Units (SI), 2019 edition, adopted in the United States
  • IEEE Std 1459-2025 — Standard Definitions for the Measurement of Electric Power Quantities Under Sinusoidal, Nonsinusoidal, Balanced, or Unbalanced Conditions; reference for AC power definitions beyond simple resistive cases
  • NFPA 70 (National Electrical Code) — conductor ampacity, overcurrent protection, and installation requirements for US electrical systems. Free read-only access available (registration required)
  • NFPA 70E — Standard for Electrical Safety in the Workplace; applies when working on circuits above 50 V
  • NEC Table 310.16 — conductor ampacity table; relevant when the calculated current is used to size wire gauge

Units

Ohm's Law uses SI-derived units that are universal across all regions:

  • Voltage in volts (V)
  • Current in amperes (A)
  • Resistance in ohms (Ω)
  • Power in watts (W) There is no Imperial alternative — electrical units are the same worldwide. The calculator accepts common metric prefixes on input (mV, kV for voltage; µA, mA for current; kΩ, MΩ for resistance; mW, kW for power) via the unit selector dropdown next to each field. Outputs are always shown in base SI units. The line-voltage classification (60 V ≤ V ≤ 277 V) is calibrated to US distribution voltages. International users can enter values directly — 230 V European mains, 12 V automotive, 3.3 V logic — all in volts.

Limitations

  • The calculator applies to purely resistive elements. For capacitive, inductive, or non-linear components the underlying physics differs — use an impedance or power-factor calculator for those cases.
  • Resistance is treated as constant. Real resistors and conductors change resistance with temperature; for tight thermal designs, the temperature coefficient must be included separately.
  • The calculator returns values for one operating point. It does not analyse circuits with multiple resistors in series or parallel — combine the network into a single equivalent resistance first.
  • For AC circuits, the calculator assumes resistive load. Real AC loads (motors, transformers, switching supplies) have a power factor below 1, so V × I overstates real power.
  • Zero and negative inputs are not accepted. Zero resistance represents a short circuit (undefined current for non-zero voltage). The calculator rejects these cases by treating zero as an empty field.
  • Exactly two of the four inputs must be filled. Providing only one value gives an underdetermined result; providing three or more is overdetermined and the calculator shows a validation message.
  • The status classification reflects typical US practice. Other regions may use different distribution voltage ranges; treat the badges as engineering orientation, not as code-compliance verdicts.

Common Mistakes to Avoid

  • Confusing P = V × I (resistive load) with P = V × I × cos(φ) (AC reactive load). For motors, transformers, and fluorescent lighting, V × I overstates real power.
  • Entering current in mA without switching the unit selector to mA, then reading the calculator output as if it were in amperes — the selected unit must match the entered number.
  • Treating resistance as zero. Zero resistance represents a short circuit where current is theoretically infinite — the calculator requires a positive non-zero resistance value.
  • Mixing line-to-neutral and line-to-line voltage in three-phase contexts. This calculator handles a single voltage value — for three-phase systems, use a dedicated three-phase power calculator.
  • Assuming the calculated power equals the maximum dissipation the resistor can handle continuously. Real resistors must be derated for ambient temperature, mounting, and duty cycle.
  • Filling three or four fields instead of exactly two. The calculator cannot determine which pair to use when more than two values are provided.
  • Reading instantaneous Ohm's Law results as steady-state values for inductive or capacitive loads. Transient behavior (motor inrush, capacitor charging) is not modelled here.

Frequently Asked Questions

What is Ohm's Law?
Ohm's Law states that voltage equals current multiplied by resistance: V = I × R. It applies to linear conductors at constant temperature and forms the basis for resistive circuit analysis. The four power formulas P = V × I, P = I² × R, and P = V² / R derive from Ohm's Law combined with the definition of electrical power.
Can I calculate watts from volts and amps?
Yes. For a purely resistive load, power is P = V × I. Enter voltage and current, and the calculator returns power in watts along with resistance. For AC loads with a power factor below 1, real power is lower than V × I and should be calculated with power factor included.
How do I calculate amps from watts and volts?
Use I = P / V. Enter power and voltage and the calculator returns current and resistance. For example, 1500 W at 120 V gives 12.5 A for a purely resistive load. For motors, transformers, or other reactive loads, divide by both voltage and power factor: I = P / (V × cos φ).
Can I use this calculator for AC circuits?
Yes, but only for purely resistive AC loads such as heaters, incandescent lamps, and electric ranges. For loads with significant reactance — motors, transformers, fluorescent lighting, switching power supplies — use a calculator that includes power factor and apparent power, because V × I will overstate real power.
Why does the calculator require exactly two inputs?
Ohm's Law determines two unknowns from two knowns. With one value alone, the result is underdetermined and infinitely many circuits satisfy the equation. With three or more values, it is impossible to know which two the user intends as inputs. Entering exactly two values removes the ambiguity and allows a unique solution.
What does the LOW-VOLTAGE POWER badge mean?
LOW-VOLTAGE POWER applies when voltage is below 60 V but current is 5 A or higher. This range covers automotive 12 V circuits with high current draw, LED strip installations, low-voltage DC bus, and battery systems. At this level, voltage drop across cables and connector heating become the limiting factors rather than insulation rating.
How does the calculator pick the unit for the output?
All outputs are shown in base SI units: volts (V), amperes (A), ohms (Ω), and watts (W). The numeric display adapts automatically — values below 0.001 show more decimal places for precision. To read milliampere or milliwatt results, multiply the displayed value by 1000 or note the magnitude from the decimal position.
How do I size a resistor for a known voltage and current?
Calculate resistance from R = V / I and power from P = V × I by entering V and I. Choose a standard resistor value close to the calculated R, then select a wattage rating with margin above the calculated power. A 2× margin is a common starting point, but final derating depends on ambient temperature, package type, mounting, and duty cycle.
What is the difference between ELECTRONICS-LEVEL and LOW-SIGNAL?
Both apply to sub-60 V circuits with less than 5 A current, but LOW-SIGNAL further requires voltage at or below 5 V and current below 100 mA. LOW-SIGNAL covers microcontrollers, logic circuits, and sensor interfaces where thermal dissipation is negligible. ELECTRONICS-LEVEL covers the broader DC electronics range — 12 V automotive, 24 V industrial, 48 V telecom — where resistor power ratings and voltage drop on longer runs still require checking.
Why does the calculator show zero for resistance when I enter V and I?
If the entered current is zero, resistance would be mathematically infinite (open circuit). The calculator outputs zero in that case rather than displaying infinity. This is an edge case — a non-zero current is expected for a live resistive circuit. If you intend to model an open circuit, note that no power is dissipated and no current flows by definition.

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Engineers often use these calculators in combination for complete project workflows:

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Single Phase Power Calculator

Breaker Size Calculator

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