Ohm's Law Calculator

Calculate voltage, current, resistance, or power using V = IR and P = VI = I²R = V²/R.

⚡ Electricity📐 V = IR🔌 Ohm's Law
Current (I) Amperes
Resistance (R) Ohms
⚠️ Enter two known values.

What Is Ohm's Law?

Ohm's Law is the fundamental relationship between voltage (V), current (I), and resistance (R): V = IR. Voltage (volts) is the electrical potential difference; current (amperes) is the rate of charge flow; resistance (ohms) opposes current. Ohm's Law is a linear relationship — double the voltage, double the current (for a fixed resistor).

The law was formulated by Georg Simon Ohm in 1827 and holds for conductors where resistance is constant (ohmic materials). Non-ohmic elements (diodes, transistors, thermistors) have resistance that varies with voltage or temperature. For AC circuits, resistance is replaced by impedance Z = √(R² + X²) where X is reactance.

Power dissipated in a resistor: P = VI = I²R = V²/R. These three forms are all equivalent via Ohm's Law and are used depending on which quantities are known. A 100 Ω resistor carrying 100 mA dissipates P = (0.1)² × 100 = 1 W — all as heat (Joule heating).

Ohm's Law is the starting point for all circuit analysis. Combined with Kirchhoff's Laws (KVL and KCL), it allows solving any linear resistive network. Real-world applications range from designing LED current-limiting resistors to analyzing transmission line losses and electronic filter networks.

Formula Reference Table

Solve ForFormulaNotes
VoltageV = I · RVolts (V)
CurrentI = V / RAmperes (A)
ResistanceR = V / IOhms (Ω)
PowerP = V·I = I²R = V²/RWatts (W)
EnergyE = P·t = V·I·tJoules (J = W·s)
ConductanceG = 1/RSiemens (S); I = GV

3 Worked Examples

Example 1
LED Resistor

5 V supply, LED needs 2 V at 20 mA. Find resistor.

  • V_R = 5 − 2 = 3 V across resistor
  • R = V/I = 3/0.020 = 150 Ω
  • P = I²R = (0.02)²×150 = 0.06 W → use 1/4 W resistor
✓ R = 150 Ω; power = 60 mW
Example 2
Heater Current

120 V, 1,200 W electric heater. Find current and resistance.

  • I = P/V = 1200/120 = 10 A
  • R = V/I = 120/10 = 12 Ω (resistance of heating element)
  • Or R = V²/P = 14400/1200 = 12 Ω ✓
✓ I = 10 A; R = 12 Ω
Example 3
Transmission Line Loss

10 kW sent over 100 Ω line at 10 kV (I = 1 A) vs 100 V (I = 100 A).

  • At 10 kV: P_loss = I²R = 1² × 100 = 100 W (1% loss)
  • At 100 V: P_loss = 100² × 100 = 1,000,000 W (10,000% — impossible)
  • High voltage minimizes I²R losses — why power grids use kV to MV
✓ High voltage reduces I²R losses by factor of (V_ratio)²

Real-World Applications

💡
Lighting
Every bulb and LED has a design current and voltage (I, V). The resistance R = V/I (or impedance for AC) determines power. LED drivers are constant-current sources ensuring precise I regardless of V variation.
🔌
Circuit Design
Every resistor in a circuit acts as a V = IR voltage drop. Kirchhoff's Voltage Law (sum of drops = supply) is Ohm's Law applied repeatedly around a loop.
🌐
Power Transmission
High-voltage AC transmission (115 kV–765 kV) minimizes I²R line losses. Doubling voltage halves current → quarter the losses. This is why power lines use transformers to step up/down voltage.
🔋
Battery Internal Resistance
Real batteries have internal resistance r. Terminal voltage V = EMF − I×r. As current increases, terminal voltage drops. This limits maximum power output: P_max = EMF²/(4r) at I = EMF/(2r).
🔬
Biomedical Devices
ECG/EEG electrodes monitor μV-level biopotentials. Input impedance must be MΩ-range to avoid loading the source. Ohm's Law (and its AC equivalent) govern signal integrity in medical monitoring.

Common Mistakes to Avoid

⚠️
Mixing AC and DC Ohm's Law

For AC, resistance is replaced by impedance Z. Pure resistance: Z = R. Inductor: Z = jωL. Capacitor: Z = 1/(jωC). Using V = IR for AC circuits with reactive components gives wrong current calculations.

⚠️
Forgetting V = terminal voltage, not EMF

For real voltage sources with internal resistance r: V_terminal = EMF − Ir. The voltage at the terminals decreases under load. Always use terminal voltage in external circuit calculations.

⚠️
Using peak vs RMS for AC

Ohm's Law for AC should use RMS values (V_rms = V_peak/√2 for sine waves). Power P = V_rms × I_rms. Using peak values gives power 2× too high for a resistive load.

⚠️
Power formula confusion

P = VI = I²R = V²/R — all equivalent. Choose based on what's known. Don't mix: P = I × V²/R (incorrect) or P = I²/R (also wrong).

⚠️
Resistance of non-ohmic elements

Ohm's Law (constant R) applies to resistors, not to diodes, transistors, or thermistors where R varies with conditions. These require different analysis (load lines, semiconductor equations).

Frequently Asked Questions

What does Ohm's Law mean physically? ▾
V = IR: a resistor impedes current flow — more resistance means more voltage needed to push the same current. Voltage is the 'pressure' driving electrons; current is the flow rate; resistance is the friction opposing flow. The law is empirical for conductors but can be derived from electron drift velocity in metals.
Is Ohm's Law always valid? ▾
No — it's valid for 'ohmic' materials where R is constant (most metals at constant temperature). Non-ohmic elements: diodes (R depends on direction of V), thermistors (R changes with T), gas discharge tubes, and superconductors (R = 0 below critical T) don't follow V = IR with constant R.
What is the difference between resistance and resistivity? ▾
Resistance R (Ω) = ρL/A, where ρ is resistivity (Ω·m), L is length, A is cross-section. Resistivity is a material property (copper: ρ = 1.68×10⁻⁸ Ω·m). Resistance depends on material and geometry. A thin, long wire has much higher R than a thick, short one of the same material.
Why do we use high voltage for power transmission? ▾
P_loss = I²R. P_transmitted = VI. For fixed P, doubling V halves I → 4× less loss. Power lines at 500 kV lose far less than at 50 kV for the same power. Transformers step voltage up for transmission and down for safe household use — this is the fundamental reason AC was adopted over DC for grids.
What is conductance? ▾
G = 1/R (siemens, S). I = GV (Ohm's Law in conductance form). High conductance = low resistance = easy current flow. Useful in parallel circuit analysis: G_total = G₁ + G₂ + ... (conductances add in parallel, not resistance).
How does Ohm's Law apply to the human body? ▾
Body resistance varies: dry skin 100 kΩ–1 MΩ; wet skin 1 kΩ; internal tissue 200–500 Ω. At 120 V: I = V/R. Dry hand-to-hand: I ≈ 1 mA (threshold of sensation). Wet: I ≈ 120 mA (fatal fibrillation threshold). Electrical codes set safety limits based on these V = IR calculations.
What is impedance? ▾
Impedance Z (Ω) is the AC generalization of resistance: Z = R + jX where X is reactance. For a resistor: Z = R. Inductor: Z = jωL (increases with frequency). Capacitor: Z = 1/(jωC) (decreases with frequency). |Z| is the impedance magnitude; V = IZ (Ohm's Law for AC). Used in filter design, audio, RF circuits.
What is short circuit current? ▾
With R → 0, I = V/R → ∞. In practice, source internal resistance r limits: I_short = EMF/r. A car battery (EMF = 12 V, r ≈ 0.005 Ω) can deliver up to 2,400 A into a short circuit — enough to weld metal, start fires, or explode. This is why fuses protect circuits.

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Interpretation: This formula links charge, voltage, current, resistance, capacitance, power or circuit time response. Assumption: Confirm DC versus AC conditions, RMS versus peak values, component topology and steady-state versus transient behavior. Ideal components may be assumed.

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