Ohm's Law Calculator

Ohm’s Law is the foundational relationship in electrical circuit analysis, describing how voltage, current, and resistance interact in a conductor. Named after German physicist Georg Simon Ohm, who published it in 1827, it remains one of the most widely applied equations in all of engineering.

The three forms of Ohm’s Law: V = I × R (Voltage = Current × Resistance) I = V / R (Current = Voltage / Resistance) R = V / I (Resistance = Voltage / Current)

Where:

• V = voltage in volts (V), the “electrical pressure” driving current
• I = current in amperes (A), the flow rate of electric charge
• R = resistance in ohms (Ω), opposition to current flow

Power formulas (derived from Ohm’s Law): P = V × I (Power = Voltage × Current) P = I² × R (Power = Current squared × Resistance) P = V² / R (Power = Voltage squared / Resistance)

Worked examples:

Example 1, finding current: A 12V car battery connected to a 6Ω resistor: I = V / R = 12 / 6 = 2 A

Example 2, finding resistance: A 120V outlet powering a device drawing 5A: R = V / I = 120 / 5 = 24 Ω

Example 3, power dissipation: A resistor with 2A flowing through 10Ω: P = I² × R = 4 × 10 = 40 watts (generates significant heat; resistor must be rated ≥40W)

Real-world applications:

• LED resistor sizing: V_supply − V_LED = I × R → R = (V_supply − V_LED) / I_desired
• Wire gauge selection: higher current needs lower resistance wire to prevent voltage drop and overheating
• Fuse sizing: match fuse amperage to circuit’s maximum design current
• Speaker impedance matching: amplifier output should match speaker impedance (4Ω, 8Ω, 16Ω) for maximum power transfer

Limitation: Ohm’s Law applies to ohmic (linear) conductors at constant temperature. Non-linear components like diodes, transistors, and incandescent bulbs (whose resistance changes with temperature) do not strictly obey it.

Where the resistance comes from. At the material level, resistance is governed by the resistivity formula:

R = ρ · L / A

where ρ is the resistivity (an intrinsic property of the material), L is the length of the conductor, and A is its cross-sectional area. Copper (ρ ≈ 1.7×10⁻⁸ Ω·m) and silver (ρ ≈ 1.6×10⁻⁸ Ω·m) are the best common conductors. Aluminum is about 60% as conductive as copper but much lighter, which is why long-distance power transmission lines use aluminum even though copper is “better.” Doubling a wire’s length doubles its resistance; doubling its diameter cuts resistance by 4× (since A scales as diameter squared).

The microscopic version: J = σE. In materials physics, Ohm’s law is written as current density J (A/m²) equals conductivity σ (1/ρ) times electric field E (V/m). This is the same statement as V = IR, just one level deeper. It is the local form, applicable point-by-point inside any material rather than only to a circuit element as a whole.

Resistance changes with temperature. Metallic conductors gain resistance as they heat up: R(T) = R₀ · (1 + α · ΔT), where α is the temperature coefficient (about 0.004 per °C for copper). An incandescent bulb filament can be 10× more resistive when glowing white-hot than when cold, which is one reason the inrush current at switch-on is so much higher than the steady current. Semiconductors do the opposite — their resistance drops with temperature, which is why thermistors are used as temperature sensors and as inrush-current limiters in power supplies.