Ohm's law calculator —
V, I, R & P from any two values.

Field guide

Ohm's law and Joule's law: the foundation of circuit analysis.

What is Ohm's Law?

Ohm's Law states that the current flowing through a conductor is directly proportional to the voltage across it and inversely proportional to its resistance. Named after German physicist Georg Simon Ohm, who published the relationship in 1827, it is expressed as:

Where V is voltage in volts (V), I is current in amperes (A), and R is resistance in ohms (Ω). This single equation is the cornerstone of all DC (direct current) circuit analysis.

Joule's Law (Power)

Joule's Law relates electrical power to current and voltage:

Where P is power in watts (W). Combining Ohm's Law with Joule's Law yields two additional expressions for power:

Together, Ohm's Law and Joule's Law create a complete system of four quantities (V, I, R, P) and twelve formulas. Any two quantities uniquely determine the other two.

The four electrical quantities

Voltage (V): volts

Voltage is the electric potential difference between two points; the "pressure" that drives current through a circuit. A 9 V battery maintains 9 volts between its terminals. Household outlets in the US supply 120 V AC (wall socket) and 240 V for heavy appliances; European outlets supply 230 V.

Current (I): amperes

Current is the rate of charge flow, the number of coulombs passing a point per second. The symbol I comes from the French intensité du courant(current intensity). A typical LED draws 20 mA; a laptop charger draws 3–5 A; a car starter motor may draw hundreds of amperes briefly.

Resistance (R): ohms

Resistance is a material's opposition to current flow, measured in ohms (Ω). It is determined by the material, cross-section, and length of a conductor. Copper wire has very low resistance (~17 nΩ·m resistivity); nichrome wire (used in heating elements) has much higher resistance; insulators have essentially infinite resistance.

Power (P): watts

Electrical power is the rate of energy conversion; how quickly electrical energy is consumed or produced. A 60 W light bulb dissipates 60 joules per second. Power is what you pay for on your electricity bill: a kilowatt-hour (kWh) is 1,000 watts consumed for one hour.

How to use this calculator

Enter any two values with their appropriate units. The calculator automatically determines which formula pair applies:

• V and I known: R = V/I, P = V × I
• V and R known: I = V/R, P = V²/R
• V and P known: I = P/V, R = V²/P
• I and R known: V = I × R, P = I² × R
• I and P known: V = P/I, R = P/I²
• R and P known: V = √(P×R), I = √(P/R)

Results are displayed with SI prefixes (μ, m, k, M, G) for easy reading. For example, 0.000047 A becomes 47 μA; 10,000 Ω becomes 10 kΩ.

Limitations and assumptions

This calculator models ideal DC circuit behaviour. In real circuits:

• Resistance is not constant: it increases with temperature for most conductors (positive temperature coefficient). The nominal resistance is only accurate at the rated temperature.
• AC circuits add reactance: inductors and capacitors oppose alternating current in ways that depend on frequency. Ohm's Law generalises to impedance (Z) in AC analysis, but this calculator handles DC (or purely resistive AC loads) only.
• All values must be positive: the calculator assumes conventional current and positive resistance. Negative values (e.g., from negative-resistance devices) are outside scope.

Practical examples

• LED current limiting resistor: A 5 V supply feeding an LED that needs 20 mA and has 2 V forward voltage. Resistor voltage = 5 − 2 = 3 V. R = V/I = 3/0.02 = 150 Ω. Power = 0.02² × 150 = 60 mW.
• Checking a fuse rating: A 1,200 W heating element on a 240 V supply. I = P/V = 1,200/240 = 5 A. Use a fuse rated above 5 A.
• Speaker impedance matching: An amplifier rated at 50 W into an 8 Ω speaker. V = √(P × R) = √(50 × 8) = √400 = 20 V RMS. I = P/V = 50/20 = 2.5 A peak.