Ohm's Law Calculator

How Does the Formula Work?

Ohm's Law is the cornerstone of electrical engineering, expressing the relationship between voltage, current, and resistance in a circuit. Named after German physicist Georg Simon Ohm, who published his findings in 1827, the law states that the current flowing through a conductor is directly proportional to the voltage across it and inversely proportional to the resistance. Combined with the power equation, this calculator solves for any two unknowns from the four fundamental electrical quantities.

The calculator takes exactly two of the four values: voltage in volts (V), current in amperes (A), resistance in ohms (Ω) or power in watts (W). It then works out the other two with the matching pair of formulas, which covers all six pairs: V+I, V+R, V+P, I+R, I+P and R+P. If a third field is filled, it asks you to clear it rather than silently choosing two.

Understanding the Four Electrical Quantities

Voltage (V) is the push that moves charge around a circuit, much like pressure in a water pipe. Current (I), measured in amperes, is how much charge passes each second. Resistance (R), in ohms (Ω), is how strongly the path holds that flow back: copper lets it through easily, rubber barely at all. Power (P), in watts, is the rate at which energy is used, and an electricity bill counts energy in kilowatt-hours, power multiplied by time. As a quick example, a 15 A circuit at 120 V reaches its rating at 1,800 W, because P = V × I = 120 × 15.

Adding Up Loads

A simple everyday use of P = V × I is checking whether appliances can share a circuit. A 20 A circuit at 120 V tops out at 2,400 W. A 1,200 W microwave on its own leaves 1,200 W spare, but adding a 1,500 W space heater brings the total to 2,700 W, more than the circuit is rated for. The same law sizes the resistor in front of an LED: for an LED rated at 20 mA and 3.3 V on a 10 V supply, the resistor has to drop the remaining 6.7 V, so R = 6.7 / 0.02 = 335 Ω.

Wire Sizing and Circuit Design

The National Electrical Code (NEC) requires wire sizing based on current capacity. 14 AWG wire handles 15 amps, 12 AWG handles 20 amps, and 10 AWG handles 30 amps. Ohm's Law turns an appliance's power into the current it draws: a 3,600 W water heater on a 240 V circuit draws I = 3600 / 240 = 15 A, the full rating of 14 AWG. Wire has resistance of its own, about 2.5 Ω per 1,000 feet for 14 AWG copper at 20 °C, so a long run loses voltage along the way (V-drop = I × R-wire). On a 100-foot run the current travels 200 feet of wire, out and back, which is 0.5 Ω; 15 A × 0.5 Ω = 7.5 V, or 6.25 percent of 120 V, exceeding the NEC's recommended 3 percent maximum. Moving up to 12 AWG, about 1.6 Ω per 1,000 feet, still loses 4.8 V (4 percent); 10 AWG, about 1 Ω per 1,000 feet, brings the drop to roughly 3 V, or 2.5 percent.

Battery and Solar System Sizing

Off-grid designs use the same arithmetic. A 12 V battery bank feeding a 600 W inverter supplies 50 A (I = 600 / 12). Four hours of that is 200 amp-hours, and if you plan to use only half of the bank's capacity, the bank needs 400 Ah; inverter losses would push both figures up. Panels wired in series add their voltages, while panels in parallel add their currents, which is why V = I × R sits behind string sizes, fuse ratings and wire gauges.

Electrical Safety

Ohm's Law also shows why electric shock is dangerous. OSHA's appendix on shock hazards (29 CFR 1910.269, Appendix C) works with a total body resistance of 1,000 Ω when it sets current limits. At 120 V, that resistance lets I = 120 / 1,000 = 120 mA flow. The same appendix estimates the current that can set off ventricular fibrillation as 116 mA divided by the square root of the shock's length in seconds, about 116 mA for one second; below 6 mA, it says, a worker can still release the conductor. A ground-fault circuit interrupter (GFCI) cuts the power within milliseconds when current leaks to ground. Heat follows the same rules: by P = I² × R, doubling the current through a wire quadruples the heat it gives off.

Electronics and Maker Projects

Small electronics circuits lean on the same formula. For an LED on a 5 V supply with a 2 V forward voltage and a target of 20 mA, the resistor is (5 - 2) / 0.02 = 150 Ω. A 10 kΩ pull-up resistor on a 3.3 V line passes only 0.33 mA, little enough to waste almost no power while still holding the input at a clear logic level. A 5 Ω heating wire on 12 V gives off P = 12² / 5 = 28.8 W. A voltage divider made of R1 and R2 scales a signal by R2 / (R1 + R2), which is how a sensor's output is brought into an input's range.