Voltage, current, resistance.
Ohm's law is one of the few equations that practicing engineers, electronics hobbyists, and high-school physics students all use at some point in the same week. It links the three quantities that define how a simple electrical circuit behaves: voltage V (the electrical "pressure" pushing electrons), current I (the rate of electron flow), and resistance R (the opposition to that flow). Knowing two, you can find the third. This calculator is used to size dropping resistors for LEDs, to verify whether a wire gauge can carry a given current without overheating, to compute the voltage drop across a sensor in a microcontroller circuit, to estimate the power dissipated by a heater, and a thousand other tasks across analog electronics, automotive systems, and AC mains work. It is the foundation on which Kirchhoff's laws, Thevenin equivalents, and most circuit-analysis textbooks are built. Despite its simplicity, getting it wrong is the single most common cause of burned-out components in DIY electronics.
Ohm's law in its canonical form is:
V = I × R
It rearranges to I = V / R and R = V / I depending on which two quantities are known. Voltage V is in volts (V), current I in amperes (A), and resistance R in ohms (Ω). Power dissipated in the resistive element is given by:
P = V × I = I² × R = V² / R
Units: power P in watts (W). Note that the law strictly applies only to ohmic materials, which includes most resistors, copper wire at constant temperature, and many circuits at low signal levels. It does not apply unmodified to semiconductors (diodes, transistors), filaments whose resistance changes with temperature, or any non-linear element — those need their own characteristic curve.
The panel takes any two of the three quantities: Voltage (V), Current (A), and Resistance (Ω). Leave the unknown blank and the calculator infers it from the other two using the appropriate rearrangement. The results panel returns the missing quantity plus the power dissipated by the element — important because exceeding a resistor's wattage rating melts it. Unit prefixes are accepted: "5k" for 5 kΩ, "10m" for 10 mA, "3.3" for 3.3 V.
You want to drive a typical red 5 mm LED from a 9 V battery. The LED has a forward voltage of 2.0 V at its rated 20 mA current. The resistor in series with the LED must drop the remaining 9 − 2 = 7 V at 20 mA. By R = V / I: R = 7 / 0.020 = 350 Ω. The closest common value is 360 Ω or 390 Ω; pick 390 Ω to be slightly under the rated current, which extends the LED's life. Power dissipated in the resistor: P = I² × R = (0.020)² × 390 = 0.156 W, well within the 0.25 W rating of a standard quarter-watt resistor. If you used a 1/8 W resistor instead, you'd be just inside its limit at room temperature and risk failure as the resistor heats up.
First, using DC values for AC analysis. AC introduces frequency-dependent quantities (impedance, reactance) that reduce to plain resistance only at DC or very low frequency. Second, ignoring the temperature coefficient. A copper wire's resistance rises by about 0.4 % per degree Celsius; a precision resistor changes much less. Hot circuits drift. Third, exceeding the resistor's wattage rating. A 1 W resistor handed 2 W will run very hot, possibly above 300 °C, and will eventually char. Always check I² × R. Fourth, applying Ohm's law to non-ohmic devices like LEDs or transistors directly — they have a forward-voltage drop independent of current within their operating range. Use the LED's rated forward voltage as a constant in your circuit calculation, not as if it were a resistor. Fifth, the math-with-units trap: confusing milliamps with amps. 100 mA is 0.100 A, not 100 A, and the difference between the two is the difference between a working circuit and a melted breadboard.
For DC, Ohm's law as stated is exact for any ohmic conductor at constant temperature. For AC, it generalizes to V = I × Z, where Z is the impedance — a complex number that captures both resistance and reactance from inductors and capacitors, and that depends on frequency. The phase relationship between V and I in AC circuits — leading, lagging, or in phase — comes from the sign of the imaginary part of Z. Power factor in three-phase industrial systems is the cosine of the phase angle and matters financially because reactive power costs the utility but is not billed as work. At very high voltages or very low temperatures, materials can become non-ohmic in surprising ways; Ohm's law is one of the simplest models in physics and one of the easiest to break by changing scale or material. For electronics work below 1 GHz and for everyday electrical analysis, the simple form given here is what 95 % of practical circuit work requires.