Ohm's Law Calculator
Pick any two of voltage, current, resistance or power, and this calculator solves for the other two using Ohm's Law (V = I × R) and Joule's Law (P = V × I). It supports unit prefixes like millivolts, kilovolts, milliamps and kilohms, shows the three equivalent power forms, and can estimate the running cost of the load over a chosen period.
Formula
Worked example
12 V across a circuit drawing 2 A: R = 12 ÷ 2 = 6 Ω and P = 12 × 2 = 24 W. Run that 24 W load 4 h/day at 0.17 per kWh and it costs about 0.016 per day, roughly 5.96 per year.
How Ohm's Law and Joule's Law work together
Ohm's Law states that the voltage across a resistor equals the current through it multiplied by its resistance: V = I × R. This holds for ohmic (linear) conductors whose resistance stays constant regardless of the applied voltage. Joule's Law adds the power relationship P = V × I, the rate at which energy is converted to heat or work. Together these two laws link four quantities (voltage in volts, current in amperes, resistance in ohms, and power in watts), and once you know any two of the four, the remaining two are fixed. That is why this calculator asks you to choose which pair you know, then solves the rest.
The power triangle: three equivalent forms
Electrical power can be written three equivalent ways for a resistive element: P = V × I, P = I² × R, and P = V² / R. All three give the same answer; which one you reach for depends on the pair of quantities you already have. If you know voltage and current, P = V × I is direct. If you know current and resistance, P = I² × R avoids computing voltage first. If you know voltage and resistance, P = V² / R is the shortcut. This calculator reports the result and shows which form it used so you can follow the arithmetic. One watt equals one joule of energy transferred per second.
Using unit prefixes correctly
Real circuits span many orders of magnitude, so this calculator accepts unit prefixes on every input: millivolts and kilovolts for voltage, milliamperes for current, and kilohms and megohms for resistance. Internally every value is converted to base SI units (volts, amperes, ohms, watts) before the math runs, then converted back for display. This avoids the single most common Ohm's Law mistake, mixing milliamps with volts without converting, which would otherwise inflate or shrink the answer by a factor of a thousand. Always confirm the prefix on each field matches the value you typed.
Estimating running cost
Power tells you the instantaneous draw, but the cost of running a load depends on how long it runs and your electricity tariff. Turn on the cost estimate and enter hours of use per day and a price per kilowatt-hour, and the calculator multiplies power (converted to kilowatts) by the hours to get energy in kilowatt-hours, then by the price to get a daily and annual cost. This is a planning figure: tariffs, standing charges and duty cycles vary, and many loads do not run continuously. It is most accurate for steady resistive loads such as heaters, incandescent lamps and resistive elements.
Limitations and edge cases
Ohm's Law applies strictly to linear, resistive components at a constant temperature; semiconductors, diodes and electrolytic solutions are non-ohmic and do not follow a simple V = IR relationship. Resistance in real conductors rises with temperature, so a resistor carrying large current may have a higher actual resistance than its rated value. The calculator does not model reactive impedance (inductors and capacitors in AC circuits), where the voltage to current relationship also depends on frequency. For AC systems, replace resistance with impedance (Z), use RMS values, and interpret results accordingly.
Ohm's Law and power formula wheel
| You know | Voltage | Current | Resistance | Power |
|---|---|---|---|---|
| V and I | given | given | R = V ÷ I | P = V × I |
| V and R | given | I = V ÷ R | given | P = V² ÷ R |
| V and P | given | I = P ÷ V | R = V² ÷ P | given |
| I and R | V = I × R | given | given | P = I² × R |
| I and P | V = P ÷ I | given | R = P ÷ I² | given |
| R and P | V = √(P × R) | I = √(P ÷ R) | given | given |
Pick the row matching the two quantities you know; the formulas give the other two.
Frequently asked questions
Can I enter power instead of voltage or current?
Yes. This calculator works from any two of the four quantities (voltage, current, resistance or power), not just voltage and current. Choose the pair you know from the 'I know' selector, type the two values, and it solves the remaining two. For example, given power and resistance it finds current from I = sqrt(P / R) and voltage from V = I × R.
What is Ohm's Law in simple terms?
Ohm's Law says the current flowing through a conductor is directly proportional to the voltage across it and inversely proportional to its resistance. Double the voltage and the current doubles; double the resistance and the current halves. It applies to resistive, linear components at constant temperature.
What units and prefixes does it support?
Voltage in millivolts, volts or kilovolts; current in milliamperes or amperes; resistance in ohms, kilohms or megohms; power in watts or kilowatts. Every value is converted to base SI units before the calculation, so you can mix prefixes freely without introducing the classic factor-of-1000 error.
How do I calculate power from Ohm's Law?
Use whichever form matches what you know: P = V × I from voltage and current, P = I² × R from current and resistance, or P = V² / R from voltage and resistance. All three give the same watts for a purely resistive load. The calculator picks the direct form for your inputs and shows the substitution.
How is the running cost worked out?
Energy in kilowatt-hours equals power in kilowatts times hours of use. Cost equals that energy times your price per kilowatt-hour. The calculator reports a daily and an annual figure. It assumes the load draws constant power while on, so it is most accurate for steady resistive loads and a planning estimate for everything else.