About the Ohm's Law Calculator
Ohm's law is the first equation of circuit analysis. It connects the voltage across a component, the current through it and its resistance, and together with the power formula it lets you size resistors, pick fuses, and predict how hot a component will get.
Most real circuits combine several resistors. This calculator also reduces a chain of resistors in series or a group in parallel to a single equivalent resistance, using exact fractions so that, for example, three 10 Ω resistors in parallel give exactly 10/3 Ω, and then works out the current, the voltage drops or branch currents, and the power.
What is Ohm's law?
Ohm's law states that the current I through a conductor is proportional to the voltage V across it, with the resistance R as the constant of proportionality: V = IR. Voltage is measured in volts, current in amperes and resistance in ohms (Ω).
Components that obey this straight-line relationship are called ohmic, which includes ordinary resistors at a steady temperature. Diodes, LEDs and filament lamps are non-ohmic: their resistance changes with current, so V = IR holds at a single operating point but not as a fixed constant.
How to use the Ohm's Law Calculator
- Choose V = IR, P = VI, series or parallel.
- For V = IR or P = VI, leave exactly one value empty.
- For series or parallel, list the resistances separated by commas.
- Optionally add the supply voltage to get currents and power.
- Press Solve circuit and read the result and the steps.
Formulas
Ohm's law
Electric power
Series
Parallel
Two in parallel
Worked example: Voltage: I = 2 A through 5 Ω
A 6 Ω and a 3 Ω resistor are connected in parallel to a 12 V battery. The equivalent resistance is , so the battery supplies A.
Each branch has the full 12 V across it, so the currents are 2 A and 4 A, which add to 6 A. The battery delivers W, split as 24 W and 48 W in the two resistors.
The solution below is generated by the same engine that powers the calculator above.
Final answer
voltage V = 10 V; P = 20 W
How we read your problem
Use the Ohm's law formula, rearranged for the unknown, in SI units.
Step-by-step solution
Formula: Ohm's law
Substitute the known values
Power dissipated
Formulas used
Ohm's law
Power
Ohm's law says the current through a resistor is proportional to the voltage across it: V = IR. It holds for ohmic conductors such as resistors at constant temperature, not for diodes or filament bulbs over wide ranges.
Verification
- Substituted every value back into the formula: both sides agree ✓
Detailed explanation
Series circuits
In series there is only one path, so the same current flows through every resistor. The supply voltage is shared, with each resistor taking a drop proportional to its resistance. That is the principle of a voltage divider, used to scale a sensor signal or set a reference voltage.
With 10, 20 and 30 Ω in series on 12 V, the total is 60 Ω and the current is 0.2 A. The drops are 2 V, 4 V and 6 V, adding back to 12 V as Kirchhoff's voltage law requires.
Parallel circuits
In parallel every resistor sees the same voltage and the current divides between the branches, with the most current through the smallest resistance. Adding another branch always lowers the total resistance and raises the total current, which is why plugging in more appliances on one household circuit can trip the breaker.
The equivalent resistance is always less than the smallest branch. Two equal resistors in parallel give half of one, and n equal resistors give 1/n of one.
Power and practical ratings
Every resistor converts electrical energy to heat at the rate P = I²R. Resistors have power ratings, often 0.25 W for small through-hole parts, and running them above that rating makes them overheat. A 100 Ω resistor carrying 0.1 A dissipates 1 W and needs a larger package.
The power formula also explains appliance currents. A 60 W bulb on a 120 V supply draws 0.5 A, while a 2000 W heater on the same supply draws about 16.7 A, close to the limit of a typical 20 A circuit.
Common mistakes
- Adding parallel resistances directly instead of their reciprocals.
- Forgetting to invert 1/R_T at the end of a parallel calculation.
- Entering milliamps or kilohms without converting.
- Assuming the current splits equally between unequal branches.
- Applying V = IR to a diode or LED as if it were a resistor.
Tips
- Use the shortcut R₁R₂/(R₁ + R₂) for two resistors in parallel.
- Reduce mixed circuits step by step, innermost groups first.
- Check that series voltage drops add up to the supply.
- Check that parallel branch currents add up to the total.
- Type 4.7k for 4700 Ω in the resistor list.
Frequently asked questions
How do I use Ohm's law?
Use V = IR. To find current divide voltage by resistance, to find resistance divide voltage by current, and to find voltage multiply current by resistance.
How do I calculate resistors in parallel?
Add the reciprocals of the resistances and take the reciprocal of the sum. For two resistors, R_T = R₁R₂/(R₁ + R₂).
How do I calculate resistors in series?
Simply add them: R_T = R₁ + R₂ + … . The total is always larger than any single resistor.
How do I calculate electrical power?
Multiply voltage by current, P = VI. You can also use I²R or V²/R when you know the resistance.
Why is the parallel total smaller than each resistor?
Each extra branch gives the current another path, so more current flows for the same voltage, which means a lower equivalent resistance.
What does the unit ohm mean?
One ohm is the resistance that allows one ampere to flow when one volt is applied across it.
Does Ohm's law work for AC circuits?
For pure resistors it holds using RMS values. Capacitors and inductors need impedance, which this calculator does not cover.
Solve a circuit
Pick Ohm's law, power, series or parallel above and enter your values.