What this calculator does
Find the total resistance of a group of resistors, and see how much current, voltage and power each one handles. Resistors are rarely used one at a time. Chains and banks of them set currents, share out voltage and make values you can't buy off the shelf.
This calculator takes a list of resistor values. They can be wired end to end (series) or side by side (parallel). It finds the single resistance that would behave the same way. That's called the equivalent or total resistance.
Add a supply voltage and it goes further. It uses Ohm's law (current equals voltage divided by resistance) on the whole group. That gives the current drawn and the total power. Then it breaks those down resistor by resistor. You can see which part carries the most voltage, current or heat. The table helps you check power ratings before you solder anything. A comparison figure shows what the same parts would give in the other arrangement.
Where it's used
Why this math matters outside the classroom:
- Series circuits. Three 100 Ω resistors in series add to 300 Ω, so a 12 V supply drives 0.04 A through all of them.
- Parallel values. Two 100 Ω resistors in parallel give 50 Ω, which is how technicians make a value they don't have on hand.
- Home wiring. Household outlets are wired in parallel so each appliance gets the full supply voltage, and each one added lowers total resistance.
- Power ratings. Hobbyists check each resistor's share of the power so none runs past its 0.25 W rating.
How to use it
- Choose Series or Parallel to match how the resistors are connected.
- Type the resistor values in ohms, separated by commas or spaces. For kilo and mega values, use e-notation: 4.7e3 for 4.7 kΩ, 1e6 for 1 MΩ.
- If you like, enter the voltage across the whole group. Leave it blank if you only need the total resistance.
- Read the total resistance. Then check the table for each resistor's voltage, current and power.
What the inputs mean
- Resistor values (Ω)
- Every value is in ohms and must be greater than zero. A zero-ohm link in series adds nothing. In parallel, it would short out the whole bank, so it isn't accepted. You can combine up to 50 values.
- Supply voltage (optional)
- The voltage across the whole group, such as a battery or bench supply. It's treated as a perfect source, so the supply's own internal resistance is ignored.
Formula and method
Series: R = R₁ + R₂ + … + Rₙ Parallel: 1/R = 1/R₁ + 1/R₂ + … + 1/Rₙ Two in parallel: R = R₁ × R₂ ÷ (R₁ + R₂) Whole group: I = V ÷ R, P = V × I Series part k: Vₖ = I × Rₖ, Pₖ = I² × Rₖ Parallel part k: Iₖ = V ÷ Rₖ, Pₖ = V² ÷ Rₖ
R is the total resistance in ohms (Ω), and R₁, R₂ … Rₙ are the separate resistors. Rₖ stands for any one of them. V is the supply voltage in volts, I the current in amps and P the power in watts. Vₖ, Iₖ and Pₖ are the voltage, current and power for resistor k alone.
In series there's only one path. So the same current flows through every resistor, and the voltage drops add up. Each drop is I × Rₖ, so the resistances add. The total is always larger than the largest part.
In parallel, every resistor sits across the same two points. So each one gets the full voltage, and the currents in the branches add. Each branch passes a current in proportion to 1/Rₖ, called its conductance. So it's the reciprocals (1 divided by each value) that add. The total is always smaller than the smallest resistor. For exactly two resistors, this becomes the well-known 'product over sum' shortcut.
Once the total is known, Ohm's law gives the current drawn from the supply. Series parts share that current and split the voltage in proportion to their resistance. Parallel parts share the voltage and split the current in inverse proportion: the smaller the resistor, the more current it takes.
Worked example
Three resistors of 100 Ω, 220 Ω and 470 Ω are connected in series across a 12 V supply.
- Total resistance: R = 100 + 220 + 470 = 790 Ω.
- Current: I = 12 ÷ 790 = 0.0151898734 A, about 15.19 mA, flowing through all three.
- Total power: P = 12 × 0.0151898734 = 0.182278481 W.
- The 470 Ω resistor drops 0.0151898734 × 470 ≈ 7.139 V and gives off about 0.1084 W as heat, the most of the three.
- Wired in parallel instead, the same three parts would give about 59.98 Ω.
Result: The string is 790 Ω, draws about 15.19 mA and gives off about 0.1823 W in total.
Understanding the result
Compare each resistor's power with its rating. Common through-hole parts are rated 0.25 W or 0.5 W. Running them near the limit makes them hot and shortens their life, so leave some room to spare.
In a series string, the largest resistor takes the largest share of the voltage and power. In a parallel bank, the smallest resistor takes the largest share of the current and power.
If the total current is more than your supply can deliver, its voltage will sag. Then the real figures will be lower than shown.
Assumptions and limitations
- Resistors are ideal and ohmic: each value stays the same whatever the voltage, current or temperature.
- The supply is a perfect voltage source, and connecting wires have no resistance.
- For AC, values are RMS (the steady DC equivalent), and the circuit contains only resistance.
- It only handles groups that are all series or all parallel. For a mixed network, work in stages. Combine an inner group first, then enter that result as one value in the next stage.
- Real resistors have a tolerance (often ±1% or ±5%). So measured totals differ from the value printed on the parts.
- For most materials, resistance rises with temperature. So a resistor running hot will drift from its marked value.
Frequently asked questions
Why is parallel resistance always smaller than the smallest resistor?
Each resistor you add in parallel opens another path for current. With more paths, more current flows for the same voltage, and that's exactly what a lower resistance means. Adding even a very large resistor in parallel lowers the total slightly.
What is the quick formula for two resistors in parallel?
Multiply them and divide by their sum: R = R₁R₂ ÷ (R₁ + R₂). For 100 Ω and 220 Ω, that's 22,000 ÷ 320 = 68.75 Ω. Two equal resistors in parallel give half of one, and n equal resistors give one nth.
How do I solve a mixed series-parallel circuit?
Work from the inside out. Combine any group that's all parallel or all series, and swap it for its single equivalent value. Repeat until one resistance remains. You can run this calculator once for each stage.
Can I make a resistor value I don't have?
Yes. Series combinations reach values above your parts, and parallel combinations reach values below them. Two 1 kΩ resistors in parallel make 500 Ω; a 1 kΩ and a 220 Ω in series make 1.22 kΩ. Check that each part's power rating is still high enough.
How this calculator is checked
Method: Kirchhoff's voltage and current laws for series and parallel resistors, with Ohm's law (V = IR) and P = VI. The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-18. Found a problem? Tell us.
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