Enter resistor values to calculate total resistance
Note: The circuit diagram updates automatically as you add or remove resistors.
Note: The circuit diagram updates automatically as you add or remove resistors.
P = V × I (Power = Voltage × Current)
P = V² / R (Power = Voltage² ÷ Resistance)
P = I² × R (Power = Current² × Resistance)
Series Connection:
Rtotal = R1 + R2 + ... + Rn
Parallel Connection:
1/Rtotal = 1/R1 + 1/R2 + ... + 1/Rn
For two resistors in parallel: Rtotal = (R1 × R2) / (R1 + R2)
| Value (Ω) | Value (kΩ) | Value (MΩ) |
|---|---|---|
| 1.0 | 1.0 | 1.0 |
| 1.2 | 1.2 | 1.2 |
| 1.5 | 1.5 | 1.5 |
| 1.8 | 1.8 | 1.8 |
| 2.2 | 2.2 | 2.2 |
| 2.7 | 2.7 | 2.7 |
| 3.3 | 3.3 | 3.3 |
| 3.9 | 3.9 | 3.9 |
| 4.7 | 4.7 | 4.7 |
| 5.6 | 5.6 | 5.6 |
| 6.8 | 6.8 | 6.8 |
| 8.2 | 8.2 | 8.2 |
| Characteristic | Description |
|---|---|
| Resistance | Opposition to current flow (measured in ohms) |
| Tolerance | Allowable deviation from nominal value (e.g., ±1%, ±5%) |
| Power Rating | Maximum power dissipation (e.g., 1/4W, 1/2W, 1W) |
| Temperature Coefficient | Change in resistance with temperature (ppm/°C) |
Given: 5Ω, 10Ω, 20Ω in series
Note: Series connection results in a total resistance greater than any individual resistor.
Given: 5Ω, 10Ω, 20Ω in parallel
Note: Parallel connection results in a total resistance less than the smallest individual resistor.
Resistors combine in two fundamental ways, and knowing the difference is essential for reading any schematic. In series, resistors sit end-to-end so the same current flows through each, and their resistances simply add: Rtotal = R1 + R2 + …. The total is always larger than any single resistor. In parallel, resistors share the same two nodes so they see the same voltage, and the reciprocals add: 1/Rtotal = 1/R1 + 1/R2 + …. The total is always smaller than the smallest resistor, because you are giving current more paths to flow through.
Series is like adding lengths of a narrow pipe — more restriction, higher resistance. Parallel is like opening extra pipes side by side — more total flow, less restriction. For just two resistors in parallel there is a handy shortcut: Rtotal = (R1 × R2) / (R1 + R2). Two equal resistors in parallel give exactly half their value.
Combining resistors lets you hit values that are not sold as standard parts (E12/E24 series), share power dissipation across several resistors so none overheats, and set precise gains and thresholds. Recognising series and parallel groups is also the first step in simplifying and analysing any resistor network before applying Ohm's law or Kirchhoff's laws.
Building non-standard resistance values, current sharing in high-power loads, ladder networks and attenuators, pull-up/pull-down arrangements, and reducing a complex network down to a single equivalent resistance for analysis.
Do parallel resistors always lower the total? Yes — the equivalent is always below the smallest branch, because current has more routes.
How do series/parallel affect power rating? Splitting a load into several resistors (series or parallel) spreads the heat, so each part dissipates less and can use a smaller wattage rating.
Series resistances add directly: R = R1 + R2 + …. Parallel resistances combine reciprocally: 1/R = 1/R1 + 1/R2 + …, which for two resistors simplifies to the product over the sum.
Two sanity checks catch most arithmetic errors instantly:
If a parallel result comes out bigger than one of its members, the reciprocal has been dropped somewhere. These checks are worth applying every time, because the parallel formula is easy to half-complete.
This is where practical designs fail. In series, every resistor carries the same current, so dissipation P = I2R is proportional to resistance — the largest resistor gets hottest. In parallel, every resistor sees the same voltage, so P = V2/R means the smallest resistor gets hottest.
Putting two 1 kΩ quarter-watt resistors in parallel does give 500 Ω, and it does give half a watt — but only because they are equal. Mixing a 1 kΩ with a 100 Ω gives a combination whose rating is governed almost entirely by the 100 Ω part, which takes ten times the power.
Standard E-series values leave gaps, and two parts in series or parallel can land very close to almost any target. Two equal resistors in parallel halve the value and double the power rating, which is a common way to reach both a non-standard value and a higher dissipation using one part number from stock.
Be aware that tolerance combines too. Two ±5% resistors in parallel give a result whose worst case is still ±5%, since both can err in the same direction — combining parts does not improve accuracy.
Add them directly: R = R1 + R2 + …. The total is always larger than the largest individual resistor, which is a useful check.
Add the reciprocals and invert: 1/R = 1/R1 + 1/R2 + …. For two resistors this reduces to the product divided by the sum, and the result is always smaller than the smallest resistor.
The largest. All carry the same current, and dissipation P = I²R is proportional to resistance.
The smallest. All see the same voltage, and P = V²/R means the lowest resistance takes the most power.
Only if they are equal. Two matched parts share dissipation evenly, but mismatched values do not — the smaller resistance takes a disproportionate share and sets the practical limit.
No. Two ±5% parts can both err in the same direction, so the combination is still ±5% in the worst case.