Free resistor calculator
Enter your resistor values and pick series or parallel to get the equivalent resistance — series values add up, parallel always comes out below the smallest — updated live, as you type.
On this page12 sections
Series: R_total = R1 + R2 + … Parallel: 1/R_total = 1/R1 + 1/R2 + …
Results are estimates. Consult a professional.
How the series and parallel resistor calculator works
This series and parallel resistor calculator combines any number of resistor values into one equivalent resistance. Pick a mode, type your resistor values in ohms, and it returns the total the rest of the circuit actually sees. Resistors in series simply add up. Resistors in parallel combine reciprocally, and the total always comes out lower than the smallest resistor in the group. Those two rules cover almost every resistor network you will build on a breadboard or a PCB.
Series resistance: the values add up
Resistors in series sit end to end on a single path, so the same current flows through every one of them. Each resistor drops part of the supply voltage, and those drops add up to the total. Because the current has only one route, the resistances simply sum — there is no shortcut to remember and no trap to fall into.
Put a 100 Ω and a 220 Ω resistor in series and the total is 100 + 220 = 320 Ω. Add a third 1 kΩ resistor and it becomes 1320 Ω. Series is how you build a larger resistance from smaller standard parts, and it is the basis of a voltage divider, where two series resistors split a voltage in proportion to their values.
Parallel resistance: the total is less than the smallest
Resistors in parallel sit side by side between the same two points, so each one gives the current an extra path to flow through. More paths mean less total opposition, which is why the parallel total is always smaller than the smallest resistor in the group — not somewhere in the middle. This catches people out constantly, so it is worth committing to memory.
For exactly two resistors, the "product over sum" shortcut is fastest: R = (R1 × R2) / (R1 + R2). For three or more, add the reciprocals and invert. A special case worth knowing: two equal resistors in parallel give exactly half their value — two 100 Ω resistors in parallel make 50 Ω, and three equal resistors in parallel give one third.
A worked example for series and parallel
Sam has a 100 Ω and a 220 Ω resistor and wants to know what the pair adds up to in each configuration before soldering them in.
In series
The same current runs through both, so the values add: R = 100 + 220 = 320 Ω. That is the equivalent series resistance.
In parallel
Each resistor offers its own path, so use product over sum: R = (100 × 220) / (100 + 220) = 22000 / 320 = 68.75 Ω. As expected, 68.75 Ω is below the smaller resistor (100 Ω), confirming the parallel rule.
Using combinations to hit non-standard resistance values
Resistors are sold in fixed steps called the E-series, so the exact value you calculated from Ohm's law often does not exist as a single part. Combining standard resistors gets you there. Need 150 Ω from a 100 Ω kit? Two 100 Ω in parallel give 50 Ω, then one more 100 Ω in series gives 150 Ω. Need 68.75 Ω? Put 100 Ω and 220 Ω in parallel. The same trick sizes the current-setting resistor for an LED series resistor when the ideal value falls between stock parts.
Knowing the standard values helps you reach for the right starting parts. The E12 series (10% tolerance) and E24 series (5% tolerance) are the two you will meet most often in hobby kits and through-hole designs.
| Series | Tolerance | Standard values per decade (×1, ×10, ×100, ...) |
|---|---|---|
| E12 | 10% | 10, 12, 15, 18, 22, 27, 33, 39, 47, 56, 68, 82 |
| E24 | 5% | 10, 11, 12, 13, 15, 16, 18, 20, 22, 24, 27, 30, 33, 36, 39, 43, 47, 51, 56, 62, 68, 75, 82, 91 |
Each value repeats in every decade — 47 means 4.7 Ω, 47 Ω, 470 Ω, 4.7 kΩ and so on. Standard E-series values are defined in IEC 60063. The narrower E48/E96 series exist for 2% and 1% precision resistors.
Series vs parallel: a quick comparison
The two arrangements behave as mirror images. Series shares current and adds voltage drops; parallel shares voltage and adds currents. This table is the at-a-glance summary.
| Property | Series | Parallel |
|---|---|---|
| Wiring | End to end, one path | Side by side, multiple paths |
| Total resistance | R1 + R2 + ... (adds up) | Less than the smallest |
| Same across all parts | Current | Voltage |
| Adds across all parts | Voltage drops | Currents (branch currents) |
| Two equal resistors R | 2R | R / 2 |
| Typical use | Voltage division, current limiting | Current sharing, higher power handling |
Both follow from Kirchhoff's laws — series resistors share current, parallel resistors share voltage.
Common mistakes with resistor combinations
- Expecting a parallel total to be the average. 100 Ω ∥ 220 Ω is 68.75 Ω, not 160 Ω. The total is always below the smallest resistor, never between the two.
- Forgetting to invert. The parallel formula gives 1/R first. Adding 1/100 + 1/220 = 0.01455 is not the answer — you still have to take the reciprocal to get 68.75 Ω.
- Using product-over-sum for three or more resistors. (R1 × R2) / (R1 + R2) only works for exactly two. For three or more, add all the reciprocals and invert, or combine two at a time.
- Treating a mixed network as one mode. Real circuits often mix series and parallel. Solve the parallel sub-groups first, then add the series sections — this calculator handles one mode at a time, so reduce the network in stages.
- Ignoring units. Enter every value in the same unit. Mixing 1 kΩ with 470 (meaning 470 Ω) without converting throws the result off by a factor of 1000.
Power rating and tolerance — what the math leaves out
The equivalent-resistance math is exact: for the values you enter, the series sum and the parallel reciprocal are computed to full floating-point precision. Two real-world factors sit outside that calculation, and both matter when you move from the calculation to the soldering iron.
Tolerance
Real resistors are not exact. A 100 Ω E24 part with a 5% tolerance is guaranteed only to fall between 95 Ω and 105 Ω; E96 precision parts hold 1%, and cheaper E12 parts can drift 10%. Combine several and the tolerances stack, so a calculated 320 Ω series chain built from 5% parts may land anywhere within roughly ±5% of that figure. Where the exact value matters, measure the finished network with a multimeter or use 1% resistors.
Power rating
Each resistor dissipates power P = I²R, and a 1/4 W part will overheat if you push more through it. In series every resistor carries the full current, so the most stressed part sets the limit. In parallel the current splits between branches, which is one reason designers wire resistors in parallel — to spread heat across several parts and handle more power than a single resistor could. Check the dissipation in each resistor with Ohm's law before trusting a combination at higher currents.
Standard resistor values and their tolerance bands are defined by the IEC 60063 preferred-number (E-series) standard; the underlying resistance theory and how series and parallel combinations are derived is set out in HyperPhysics (Georgia State University).Frequently asked questions about the free resistor calculator
About this Resistor (series / parallel) calculator
This resistor calculator runs entirely in your browser — nothing you enter is sent anywhere. Type any number of resistor values in ohms, choose series or parallel, and it returns the equivalent resistance: series values add directly, while parallel values combine reciprocally and always total less than the smallest resistor.
Built for students, hobbyists and engineers reducing resistor networks or hitting a non-standard value from standard parts. Browse more electronics calculators or see the full calculator library.