Parallel Resistor Calculator
Answer
Parallel: 1/Req = 1/R1 + 1/R2 + … + 1/Rn. Two equal resistors in parallel give half the value. Series: Req = R1 + R2 + … + Rn. Enter a list of ohmic values; the calculator returns the equivalent and the conductance.
Calculator
How it works
In parallel every resistor sees the same voltage, so the currents add and the conductances add. Invert the sum of the conductances to get Req. In series the currents are equal and the voltages add, so the resistances add.
Use parallel when you need a value below the parts on hand, or when you want to share power. Use series when you need a higher value or a higher voltage rating. The calculator does both from the same list so you can compare the two networks without retyping.
Parameters used on this page
| Parameter | Value | Source |
|---|---|---|
| Parallel equivalent | 1/Req = Σ 1/Ri | Kirchhoff's current law; each branch sees the same voltage |
| Series equivalent | Req = Σ Ri | Kirchhoff's voltage law; the same current through every part |
| Two-resistor parallel shortcut | Req = R1 R2 / (R1 + R2) | Algebraic rearrangement of the conductance sum |
| Conductance | G = 1/Req (siemens) | Definition of conductance |
| Preferred values | IEC 60063 E12 / E24 / E96 | IEC 60063 |
| Power share in parallel | The smaller resistor takes more current and more power | I = V/R at a shared voltage |
Worked example
Two 10 kΩ resistors in parallel: Req = 5.00 kΩ. A 4.7 kΩ in parallel with a 10 kΩ is 1 / (1/4700 + 1/10000) = 3.197 kΩ. The same three resistors in series would be 24.7 kΩ. If those two 10 kΩ parts share 10 V, each dissipates 10 mW; a 1 kΩ sitting across the same 10 V would dissipate 100 mW by itself.
Pitfalls
- Adding a 'small helper' resistor across a precision divider and changing the ratio more than you meant to.
- Assuming power splits equally in parallel. It splits with conductance: the smaller ohmic value runs hotter.
- Forgetting that a 0 Ω reading in parallel with anything is still 0 Ω.
- Mixing up series and parallel when you only needed a value the shop did not stock. Series raises the value; parallel lowers it.
FAQ
How do I calculate two resistors in parallel?
Req = R1 R2 / (R1 + R2), or invert each value, add the conductances, and invert again. Two 10 kΩ parts become 5 kΩ.
What is the formula for more than two parallel resistors?
Add every 1/Ri, then take the reciprocal. The calculator accepts a comma-separated list.
How do series resistors combine?
Add the ohmic values. Switch the calculator to series mode if that is the network you have.
Can I make a non-standard value from two preferred parts?
Yes. Parallel a larger E-series part with a much larger one to nudge the value down a little, or put two parts in series to step up. Check the tolerance stack.
Related
Sources
- Series and parallel equivalents from Kirchhoff's laws.
- IEC 60063 preferred values when you need to synthesise a target.