Calculator
Formula used
For resistors in parallel, the reciprocals add:
1 / Req = (1 / R1) + (1 / R2) + … + (1 / Rn)
So the equivalent resistance is:
Req = 1 / Σ(1 / Ri)
Conductance is the inverse of resistance: G = 1 / R. For parallel branches, Gtotal = ΣGi.
How to use this calculator
- Enter at least two resistor values.
- Select the correct unit for each resistor.
- Use “Add Resistor” for extra parallel branches.
- Optionally enter a supply voltage for current and power.
- Press Calculate to see results above the form.
Example data
These sample values show typical outputs for a simple three-branch network.
| R1 (Ω) | R2 (Ω) | R3 (Ω) | Voltage (V) | Req (Ω) | Total current (A) | Total power (W) |
|---|---|---|---|---|---|---|
| 100 | 220 | 330 | 12 | 56.8966 | 0.2109 | 2.5309 |
Parallel resistor totals in real circuits
1) Why parallel resistance drops
In a parallel network, every branch shares the same voltage. Adding a branch creates an additional current path, so the total conductance increases. As a result, the equivalent resistance is always lower than the smallest individual resistor, unless a branch is open.
2) Conductance is the cleanest viewpoint
Engineers often compute G in siemens because it adds directly: Gtotal = Σ(1/Ri). This calculator reports both Req and G, which is useful when checking sensitivity to small-value resistors.
3) Typical component data you should consider
Common through‑hole resistors are 1/4 W or 1/2 W, while many surface‑mount parts range from 1/16 W to 1/2 W. Tolerances are often 1%, 5%, or better. Temperature coefficients can be 50–200 ppm/°C for general parts, and much lower for precision types.
4) Current splits by resistance
When you enter an optional supply voltage, the calculator estimates branch currents using Ii = V/Ri. A smaller resistor carries more current. This is critical in shunt sensing and in parallel power resistors, where one branch can hog current if values differ.
5) Power checks prevent overheating
Branch power follows Pi = V·Ii = V²/Ri. For example, 12 V across 100 Ω dissipates 1.44 W, far above a 1/4 W resistor rating. The total power equals the sum of branch power, helping you verify safe operation.
6) Handling shorts and opens
A 0 Ω branch represents a short circuit path. In an ideal model, that drives Req toward zero and current toward infinity for a fixed voltage. An empty input is treated as an open branch and does not affect the total.
7) Measurement and tolerance effects
Real measurements differ from nominal values due to tolerance, lead resistance, contact resistance, and temperature. If you need a worst‑case estimate, compute totals using minimum and maximum resistor values, then compare the resulting Req range.
8) Practical uses in design workflows
Parallel networks appear in pull‑ups/pull‑downs, LED current sharing, divider loading, and impedance matching. Use this tool early in design to confirm targets (like an effective 50 Ω load) and later to document final numbers with CSV or PDF exports.
FAQs
1) Is the equivalent resistance always smaller than the smallest resistor?
Yes for any finite, positive resistor values. Parallel branches increase total conductance, so Req drops below the smallest branch resistance. Empty inputs are ignored and do not change the result.
2) What happens if I enter a zero‑ohm resistor?
A zero value represents an ideal short. The calculator reports Req near zero and conductance as extremely large. With a voltage entered, current and power become unbounded in the ideal model.
3) Why does adding a large resistor change the result only slightly?
A very large resistance contributes little conductance because 1/R is tiny. The total is dominated by smaller resistors, which provide much larger conductance and carry most of the current.
4) Do branch currents always add up to the total current?
With a supplied voltage and finite resistors, yes. The calculator uses Itotal = ΣIi. Small rounding differences may appear if you select a low display precision.
5) Can I use this for AC circuits?
It models ideal resistors, so it works for AC only when impedance is purely resistive. For capacitors or inductors, you must use complex impedance calculations instead of simple resistance.
6) How many resistors can I include?
You can add up to twelve branches using the “Add Resistor” button. Leave any unused branch blank and it will be ignored automatically.
7) What should I export for documentation?
Use CSV for spreadsheets and quick audits. Use PDF for lab notes, reviews, and sharing. Both exports include inputs, equivalent resistance, conductance, and optional current and power results.