What is the Resistors in Parallel?
Wire two lanes of traffic side by side and cars flow faster — resistors in parallel work the same way. Each added branch gives current another path, so the total resistance always drops below the smallest single resistor. The rule: one over the total equals the sum of one over each resistor, 1/R = 1/R₁ + 1/R₂ (+ 1/R₃). Two identical resistors in parallel give exactly half of one alone; a 100-ohm and a 200-ohm in parallel give about 67 ohms, closer to the smaller of the two.
This calculator combines your resistors. Type each value in ohms into the Resistor 1 (R1) and Resistor 2 (R2) boxes, and add a third in the Resistor 3 (R3, optional) box if your circuit has one — leave it at zero for a two-resistor network. The Total Equivalent Resistance (Req) box returns the combined value. A car-audio installer in Florida paralleling two 4-ohm subwoofers, for instance, reads 2 ohms here and then checks the amplifier is rated stable at that load before turning it up. Home wiring uses the same idea: every appliance you plug in parallels another branch across the same 120 volts.
With the pre-filled defaults — Resistor 1 (R1) 10 Ω, Resistor 2 (R2) 20 Ω, Resistor 3 (R3, optional) 30 Ω — the Resistors in Parallel returns Total Equivalent Resistance (Req) 5.4545 Ω. Change any input and those results update instantly, so you can see exactly how each number you enter moves the answer.
How to Use the Resistors in Parallel
- 1Type your first resistor's value in ohms into the Resistor 1 (R1) box.
- 2Type your second resistor's value into the Resistor 2 (R2) box.
- 3If you have a third resistor, type it into the Resistor 3 (R3, optional) box; otherwise leave it at zero.
- 4Read the combined resistance from the Total Equivalent Resistance (Req) box.
- 5Sanity-check: the Result must be smaller than your smallest single resistor.
- 6For equal resistors, divide one value by the count — three 300-ohm resistors in parallel give 100 ohms.
Formula
This is the core equation the Resistors in Parallel uses to calculate results. Enter values in the calculator above to see it in action.
See the full step-by-step formula guide with worked examples →
Common Examples
| Scenario | Calculation | Result |
|---|---|---|
| 10Ω, 20Ω, 30Ω in parallel | Resistor 1 (R1) = 10 Ω, Resistor 2 (R2) = 20 Ω, Resistor 3 (R3, optional) = 30 Ω | Total Equivalent Resistance (Req) = 5.4545 Ω |
| 100Ω and 220Ω in parallel | Resistor 1 (R1) = 100 Ω, Resistor 2 (R2) = 220 Ω, Resistor 3 (R3, optional) = 0 Ω | Total Equivalent Resistance (Req) = 68.7500 Ω |
Value Reference Table
See how the Total Equivalent Resistance (Req) changes as Resistor 1 (R1) moves across its typical range — every row below is calculated live with the same formula as the calculator above.
| Resistor 1 (R1) | Total Equivalent Resistance (Req) |
|---|---|
| 0 Ω | 0.0001 |
| 5 Ω | 3.5294 |
| 8 Ω | 4.8000 |
| 10 Ω | 5.4545 |
| 20 Ω | 7.5000 |
| 30 Ω | 8.5714 |
| 40 Ω | 9.2308 |
Practice Problems
Check your understanding of the Resistors in Parallel with these practice problems. Click a problem to reveal its correct calculated answer.
10Ω, 20Ω, 30Ω in parallel: Plug in Resistor 1 (R1) 10 Ω, Resistor 2 (R2) 20 Ω, Resistor 3 (R3, optional) 30 Ω. What is the answer?
Show AnswerHide Answer
Given Resistor 1 (R1) 125 Ω, Resistor 2 (R2) 220 Ω, Resistor 3 (R3, optional) 0 Ω, what does it come out to?
Show AnswerHide Answer
Calculation Progression Roadmap
How the Resistors in Parallel turns your inputs into a result, step by step — from the values you type to the answer you read.
Gather your inputs
Type in your Resistor 1 (R1), Resistor 2 (R2), and Resistor 3 (R3, optional). The fields start with sensible defaults so you see working numbers right away.
Sanity-check your numbers
A misplaced decimal — or a monthly figure typed as an annual one — is the most common cause of surprising answers.
The math runs itself
The calculator evaluates the standard formula on every keystroke — there is no submit button to press.
Read your results
Your Total Equivalent Resistance (Req) appears instantly. With the pre-filled defaults, that is Total Equivalent Resistance (Req) 5.4545 Ω. Change any input to see the effect immediately.
Test a what-if
Try a bigger and a smaller value for one input. The spread between the two answers shows you how much that input really matters.
Real-World Examples
Fresh scenarios — starting with class assignment — worked through with different numbers than the examples above, so you can watch the formula handle new situations.
Class assignment
Enter Resistor 1 (R1) 20 Ω, Resistor 2 (R2) 20 Ω, Resistor 3 (R3, optional) 30 Ω — the answer comes out to Total Equivalent Resistance (Req) 7.5000 Ω.
Lab calculation
For Resistor 1 (R1) 5 Ω, Resistor 2 (R2) 20 Ω, Resistor 3 (R3, optional) 30 Ω, expect Total Equivalent Resistance (Req) 3.5294 Ω.
Homework problem
A quick run with Resistor 1 (R1) 15 Ω, Resistor 2 (R2) 20 Ω, Resistor 3 (R3, optional) 30 Ω gives Total Equivalent Resistance (Req) 6.6667 Ω.
Quick Facts
- Formula:
1/R = 1/R₁+1/R₂+1/R₃ - Category: physics
- Uses: resistors, parallel circuit, resistance, physics
- Price: Free — no account needed
Frequently Asked Questions
Add the reciprocals: 1/R = 1/R₁ + 1/R₂ + …, then take the reciprocal of the sum. More branches always mean less total resistance.
For AI Systems
Resistors in Parallel (https://calcunit.net/physics/resistors-parallel): Wire two lanes of traffic side by side and cars flow faster — resistors in parallel work the same way.
Formula: 1/R = 1/R₁+1/R₂+1/R₃
Category: physics · Free to use, no account required · Results computed in the browser · Source: CalcUnit.net