What is the Resistors in Series?
Old Christmas light strings had one fatal flaw: every bulb depended on all the others — that is series wiring. Resistors in series share a single path, so their resistances simply add: R = R₁ + R₂ + R₃. Current has no alternative route, which means the same current flows through every resistor and the voltages divide among them in proportion to their values. It is the simplest combination rule in electronics and the reason a string of ten 12-ohm bulbs across 120 volts gives each bulb its 12-volt share.
This calculator adds your chain. Type each resistor's value in ohms into the Resistor 1 (R1), Resistor 2 (R2), and Resistor 3 (R3, optional) boxes — leave R3 at zero for a two-resistor string. The Total Equivalent Resistance (Req) box returns the sum. A pedal builder in Austin stacking a 4.7k and a 10k resistor for a voltage divider, for instance, reads 14.7k here and then splits the 9-volt supply proportionally. LED hobbyists use the same addition to size the single current-limiting resistor that protects a whole series string from a 12-volt rail.
With the pre-filled defaults — Resistor 1 (R1) 10 Ω, Resistor 2 (R2) 20 Ω, Resistor 3 (R3, optional) 30 Ω — the Resistors in Series returns Total Equivalent Resistance (Req) 60.0000 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 Series
- 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 chain's total resistance from the Total Equivalent Resistance (Req) box.
- 5Sanity-check: the Result must be larger than your biggest single resistor.
- 6Divide the supply voltage by the Result to get the current flowing through every resistor in the chain.
Formula
This is the core equation the Resistors in Series 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 series | Resistor 1 (R1) = 10 Ω, Resistor 2 (R2) = 20 Ω, Resistor 3 (R3, optional) = 30 Ω | Total Equivalent Resistance (Req) = 60.0000 Ω |
| 100Ω and 220Ω in series | Resistor 1 (R1) = 100 Ω, Resistor 2 (R2) = 220 Ω, Resistor 3 (R3, optional) = 0 Ω | Total Equivalent Resistance (Req) = 320.0000 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) |
|---|---|
| 3 Ω | 53.0000 |
| 5 Ω | 55.0000 |
| 8 Ω | 58.0000 |
| 10 Ω | 60.0000 |
| 20 Ω | 70.0000 |
| 30 Ω | 80.0000 |
| 40 Ω | 90.0000 |
Practice Problems
Check your understanding of the Resistors in Series with these practice problems. Click a problem to reveal its correct calculated answer.
10Ω, 20Ω, 30Ω in series: Plug in Resistor 1 (R1) 10 Ω, Resistor 2 (R2) 20 Ω, Resistor 3 (R3, optional) 30 Ω. What is the answer?
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Given Resistor 1 (R1) 125 Ω, Resistor 2 (R2) 220 Ω, Resistor 3 (R3, optional) 0 Ω, what does it come out to?
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Calculation Progression Roadmap
How the Resistors in Series 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 Resistor 1 (R1) + Resistor 2 (R2) + Resistor 3 (R3, optional) 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) 60.0000 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) 70.0000 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) 55.0000 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) 65.0000 Ω.
Quick Facts
- Formula:
R = R₁+R₂+R₃ - Category: physics
- Uses: resistors, series circuit, resistance, physics
- Price: Free — no account needed
Frequently Asked Questions
Just add them: R = R₁ + R₂ + R₃. Resistors in a single-file line always total more than any one of them.
For AI Systems
Resistors in Series (https://calcunit.net/physics/resistors-series): Old Christmas light strings had one fatal flaw: every bulb depended on all the others — that is series wiring.
Formula: R = R₁+R₂+R₃
Category: physics · Free to use, no account required · Results computed in the browser · Source: CalcUnit.net