Series Resistor Calculator
Add up to four resistors in series to find total resistance, then — if you know the supply voltage — see the current and the voltage drop across each resistor. A live 3D resistor chain and charts show how series resistance and the voltage divider work.
Reviewed by the ToolNestr Editorial Team — July 2026
Two ideas that make series circuits click
1. Resistors chained end-to-end
Three resistor blocks wired in a single loop. The bars above each block show a fixed example voltage-drop split — the larger the resistor, the taller its bar, since a bigger resistance always claims a bigger share of the supply voltage.
2. R_total grows in a straight line
Each line traces R_total as more equal-sized resistors are added — the more resistors in the chain, the higher the line climbs, always linearly, and a bigger per-resistor value produces a steeper line.
Series resistance graphs
How it works
The core idea in one line: resistors in series share one current path, so their resistances simply add, and the supply voltage divides across them in proportion to each resistance.
Rtotal = R₁ + R₂ + R₃ + ...
series resistances simply add
Vi = V × Ri / Rtotal
voltage divider — drop across resistor i
I = V / Rtotal
Ohm's law — same current through every resistor
Once R_total is known, Ohm's law gives the single current flowing through the whole chain: I = V / R_total. That same current, multiplied by each individual resistance, gives the voltage drop across that resistor — the voltage divider rule V_i = V × R_i / R_total.
Worked example 1 — three resistors with a 9 V supply
Given: R₁ = 100 Ω, R₂ = 220 Ω, R₃ = 330 Ω in series, driven by a 9 V supply. Find R_total, the current, and each voltage drop.
Worked example 2 — four resistors with a 5 V supply
Given: R₁ = 47 Ω, R₂ = 100 Ω, R₃ = 150 Ω, R₄ = 220 Ω in series, driven by a 5 V supply. Find R_total, the current, and each voltage drop.
Sum of drops: 0.45 + 0.97 + 1.45 + 2.13 = 5.00 V, matching the 5 V supply.
Series vs parallel resistor combination
The two basic ways to combine resistors behave oppositely.
| Property | Series | Parallel |
|---|---|---|
| Total resistance formula | R_total = R₁ + R₂ + ... | 1/R_total = 1/R₁ + 1/R₂ + ... |
| Current | Same through every resistor | Same voltage; current splits |
| Voltage | Divides across resistors | Same across every resistor |
| R_total vs individual R | Always larger than the largest R | Always smaller than the smallest R |
| Adding another resistor | Total resistance increases | Total resistance decreases |
Series resistors share one current path; parallel resistors share one voltage across multiple paths.
Where series resistance actually matters
🎄 Old-style Christmas lights
Classic strings wired the bulbs in series, so the same small current ran through every bulb — but if one filament failed, the loop broke and the entire string went dark, which is why modern strings use parallel or shunt-protected wiring instead.
🎚️ Voltage divider circuits
Two or more resistors in series tap off a fraction of a supply voltage at their junction — the basis of potentiometers, sensor bias circuits, and level-shifting between different logic voltages.
🛡️ Current-limiting resistors
A single resistor placed in series with an LED or other component limits the current to a safe value using I = V/R_total, protecting the component from drawing too much current.
Common misconceptions
"Current is different through each resistor in series."
False — in a series loop there is only one path for charge, so the current is identical through every resistor and every point in the loop. It is the voltage, not the current, that divides.
"Adding more resistors in series decreases total resistance."
False — series resistances add directly (R_total = R1 + R2 + ...), so every additional resistor can only increase the total, never decrease it.
"The largest resistor gets the smallest voltage drop."
False — it is the opposite. The voltage divider V_i = V × R_i/R_total means a larger resistance takes a larger share of the supply voltage, since current is fixed and V = IR grows with R.
"Series and parallel formulas are interchangeable."
False — series adds resistances directly; parallel adds their reciprocals (conductances). Mixing up the two formulas gives a total resistance that is completely wrong.
Formula sources & further reading
The formulas here are standard, traceable to:
- • OpenStax, University Physics Volume 2 — Resistors in Series and Parallel (free, peer-reviewed). openstax.org
- • Halliday, Resnick & Walker, Fundamentals of Physics — Chapter 27, Circuits: resistors in series.
- • Serway & Jewett, Physics for Scientists and Engineers — DC circuits and Kirchhoff's rules.
R_total = R1 + R2 + ... for any number of series resistors; voltage divides as V_i = V × R_i/R_total. Results are rounded for display.
How to use this calculator
Enter resistances
Fill in 2 to 4 resistor values in ohms; leave extra rows blank.
Add a supply voltage (optional)
Enter a supply voltage to also see current and each voltage drop.
See it in the chain
Use the sliders to watch the 3D resistor chain and R_total update live.
Related tools
Frequently asked questions
What happens to current in a series circuit?
The current is exactly the same at every point in a series loop, through every resistor, because there is only one path for charge to flow. If 20 mA flows through the first resistor, 20 mA flows through all of them.
What happens to voltage in a series circuit?
The supply voltage divides across the resistors in proportion to their resistance: V_i = V × R_i / R_total. Larger resistors take a larger share of the voltage, and all the individual drops add up to the total supply voltage.
Why does adding a resistor in series always increase total resistance?
Resistors in series are like extra length added to a single narrow pipe — each one adds its own opposition to the same current path, so R_total = R1 + R2 + ... only ever grows as you add terms. There is no way to combine series resistances to get a smaller value.
How is series different from parallel?
In series, resistances add directly and current is shared equally; in parallel, conductances (1/R) add and voltage is shared equally while current splits. Series total resistance is always larger than the largest individual resistor; parallel total resistance is always smaller than the smallest.
How do I find the current once I know R_total?
Apply Ohm's law to the whole chain: I = V / R_total, where V is the supply voltage across the entire series combination. That same current I then flows through every resistor in the chain.