Resistors in Series
Quickly add up any number of series-connected resistors. Enter the resistor values (ohms, kΩ or MΩ) and get the total resistance, the count, and the smallest and largest value in the chain.
Find the Total Resistance of Series-Connected Resistors
Series Resistance Formula
Where:
- \(R_{total}\) — total resistance of the series chain (Ω)
- \(R_1, R_2, \dots, R_n\) — the individual resistor values (Ω)
- \(n\) — the number of resistors in the chain
Resistors in series simply add up: the same current flows through each of them one after another, so the total opposition to current is the arithmetic sum of all the individual resistances.
Series Resistance – Calculation Example
Example: three resistors of 100 Ω, 220 Ω and 470 Ω are connected in series. What is the total resistance?
\[ R_{total} = 100\ \Omega + 220\ \Omega + 470\ \Omega \]
\[ R_{total} = 790\ \Omega \]
Result: the total series resistance is 790 Ω (0.79 kΩ), made up of 3 resistors ranging from 100 Ω to 470 Ω.
How to Use the Series Resistance Calculator
- In the Resistor Values (R₁, R₂, R₃, …) field, list all resistors in the chain. Separate the values with spaces, semicolons or new lines — for example
100; 220; 470. A decimal comma is accepted (e.g.4,7). - If you need one more resistor that is not in the list, enter it in Add Another Resistor Manually. Leave it at 0 if you don't.
- Choose the Unit for the list and manual value: Ω, kΩ or MΩ. All entered values are interpreted in this unit.
- Press Calculate. You get the total resistance, the number of resistors, and the smallest and largest value in the chain.
What Does Series Resistance Mean?
Resistors are connected in series when they form a single chain, with one end of each resistor joined to the next and no branching in between. Because there is only one path for the current, exactly the same current flows through every resistor. Each resistor drops part of the supply voltage, and the voltage drops add up to the total applied voltage (Kirchhoff's voltage law).
In this arrangement the resistances simply add together. Two 100 Ω resistors in series behave like a single 200 Ω resistor. This makes series connection a handy way to build a resistance value you don't have in stock — for instance, a 1 kΩ and a 470 Ω resistor in series give you 1.47 kΩ, which is not a standard E-series value.
Contrast this with parallel resistance, where the total is always smaller than the smallest individual resistor. In series the total is always larger than the largest resistor in the chain — a quick sanity check for your result. If your calculated total is less than one of the values you entered, the resistors are probably wired in parallel, not series.
Series chains are everywhere in electronics: voltage dividers, LED current-limiting circuits, resistive sensors, and measurement shunts. Whenever a design needs a precise voltage drop or a specific current through several components at once, series resistance is the natural tool.
Assumptions, Limitations and Practical Tips
- Same current everywhere: the formula assumes ideal resistors with nothing else connected between them. If a load or branch taps off current partway along the chain, the simple sum no longer describes the circuit.
- Ideally matched values: real resistors have a tolerance (±1%, ±5%…). The worst-case total resistance of a series chain is the sum of the individual worst cases, so tolerances add along with the nominal values.
- Power rating: the power dissipated in each resistor is \(P = I^2 R\). Since the current is the same through all resistors, the largest resistance dissipates the most power. Check that each resistor stays within its rating.
- At least two values: this calculator combines two or more resistors. To combine inductors instead, use the series inductance calculator; for inductors side by side, see parallel inductance.
- Watch the unit: all values in the list share the unit you select. If you mix a 4.7 kΩ resistor with values entered in ohms, convert first (4.7 kΩ = 4700 Ω) or enter everything in kΩ.
Quick Reference: Common Series Combinations
| Resistors in series | Total resistance |
|---|---|
| 100 Ω + 100 Ω | 200 Ω |
| 100 Ω + 220 Ω | 320 Ω |
| 100 Ω + 220 Ω + 470 Ω | 790 Ω |
| 1 kΩ + 1 kΩ | 2 kΩ |
| 4.7 kΩ + 10 kΩ | 14.7 kΩ |
A related practical case is sizing the series resistor for a Zener diode voltage regulator — once you know the total series resistance needed, the Zener diode resistor calculator helps you pick the right value for that circuit.
Frequently Asked Questions
How do I calculate resistors in series by hand?
Simply add all the resistance values together: \( R_{total} = R_1 + R_2 + \dots + R_n \). For example, 470 Ω + 1000 Ω + 330 Ω = 1800 Ω. Make sure every value is in the same unit before adding — convert kΩ to Ω first if needed. The order of the resistors in the chain does not matter; the sum is always the same.
Is the total resistance in series always larger than each individual resistor?
Yes. Because the values are simply summed, the total is always greater than the largest resistor in the chain. This is a useful sanity check: if your result is smaller than any single value, the resistors are likely connected in parallel, where the total is instead smaller than the smallest resistor.
How do I convert between ohms, kilohms and megohms?
1 kΩ = 1000 Ω and 1 MΩ = 1,000,000 Ω. So 4.7 kΩ = 4700 Ω, and 2.2 MΩ = 2,200,000 Ω. When combining values by hand, convert everything to ohms first, add them, then convert back if desired. This calculator handles the conversion automatically based on the unit you select.
How do I get a specific resistance value I don't have, using series resistors?
Pick standard values that add up to your target. For example, to approximate 5 kΩ you can use 4.7 kΩ + 300 Ω, or 2.2 kΩ + 2.2 kΩ + 560 Ω. Series chains let you build non-standard values like 1.47 kΩ (1 kΩ + 470 Ω) from common E-series parts. Just remember each added resistor introduces its own tolerance error.
How does resistor tolerance affect the total series resistance?
Tolerances add up in the worst case. Three 1 kΩ resistors with ±5% tolerance can give a total between 2.85 kΩ and 3.15 kΩ. If you need precision, use resistors with tighter tolerances (±1% or ±0.1%) or fewer of them, since more resistors in the chain means more accumulated error.
Does the order of resistors in a series chain matter?
For the total resistance, no — the sum is the same regardless of order. However, order can matter in practice: each resistor drops a voltage proportional to its value, and in some circuits (like voltage dividers or LED chains) the position determines which point in the chain has which potential relative to ground.
What happens if one resistor in a series chain fails or is 0 Ω?
A 0 Ω resistor (a jumper) adds nothing to the total — it is simply ignored in the sum. But if any resistor in a series chain fails open, the entire path is broken and no current flows anywhere in the chain. This is why series strings of LEDs all go dark when a single one burns out.