Calculation
Rtotal = R1 + R2 + R3
In series, individual resistances add and the same current flows through each part.
Kirchhoffsche Regeln
Series Resistor Calculator
In series, individual resistances add and the same current flows through each part.
MINTSI
02
Result
Select a target and calculate.
Understand the inputs
- Total resistance Rtotal — The equivalent resistance the whole series chain presents from outside – as a result the sum of all individual resistances. The same current flows through every component.
- Resistance R1 — The first resistor in the series chain. Source: printed value/colour code on the part, or measured with an ohmmeter.
- Resistance R2 — The second resistor in the series chain.
- Resistance R3 — An optional third resistor; enter 0 if only two resistors are in series.
Example
10 Ω + 15 Ω + 5 Ω = 30 Ω.
Assumptions and limits
Ideal ohmic resistors without temperature coefficient.
Understand Series Resistor Calculator
This calculator finds the total resistance of a series connection of up to three resistors, or solves for a missing individual resistor. It explains why the same current flows through every resistor in a series circuit — and why, on old Christmas tree light strings, a single burned-out bulb could darken the entire string.
What does this quantity describe?
In a series connection, individual resistances add to give the total resistance: Rtotal = R1 + R2 + R3. The same current flows through every resistor, while total voltage divides across the individual resistors.
Old Christmas tree light strings were wired in series: every bulb sat on the same current path. If a single bulb's filament broke, the current path was interrupted and the whole string went dark — a vivid example of a series connection only working as a whole. Modern light strings avoid this with a bypass circuit built into each bulb.
Formula and variables
Rtotal = R1 + R2 + R3
Rtotal = R1 + R2 + R3R3 = Rtotal − R1 − R2
| Symbol / input | Meaning |
|---|---|
| Total resistance Rtotal | The equivalent resistance the whole series chain presents from outside – as a result the sum of all individual resistances. The same current flows through every component. |
| Resistance R1 | The first resistor in the series chain. Source: printed value/colour code on the part, or measured with an ohmmeter. |
| Resistance R2 | The second resistor in the series chain. |
| Resistance R3 | An optional third resistor; enter 0 if only two resistors are in series. |
Choose the inputs correctly
Enter the known individual resistances; a value of 0 Ω for R3 means only two resistors are in series. The calculator adds the values to the total resistance or solves for a missing individual resistor.
How to use the calculator
Enter the known resistors and read off the total resistance, or enter the total resistance and known individual resistors to find the missing one.
Worked example
Given R1 = 10 Ω, R2 = 15 Ω and R3 = 5 Ω, substitution gives Rtotal = 10 + 15 + 5 = 30 Ω.
Understand the result and units
A total resistance of 30 Ω means the series connection allows the same current at a given voltage as a single 30 Ω resistor. Since the same current flows through all three resistors, total voltage divides proportionally to the individual resistances — the largest resistor takes the largest voltage share.
Resistance is given in ohms (Ω), larger values in kΩ or MΩ. Rtotal = R1+R2+R3 holds regardless of unit choice, as long as all values are converted consistently.
Typical applications
Series connections are used for LED series resistors, simple voltage-divider chains, current limiting in test circuits, and in older light-string and heating-element designs.
Assumptions, limits and common mistakes
The formula applies to ideal, linear resistors. For components with tolerances, temperature dependence, or nonlinear behaviour (e.g. incandescent filaments, whose resistance rises with temperature), the real total resistance deviates from the simple sum.
Common mistake: Do not confuse series with parallel connection: in series, resistances add directly; in parallel, their reciprocals add instead. Also, always assume the same current through every resistor in a series connection, not the same voltage.
Frequently asked questions
Is it current or voltage that's the same through every resistor in series?
Current. Voltage instead divides proportionally to the individual resistances across the components.
Why did the whole old-style light string go dark when one bulb failed?
Because the bulbs were wired in series and a broken filament interrupted the single current path. Modern light strings use a bypass circuit so individual failures don't switch off the rest.
What happens with a fourth resistor added in series?
It simply adds to the existing total; the formula extends with any number of additional terms.