The formula this page uses
R_total = R₁ + R₂ + R₃ I = V / R_total Vₙ = I · Rₙ
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Series Circuit Calculator
Solve series circuit problems with clear steps, notation, and a final check.
Ω
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Evaluate the governing formula locally in your browser. Define each known quantity once, then change values to test another case instantly.
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Applied math
Series Circuit Calculator explained
The short version
- In a series circuit there is only one path, so the same current flows through every part.
- Resistances simply add up, and the supply voltage gets shared out in proportion to them.
- Break the loop anywhere and the whole circuit stops, which is why old fairy lights all died together.
What each part means
SymbolWhat it means
V — Supply voltageThe battery or source, in volts.
Rₙ — Each resistanceIn ohms. Convert kΩ to Ω before adding: 4.7 kΩ = 4700 Ω.
I — CurrentIn amps, and identical at every point in the loop.
Vₙ — Voltage across one resistorAlso called the voltage drop. All the drops add back to V.
Show your work: a full example
- The circuita 12 V battery in series with 100 Ω, 220 Ω and 330 Ω
- Add the resistances100 + 220 + 330 = 650 Ω
- Current, the same everywhereI = 12 ÷ 650 = 0.01846 A, or 18.46 mA
- Voltage across the 100 Ω0.01846 × 100 = 1.846 V
- Voltage across the 220 Ω0.01846 × 220 = 4.062 V
- Voltage across the 330 Ω0.01846 × 330 = 6.092 V
- Check the drops add to the supply1.846 + 4.062 + 6.092 = 12.00 V ✓, and total power is 12 × 0.01846 = 0.2215 W
A second, different case
- A different case: a two-resistor voltage divider9 V across 4.7 kΩ in series with 10 kΩ
- Total resistance in ohms4700 + 10000 = 14700 Ω
- Current9 ÷ 14700 = 0.0006122 A, or 0.612 mA
- Output taken across the 10 kΩ0.0006122 × 10000 = 6.122 V
- The divider shortcut gives the same thing9 × 10000 ÷ 14700 = 6.122 V
- Power in the 4.7 kΩ resistorI²R = (0.0006122)² × 4700 = 0.00176 W, about 1.8 mW
- Read itthe bigger resistor takes the bigger share of the voltage, 6.122 V against 2.878 V
Copy-ready example
a 12 V battery in series with 100 Ω, 220 Ω and 330 Ω
The circuit
Questions about the Series Circuit Calculator
Why is the current the same everywhere in a series circuit?
Because there is only one path and charge cannot pile up. Every electron that leaves the battery has to pass through all three resistors in turn, so the same 18.46 mA is measured at any point in the loop.
How do I check my answer quickly?
Add the individual voltage drops. They must total the supply voltage exactly, which is Kirchhoff's voltage law. Here 1.846 + 4.062 + 6.092 = 12.00 V, so the current must have been right.
What is a voltage divider used for?
Getting a smaller voltage from a bigger supply, for example feeding a 3.3 V sensor from a 9 V battery. The output is V × R₂/(R₁ + R₂), which is 6.122 V for the pair above.
Does the order of the resistors matter?
No. Swapping the 100 Ω and the 330 Ω changes nothing about the total, the current or any individual drop. Only the sum matters in a series loop.