How to calculate resistors in series
Resistors are in series when they sit one after another in a single path, so the same current flows through every one of them. This calculator works out the total (equivalent) resistance of any number of series resistors and, for the source voltage you enter, the current, the voltage across each resistor and the power it turns into heat. The circuit drawing follows every value you type; past eight resistors it shows the first few and the last two, with a ⋯ element standing for the rest.
How to use the series resistor calculator
- Enter the source voltage. It is shared out across the resistors. Leave it at 0 V if you only need the total resistance.
- Choose how many resistors with the + and − buttons or by typing the number: 2, 10, 100, anything up to 500.
- Type each resistance. Write values the way they appear on parts and schematics: 4700, 4.7k,
4k7,470R, 2.2M or2M2. A lower-case m means milli and a capital M means mega. - Read the results under the drawing: total resistance, the current, the total power and the largest voltage drop. Click a resistor in the drawing for its own calculation.
- Open the Calculation tab for the maths written out step by step, or the Results table for each resistor's voltage drop, share, power and a suggested power rating. Copy results puts everything on the clipboard.
The series resistance formula
In a series circuit one current flows through everything, and the voltage drops add up to the source voltage: V = I R1 + I R2 + … + I Rn = I (R1 + R2 + … + Rn). So the resistances simply add:
Req = R1 + R2 + R3 + R4
Your 4 resistors Req = 1 kΩ + 2.2 kΩ + 4.7 kΩ + 10 kΩ = 17.9 kΩ.
The total is always larger than the largest single resistor: every resistor you add makes the path harder for the current.
Equal resistors
Req = R × n
Two 10 kΩ resistors give 20 kΩ, and five 100 Ω resistors give 500 Ω. Equal resistors also share the voltage and the power equally.
Current, voltage drops and the voltage divider
The current is the source voltage over the total resistance, and it is the same in every resistor. Each resistor then drops a voltage in proportion to its resistance:
I = V / Req Vk = I × Rk = V × Rk / Req
That last form is the voltage divider: the biggest resistor takes the biggest share of the voltage. Two resistors in series are the usual way to make a smaller voltage from a larger one, for example to read a 12 V battery with a 5 V microcontroller. The power in each resistor is Pk = I² × Rk.
Your circuit, step by step
This section follows the values panel: 4 resistors across 12 V.
- Add the resistances: Req = 1 kΩ + 2.2 kΩ + 4.7 kΩ + 10 kΩ = 17.9 kΩ, above the largest resistor, R4 = 10 kΩ, which alone is 56% of the total.
- Find the current: I = V / Req = 12 V / 17.9 kΩ = 670.4 µA, the same through every resistor.
- Each resistor drops V = I × R and heats up by P = I² × R:
| Resistor | Voltage V = I × R | Power P = I² × R | Share of V |
|---|---|---|---|
| R1 = 1 kΩ | 670 mV | 449 µW | 5.6% |
| R2 = 2.2 kΩ | 1.47 V | 989 µW | 12% |
| R3 = 4.7 kΩ | 3.15 V | 2.11 mW | 26% |
| R4 = 10 kΩ | 6.7 V | 4.49 mW | 56% |
| Total: 17.9 kΩ | 12 V | 8.04 mW | 100% |
Worked example: 4.7 kΩ, 10 kΩ and 22 kΩ at 12 V
Add the resistances: 4.7 kΩ + 10 kΩ + 22 kΩ = Req = 36.7 kΩ. The current is 12 V / 36.7 kΩ = 327 µA through all three, and the circuit uses 3.92 mW in total.
| Resistor | Voltage drop | Share of 12 V | Power |
|---|---|---|---|
| R1 = 4.7 kΩ | 1.54 V | 13% | 502 µW |
| R2 = 10 kΩ | 3.27 V | 27% | 1.07 mW |
| R3 = 22 kΩ | 7.19 V | 60% | 2.35 mW |
| Total: 36.7 kΩ | 12 V | 100% | 3.92 mW |
The voltage drops add up to the 12 V of the source, which is a quick way to check any series calculation.
Good to know
- The total is always above the largest resistor. Adding any resistor in series raises the total.
- One break stops everything. If any series resistor fails open, no current flows anywhere in the loop, which is why old Christmas lights all went out together.
- A much larger resistor dominates. 1 MΩ in series with 100 Ω is still about 1 MΩ, and it takes almost all of the voltage.
- Current limiting. A series resistor is how an LED gets its current: R = (Vsupply − VLED) / ILED.
- Mind the power rating. Choose resistors rated for at least about twice the power they dissipate; the Results table suggests a standard rating for each one.
Resistor colour codes in the drawing
Each resistor in the drawing carries the colour bands its value would have. Values with two significant digits, such as 4.7 kΩ (yellow, violet, red), get four bands: two digits, a multiplier and a gold 5% tolerance band, on a beige body. Values that need three digits, such as 4.12 kΩ, get five bands with a brown 1% tolerance band, on a blue body like metal-film resistors. Values needing more digits, or below 0.1 Ω, are drawn plain grey because no standard colour code shows them.
Questions
Is the current the same in every series resistor?
Yes. There is only one path, so whatever current leaves the source passes through each resistor in turn and returns to the source.
Which resistor gets the most voltage?
The largest one. Voltage drops are I × R with the same I everywhere, so they are in proportion to the resistances; a resistor with half the total resistance takes half the voltage.
How do I make a value I don't have?
Put standard values in series: 4.7 kΩ + 2.2 kΩ makes 6.9 kΩ, and 1 kΩ + 220 Ω makes 1.22 kΩ. Type the combination here to check it before you solder.
What is the difference between series and parallel?
In series the same current flows through every resistor and the resistances add (Req = R1 + R2 + …). In parallel every resistor has the same voltage and the conductances add, which always gives less than the smallest resistor; the parallel resistor calculator works those out.