Series Circuit Calculator for Resistance, Current, Voltage Drop, and Power

A series circuit has a single current path, so the same current flows through every resistor. Enter the source voltage and resistor values to calculate total resistance, circuit current, each resistor’s voltage drop, and power dissipation.
This guide also explains how to identify series-connected components, derive the formulas, verify the voltage and power totals, and distinguish a series circuit from a parallel circuit.

The same current flows through every resistor in the series string. The results should also show that the sum of the resistor voltage drops equals the source voltage and that the total resistor power dissipation equals the power supplied by the source. The derivation and calculation steps are explained in “How to Calculate a Series Circuit“.
The results assume nominal input values and ignore wiring resistance and source internal resistance. For a real design, include source-voltage tolerance, resistor tolerance, and temperature effects.

How to Identify a Series Connection

To identify a series-connected section in a schematic, examine the node shared by adjacent components and check whether any other branch leaves that node. This separates the components that carry the same current from sections where current divides.

Two Components Are in Series When the Shared Node Has No Branch

Two-terminal components are in series when they share a node and no other branch leaves that node. A node consists of points connected by ideal conductors. All points on the node are treated as being at the same electrical potential.
In Figure 1, the only path from the positive terminal of the source to the negative terminal passes through resistor R₁, node A, and resistor R₂ in sequence. The blue arrow indicates the circuit current I. Because no branch leaves node A, the current through R₁ continues through R₂.

Figure 1. Two resistors connected in series with no branch at node A. Current I flows through R₁ and R₂ in sequence.

If a component or conductor in this path fails open, the only closed current path is interrupted. In the ideal circuit, the circuit current becomes 0 A.

A Branch Means the Components Are Not a Simple Series Pair

If another branch leaves the node shared by two components, the same current does not necessarily flow through both components. They therefore cannot be treated as a simple series pair. Figure 2 shows current division at node A after resistor R₁. The current I through R₁ equals the sum of branch currents I₂ and I_L.

Figure 2. Current branches at node A, so R₁ and R₂ are not a simple series pair.

In this circuit, R₂ and load resistance R_L are connected between the same two nodes and are therefore in parallel. R₁ is in series with the parallel equivalent of R₂ and R_L. The equivalent resistance must be calculated from the actual connection topology rather than by adding R₁ and R₂ alone.
Conversely, components can be connected in series even when they are drawn far apart. Series connection is determined by the node connections and current paths, not by the visual layout of the schematic.

Three Rules for a Series Circuit

A resistive series circuit follows three relationships: the same current flows through every resistor, the source voltage is divided among the resistors, and the resistor values add. These relationships follow from Ohm’s law and Kirchhoff’s laws applied to a current path with no branches.

The Same Current Flows Through Every Resistor

Every resistor in a series string carries the same current. For resistors R₁ through R_n connected in series,

\(I=I_1=R_2=⋯=I_n\)

Because there is no branch between the resistors, current entering one resistor continues into the next. The resistor values determine the magnitude of the circuit current, but every resistor in the series string carries that same current. Different resistor values therefore produce different voltage drops.

Voltage Drops Add Up to the Source Voltage

When current I flows through resistor R_i, Ohm’s law gives the voltage drop V_i across that resistor:

\(V_i=IR_i\)

For a closed loop containing one source and several resistors, the sum of the resistor voltage drops equals the source voltage V_S:

\(V_S=V_1+V_2+⋯+V_n\)

Because the same current flows through every resistor, the voltage drop is proportional to resistance. The voltage drop across R_i can also be written as

\(V_i=V_S\displaystyle \frac{R_i}{R_{total}}\)

This voltage-division relationship applies only when the same current flows through the resistor string. Connecting a load to an intermediate node creates a branch, so the loaded circuit must be recalculated.

Total Resistance Is the Sum of the Resistor Values

The total resistance, also called the equivalent resistance, is the resistance that can replace the entire series string. Because the current I is common to every resistor,

\(V_S=IR_1+IR_2+⋯+IR_n\)

Factoring out I

\(V_S=I(R_1+R_2+⋯+R_n)\)

Comparing this expression with Ohm’s law for the complete circuit, V_S = IR_total, gives

\(R_{total}=R_1+I_2+⋯+R_n\)

Adding another positive-valued resistor in series increases the total resistance. At a fixed source voltage, the circuit current therefore decreases. For the general relationship among voltage, current, resistance, and power, see Ohm’s Law: Voltage, Current, and Resistance.

How to Calculate a Series Circuit

First, identify the components that form one series-connected section. Calculate the total resistance of that section, then use it to find the circuit current. Use the common current to calculate each voltage drop and power dissipation, and verify the result with the voltage and power totals.

Calculate Total Resistance, Current, Voltage, and Power in This Order

The calculation is easier to follow in the following order:

1. Add the resistor values to obtain total resistance R_total .
2. Divide source voltage V_S by total resistance to obtain circuit current I .
3. Use the circuit current and each resistor value to obtain voltage drop V_i .
4. Calculate power dissipation P_i for each resistor.
5. Verify the calculation from the voltage and power totals.

Use the following equations:

\(R_{total}=R_1+R_2+⋯+R_n\)

\(I=\displaystyle \frac{V_S}{R_{total}}\)

\(V_i=IR_i\)

\(P_i=V_i I=I^2 R_i=\displaystyle \frac{V_i^2}{R_i}\)

Use consistent units for voltage, current, and resistance before substituting numerical values.

Worked Example: 12 V with 3.3 kΩ and 6.8 kΩ in Series

Entering this example in the Series Circuit Calculator should produce the same results shown below. A 12 V source is connected to R₁ = 3.3 kΩ and R₂ = 6.8 kΩ in series. The calculation finds total resistance, circuit current, each voltage drop, and each resistor’s power dissipation. Figure 3 shows the circuit. Wiring resistance and source internal resistance are ignored, and the resistor values are treated as nominal.

Figure 3. Series circuit used in the worked example: 12 V, 3.3 kΩ, and 6.8 kΩ.

Start with the general total-resistance equation, then substitute the resistor values.

\(R_{total}=R_1+R_2\)

\(R_{total}=3.3 kΩ+6.8 kΩ=10.1 kΩ\)

Next, apply Ohm’s law to the complete circuit.

\(I=\displaystyle \frac{V_S}{R_{total}}\)

\(I=\displaystyle \frac{12 V}{10.1 kΩ}≈1.188 mA \)

The following calculations retain 1.188 mA to limit rounding error. Calculate each voltage drop from V_i = IR_i .

\(V_1=IR_1 \)

\(V_1=1.188 mA×3.3 kΩ≈3.92 V \)

\(V_2=IR_2 \)

\(V_2=1.188 mA×6.8 kΩ≈8.08 V \)

R₂ has the larger resistance, so it also has the larger voltage drop.
Calculate each resistor’s power dissipation from P_i = I²R_i .

\(P_1=I^2 R_1 \)

\(P_1=(1.188 mA)^2×3.3 kΩ≈4.66 mW \)

\(P_2=I^2 R_2 \)

\(P_2=(1.188 mA)^2×6.8 kΩ≈9.60 mW \)

These values are calculated from nominal inputs. Actual current, voltage, and power vary with source-voltage accuracy, resistor tolerance, and other circuit conditions.

Verify the Voltage and Power Totals

First, verify that the sum of the resistor voltage drops equals the source voltage.

\(V_S=V_1+V_2 \)

\(V_S≈3.92 V+8.08 V=12.00 V \)

Next, calculate the total power dissipated by the resistors.

\(P_R=P_1+P_2 \)

\(P_R≈4.66 mW+9.60 mW=14.26 mW \)

The power supplied by the source is

\(P_S=V_S I \)

\(P_S=12 V×1.188 mA≈14.26 mW \)

Apart from rounding error, the total power dissipated by the resistors equals the power supplied by the source. If the checks do not agree, review the circuit topology, unit conversions, voltage signs, and rounding of intermediate values.

Series vs. Parallel Circuits

In a series circuit, the same current flows through every component. In a parallel circuit, every branch is connected across the same two nodes, so the same voltage appears across every branch. Figure 4 compares the two connection types.

Figure 4. Connection, current, and voltage in series and parallel circuits.

In a circuit that contains both series and parallel sections, identify components that carry the same current and branches connected across the same two nodes. Replace clearly reducible sections with their equivalent resistance one step at a time. Some networks, including bridge circuits, cannot be reduced by simple series and parallel combinations alone.

Related Applications of Series Connections

Series connections are used to divide voltage and to limit current. The detailed design depends on loading and on the electrical behavior of the connected components.

Voltage Divider Circuits

A voltage divider is one application of a series resistor network. When a load is connected to the output node, the lower resistor and the load form a parallel combination, so the circuit is no longer an unloaded two-resistor series string. Use the Voltage Divider Circuit guidance to include load resistance and select the resistor values.

LED Current-Limiting Resistors

A series resistor used with a low-power indicator LED can limit forward current from a voltage source. Because LED forward voltage varies with current, temperature, and device variation, do not treat the LED as a fixed resistor. Refer to LED Circuit Configuration when selecting the resistance and checking the operating range.

Practical Limits and Resistor Ratings

The worked example uses a fixed source voltage and nominal resistor values. For a real circuit, combine the minimum and maximum source voltage with resistor tolerance to determine the possible range of circuit current, voltage drop, and power dissipation. Include resistance temperature coefficient and wiring resistance when the required accuracy makes them significant.
Resistor power dissipation produces heat. Compare the worst-case P_i with the resistor’s rated power after applying the derating curve for the specified ambient or terminal temperature.
Also, verify that the voltage across each resistor is within the rated voltage and maximum element voltage limits stated in the datasheet. A resistor can meet its power limit while exceeding a voltage limit, particularly at high resistance values. For details on rated power and derating, see the Chip Resistor Specifications.
To calculate a series circuit, first identify the section in which the same current flows. Then calculate total resistance, circuit current, each voltage drop, and each power dissipation. Verify the result from the voltage and power totals. If a load or branch is added, recalculate the circuit from the updated node connections.