Series & Parallel Resistor Calculator
This Series and Parallel Resistor Calculator finds the equivalent resistance of resistor networks with mixed Ω, kΩ, and MΩ inputs. Add each component, select the network topology, and review the real-time result in ohms and a readable engineering unit.
Equivalent resistance checks are useful when developing voltage dividers, current-sharing branches, sensor circuits, and pull-up or pull-down networks. They also help engineers simplify part of a schematic before applying Ohm's law or analyzing circuit loading.
The calculator models ideal resistors connected entirely in series or entirely in parallel. More complex series-parallel networks can be reduced one group at a time using the same equations.
Series & Parallel Resistor Calculator
Add resistor values and switch between series and parallel networks. The equivalent resistance updates immediately as values or units change.
Equivalent resistance
3.2 kΩ
Series Network - 2 resistors
- Equivalent resistance
- 3,200Ω
- Human readable value
- 3.2kΩ
- Calculation type
- Series Network
Series and Parallel Resistance Formulas
Series: Req = R1 + R2 + R3 + ...Parallel: 1 / Req = 1 / R1 + 1 / R2 + 1 / R3 + ...- Req = Equivalent resistance of the complete network in ohms (Ω)
- R1, R2, R3 = Individual resistor values in ohms (Ω)
- Series resistors carry the same current and their voltage drops add
- Parallel resistors share the same voltage and their branch currents add
How to Use This Calculator
- Select Series when all resistors form one current path, or Parallel when every resistor is connected across the same two circuit nodes.
- Enter each resistance and select Ω, kΩ, or MΩ. Mixed units are converted to ohms before the network calculation.
- Add or remove resistor rows to match the network. The equivalent resistance updates immediately after any value, unit, or mode change.
- Compare the result with available standard resistor values and check tolerance, current, voltage, and power limits before finalizing a design.
Worked Examples
Example 1: Series Network
R1 = 1 kΩ and R2 = 2.2 kΩ.
Req = R1 + R2
Req = 1 kΩ + 2.2 kΩ
Req = 3.2 kΩ
The two components create a single current path, so their resistances add directly.
Example 2: Parallel Network
R1 = 1 kΩ and R2 = 2.2 kΩ.
Req = (R1 × R2) / (R1 + R2)
Req = (1,000 Ω × 2,200 Ω) / (1,000 Ω + 2,200 Ω)
Req = 687.5 Ω
The added branch increases conductance, making the equivalent resistance lower than either individual resistor.
Engineering Notes
Series networks increase resistance
Adding a resistor in series always raises Req. The same current flows through every component, while the applied voltage divides across them.
Parallel networks reduce resistance
Each added parallel branch increases total conductance. Req is therefore always below the smallest nonzero branch resistance.
Equal resistors share current
Equal resistors connected in parallel carry equal branch currents under ideal conditions. Current sharing can change when resistance, temperature, or connection resistance differs.
Power ratings still apply
Equivalent resistance alone does not show individual dissipation. Calculate branch current and resistor power, then apply suitable voltage, thermal, pulse, and derating margins.
Tolerance changes the real result
Nominal values produce a nominal Req. Precision dividers, sensor interfaces, and bias networks may require worst-case tolerance analysis or matched resistor networks.
Common Mistakes
- Adding parallel resistance values instead of their reciprocals.
- Mixing Ω, kΩ, and MΩ without converting to a common unit.
- Assuming a circuit is parallel when its branches do not share both nodes.
- Ignoring load resistance that appears in parallel with the intended network.
- Using nominal Req without checking component tolerance and power dissipation.
FAQ
How do you calculate resistors in series?
Add every resistance in the current path. For example, 1 kΩ and 2.2 kΩ in series have an equivalent resistance of 3.2 kΩ.
How do you calculate resistors in parallel?
Add the reciprocal of each resistance, then take the reciprocal of that sum: 1 / Req = 1 / R1 + 1 / R2 + ... . For two resistors, Req can also be calculated as R1 × R2 / (R1 + R2).
Why is parallel resistance always lower than the smallest resistor?
Each parallel branch adds another current path. The total conductance therefore increases, so the equivalent resistance must be lower than the resistance of any individual branch.
What happens if one resistor in a parallel network is very small?
The smallest branch dominates the equivalent resistance because it carries most of the current. A zero-ohm branch represents a short circuit and makes the ideal equivalent resistance zero.
Do resistor tolerances affect equivalent resistance?
Yes. The nominal result assumes exact values, while real components vary within their tolerance bands. Use worst-case values or tolerance analysis when the network ratio or absolute resistance is critical.
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Browse all available and planned tools in the Resistors calculator category, or review supporting component information in the Engineering Reference Center.
This calculator provides ideal theoretical results for engineering reference. Verify topology, resistor tolerance, voltage rating, power dissipation, temperature behavior, and measured circuit performance before using the result in production hardware.