Equivalent resistance
What is equivalent resistance?
Equivalent resistance is the single resistance value that can replace a group of resistors without changing the overall electrical behavior seen across the network terminals.
The method used to calculate equivalent resistance depends on whether the resistors are connected in series or in parallel.
One current path
Series resistance formula
Resistors are connected in series when current passes through each resistor one after another along a single path.
Equivalent series resistanceReq = R1 + R2 + R3 + ...
Every resistor contributes additional opposition to current, so series resistance increases as more resistors are added.
Worked series example
Calculate three resistors in series
Suppose three resistors have values of 100 Ω, 220 Ω, and 330 Ω.
- Write the equation: Req = R1 + R2 + R3.
- Substitute the values: Req = 100 + 220 + 330.
- Add the resistance values: Req = 650 Ω.
Multiple current paths
Parallel resistance formula
Resistors are connected in parallel when each resistor is connected across the same two circuit nodes. Current can split between the available branches.
General parallel equation1/Req = 1/R1 + 1/R2 + 1/R3 + ...
After adding the reciprocals, take the reciprocal of the total to obtain the equivalent resistance.
Two-resistor shortcut
Parallel formula for two resistors
When exactly two resistors are connected in parallel, the general equation can be simplified.
Two parallel resistorsReq = R1 × R2 ÷ (R1 + R2)
This shortcut gives the same result as the reciprocal method and is often faster for manual calculations.
Worked parallel example
Calculate two resistors in parallel
Consider a 100 Ω resistor and a 220 Ω resistor connected in parallel.
- Write the shortcut formula: Req = R1 × R2 ÷ (R1 + R2).
- Substitute the values: Req = 100 × 220 ÷ (100 + 220).
- Multiply the numerator: 100 × 220 = 22,000.
- Add the denominator: 100 + 220 = 320.
- Divide to obtain Req = 68.75 Ω.
Circuit behavior
Series versus parallel resistance
- Series resistance is the sum of all resistor values.
- Series equivalent resistance is greater than every individual resistor.
- Parallel networks provide multiple paths for current.
- Parallel equivalent resistance is lower than the smallest branch resistance.
- Adding another resistor in series increases total resistance.
- Adding another resistor in parallel decreases total resistance.
Identical resistor shortcut
Equal resistors in series or parallel
When all resistor values are equal, simple shortcuts can be used.
Equal resistors in seriesReq = n × R
Equal resistors in parallelReq = R ÷ n
Here, R is the value of one resistor and n is the number of identical resistors.
For example, three 1,000 Ω resistors in parallel have an equivalent resistance of approximately 333.333 Ω.
Consistent measurements
Resistance units and conversions
This calculator accepts resistance values in ohms. Convert larger units before entering them.
- 1 kilo-ohm equals 1,000 ohms.
- 1 mega-ohm equals 1,000,000 ohms.
- 4.7 kΩ should be entered as 4,700 Ω.
- 2.2 MΩ should be entered as 2,200,000 Ω.
The result display automatically converts large equivalent values to kilo-ohms or mega-ohms for readability.
Result validation
Quick checks for your answer
These rules can help detect common input or calculation mistakes.
- A series result must be larger than each positive resistor value.
- A parallel result must be smaller than the smallest positive branch resistance.
- Two equal resistors in parallel produce half the resistance of either resistor.
- Two equal resistors in series produce twice the resistance of either resistor.
Common calculation errors
Mistakes to avoid
- Do not add parallel resistor values directly.
- Do not forget to take the final reciprocal in the general parallel equation.
- Convert kilo-ohms and mega-ohms to ohms before mixing them with values already expressed in ohms.
- Confirm that the circuit really is a pure series or pure parallel network before applying these formulas.
Model assumptions
Assumptions and limitations
This calculator assumes ideal, positive, finite resistors arranged as one complete series group or one complete parallel group.
It does not automatically reduce mixed series-parallel networks, bridge circuits, resistor tolerances, temperature effects, nonlinear components, or frequency- dependent impedance.
Real resistor values may differ from their nominal ratings because of manufacturing tolerance and operating temperature.
Common questions
Series and parallel resistance FAQ
How do you calculate resistance in series?
Add every resistor value directly. For example, three resistors of 100 ohms, 220 ohms, and 330 ohms have an equivalent series resistance of 650 ohms.
How do you calculate resistance in parallel?
Add the reciprocals of the resistor values and then take the reciprocal of that sum. The general equation is 1 divided by equivalent resistance equals 1 divided by R1 plus 1 divided by R2 and so on.
Is parallel resistance always lower than the smallest resistor?
Yes. For positive finite resistor values, the equivalent resistance of a parallel network is always lower than the smallest individual branch resistance.
Is series resistance always greater than each resistor?
Yes. Because all positive resistor values are added, the equivalent series resistance is greater than every individual resistor in the series network.
Can I enter resistance values in kilo-ohms?
The calculator interprets entries as ohms. Convert kilo-ohms to ohms before entering them, so 1 kilo-ohm should be entered as 1000 ohms.