Series & Parallel Resistance
Calculate total resistance for resistors connected in series or parallel. Add up to 10 resistors.
How series and parallel circuits differ
How to calculate series and parallel resistance
In a series circuit, resistors sit on a single path, so you simply add their values. In a parallel circuit, resistors share multiple paths, so you add their reciprocals to find the reciprocal of the total.
For a mixed (series-parallel) circuit, reduce it in stages: first combine the purely parallel groups into single equivalent resistors, then add those equivalents in series with the rest. For example, if 6 Ω and 3 Ω in parallel (= 2 Ω) are then in series with 10 Ω, the total is 2 + 10 = 12 Ω.
Quick reference values
| Configuration | Total resistance |
|---|---|
| Two equal resistors R in parallel | R ÷ 2 |
| Three equal resistors R in parallel | R ÷ 3 |
| n equal resistors R in parallel | R ÷ n |
| Two resistors R1, R2 in parallel | (R1 × R2) ÷ (R1 + R2) |
| n equal resistors R in series | R × n |
Parallel total is always smaller than the smallest resistor; series total is always larger than the largest.
Frequently asked questions
How do I calculate total resistance in series?
For resistors in series, add all the individual resistances together: R_total = R1 + R2 + ... + Rn. The total is always larger than the largest single resistor. For example, 100 Ω, 220 Ω and 330 Ω in series give 100 + 220 + 330 = 650 Ω.
How do I calculate parallel resistance?
For resistors in parallel, add the reciprocals: 1/R_total = 1/R1 + 1/R2 + ... + 1/Rn, then take the reciprocal of that sum. The total is always less than the smallest resistor. For example, 6 Ω and 3 Ω in parallel: 1/R = 1/6 + 1/3 = 1/2, so R_total = 2 Ω.
What is the formula for two resistors in parallel?
For exactly two resistors, use the "product over sum" formula: R_total = (R1 × R2) / (R1 + R2). For example, 4 Ω and 12 Ω in parallel give (4 × 12) / (4 + 12) = 48/16 = 3 Ω.
Why is parallel resistance always less than the smallest resistor?
In a parallel circuit, adding more resistors provides additional paths for current to flow. More current paths means less overall opposition to current, so total resistance decreases. Mathematically, 1/R_total is always greater than any individual 1/R_n, so R_total is always less than any individual R_n.
What is the formula for two resistors in parallel?
For exactly two resistors: R_total = (R1 × R2) / (R1 + R2). This is the "product over sum" formula. For example, 4Ω and 12Ω in parallel: R_total = (4 × 12) / (4 + 12) = 48/16 = 3Ω.
Do identical resistors in parallel give half the resistance?
Yes. Two identical resistors R in parallel give R/2. Three give R/3. n identical resistors R in parallel give R/n. This is because 1/R_total = n/R, so R_total = R/n.
How do home electrical circuits use parallel connections?
Household electrical circuits connect appliances in parallel so each device gets the same voltage (230V in India) and can be switched independently. If they were in series, switching off one device would break the circuit for all others.
What happens to total resistance when you add a resistor in parallel?
Adding any resistor in parallel always decreases the total resistance, even if the added resistor is very large. This is because any finite resistance provides some additional current path. Adding a very large resistor has minimal effect, but the total will always be slightly lower.