Calculate Equivalent Resistance for Series/Parallel Networks
Resistor Values (Ω, separate with commas)
Calculation Result
Equivalent Resistance Rtotal
Detailed Derivation
Series & Parallel Formulas
Series: Rtotal = R₁ + R₂ + ... + Rn
Parallel: 1/Rtotal = 1/R₁ + 1/R₂ + ... + 1/Rn
2 Parallel Resistors: Rtotal = (R₁×R₂)/(R₁+R₂)
Series/parallel resistors are basic circuit concepts. Series increases total resistance, parallel decreases it.
⚠Separate multiple values with commas. For equal parallel resistors: Rtotal = R/n (n=number of resistors).
What is Series & Parallel Resistance?
Series/parallel are the most basic resistor connections. Series: resistors connected end-to-end (one current path). Parallel: resistors connected side-by-side (multiple current paths). Calculating equivalent resistance is the first step in circuit analysis.
Series Circuit
Same current, total voltage = sum of voltages. Total resistance = sum of resistors. One broken resistor breaks the whole circuit.
Parallel Circuit
Same voltage, total current = sum of branch currents. Total resistance < smallest resistor. One broken branch does not affect others.
Series-Parallel Mixed
Complex circuits use both. Simplify step by step: solve local series/parallel first, then reduce to total resistance.
Practical Uses
LED current-limiting (series); voltmeter (parallel, high resistance); ammeter (series, low resistance); voltage divider (series).
What is the difference between series and parallel?▼
Series: Resistors connected end-to-end, same current flows through all. Total resistance = sum of all resistors (Rtotal=R1+R2+...), always larger than any single resistor. Parallel: Resistors connected side-by-side, same voltage across all. Reciprocal of total resistance = sum of reciprocals (1/Rtotal=1/R1+1/R2+...), always smaller than the smallest resistor.
How to calculate two parallel resistors?▼
Simplified formula for two parallel resistors: Rtotal = (R1×R2)/(R1+R2). Example: R1=10Ω, R2=20Ω → Rtotal=(10×20)/(10+20)=200/30≈6.67Ω, smaller than the smallest resistor (10Ω).
Why is parallel resistance smaller than the smallest one?▼
Parallel connection adds more current paths. More paths mean lower total resistance, just like multiple parallel water pipes have less resistance than a single pipe.
What is voltage division and current division?▼
Series (Voltage Division): Same current, voltage splits proportionally to resistance. Parallel (Current Division): Same voltage, current splits inversely proportional to resistance. These are core principles for analyzing resistor networks.
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