Circuit Solver: Series, Parallel, and AC Impedance
A free circuit solver and resistance calculator covering the parallel resistor formula, series parallel circuit formula, AC impedance, and power-triangle math. Use it for homework, troubleshooting, or sanity-checking your design before energizing.
Resistance Calculator
Calculate total resistance for series and parallel resistor combinations
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Parallel resistor formula and how to find resistance in a parallel circuit
The parallel resistor formula is the reciprocal sum: 1/R_total = 1/R₁ + 1/R₂ + 1/R₃ + … and so on. Take the reciprocal of the answer to get the equivalent resistance. The total is always smaller than the smallest individual resistor — that's the quick mental check when you're troubleshooting and want to know how to calculate resistance in a parallel circuit without grabbing a calculator.
For two resistors in parallel, the formula collapses to the product-over-sum shortcut: R_total = (R₁ × R₂) / (R₁ + R₂). Two equal resistors in parallel always give half the value of one. Three equal resistors in parallel give one-third. This pattern shows up constantly in circuit diagrams for current dividers, power supplies, and load banks.
Use the "Resistance" tab above for any number of resistors in series or parallel. Use the "Series/Parallel" tab when you have full complex impedances (R + jX) and need the polar magnitude and phase angle.
Series parallel circuit formula reference
| Circuit type | Formula | Behavior |
|---|---|---|
| Series resistors | R_t = R₁ + R₂ + ... + R_n | Same current, voltage divides |
| Parallel resistors | 1/R_t = 1/R₁ + 1/R₂ + ... + 1/R_n | Same voltage, current divides |
| Two parallel | R_t = (R₁ × R₂) / (R₁ + R₂) | Product-over-sum shortcut |
| Series impedance | Z_t = Z₁ + Z₂ (complex addition) | Add real and imaginary parts |
| Parallel impedance | Z_t = (Z₁ × Z₂) / (Z₁ + Z₂) | Complex multiplication and division |
For mixed series-parallel networks, reduce one section at a time: collapse parallel branches first, then sum the resulting series sections. Repeat until you have a single equivalent.
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What is the parallel resistor formula?
1/R_total = 1/R₁ + 1/R₂ + 1/R₃ + …, then take the reciprocal. For two resistors, the product-over-sum shortcut works: R_total = (R₁ × R₂) / (R₁ + R₂). Two equal resistors in parallel always give half the value of one.
How do I find resistance in a parallel circuit?
Use the parallel resistor formula above. The result is always smaller than the smallest individual resistor — that's the quick mental check. The Resistance tab lets you add any number of resistors and reports the total plus current distribution at 1 V across the network.
How do I solve a mixed series-parallel circuit?
Reduce one section at a time. Collapse parallel branches first using the parallel resistor formula. Then sum the resulting series sections. Repeat until you have a single equivalent. The Series/Parallel tab handles complex impedances (real + j × imaginary) the same way.