Series and Parallel Calculator
100 Ω, 220 Ω and 470 Ω add to 790 in series, while in parallel they give 59.98 Ω, less than the smallest one.
Separate with commas or spaces, e.g. 100, 220, 470 (Ω), or 10, 22 (µF). The result is in the same unit.
790
- Parallel equivalent
- 59.97679814
Step-by-step solution
- Resistors in series add: 100 + 220 + 470 = 790
- In parallel: 1/X = 1/100 + 1/220 + 1/470, so X = 59.97679814
Series and Parallel Formula
R_s = R₁ + R₂ + …, 1/R_p = 1/R₁ + 1/R₂ + …
inductors combine like resistors; capacitors the other way round (parallel adds)
Worked Example
Resistors of 100 Ω, 220 Ω and 470 Ω:
- Resistors in series add: 100 + 220 + 470 = 790
- In parallel: 1/X = 1/100 + 1/220 + 1/470, so X = 59.97679814
GATE tip
Two equal resistors in parallel give R/2, and n equal ones give R/n. For two unequal ones use product over sum, R₁R₂/(R₁ + R₂), the fastest mental method in the exam.
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with a load R_L across R₂, replace R₂ by R₂∥R_L; current divider: I₁ = I R₂/(R₁ + R₂)
Example: 12 V across R₁ = 10 kΩ and R₂ = 4.7 kΩ, unloaded: Output voltage Vₒᵤₜ = 3.83673 V.
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R_a = R_ab R_ca / (R_ab + R_bc + R_ca)
star → delta: R_ab = (R_aR_b + R_bR_c + R_cR_a) / R_c
Example: A delta of R_ab = 30 Ω, R_bc = 60 Ω and R_ca = 90 Ω: R_a = 15 Ω.
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RC & RL Time Constant Calculator
τ = RC, v_C(t) = V(1 − e^(−t/τ))
RL circuit: τ = L/R, i(t) = (V/R)(1 − e^(−t/τ)); discharging uses e^(−t/τ)
Example: A 10 kΩ resistor charging a 100 µF capacitor from 10 V, after 1 s: Time constant τ = 1 s.
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RLC Resonance Calculator
f₀ = 1 / (2π√(LC)), Q = (1/R)√(L/C) (series)
parallel: Q = R√(C/L); bandwidth = f₀/Q; ζ = 1/(2Q)
Example: A series circuit with R = 10 Ω, L = 10 mH and C = 1 µF: Resonant frequency f₀ = 1591.55 Hz.
Frequently asked questions
Why is the parallel result smaller than any resistor?
Each branch adds another path for current, so the combined conductance is the sum of conductances and the resistance falls below the smallest branch.
Why are capacitors the other way round?
Capacitance adds when plates add (parallel), while in series the charges are equal and the voltages add, so 1/C adds.
Sources
- The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
Cite this page
APA
Scientific Converters. (2026, October 15). Series and Parallel Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/series-parallel-calculator/
IEEE
Scientific Converters, "Series and Parallel Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/series-parallel-calculator/