Impedance Calculator
R = 10 Ω, L = 100 mH and C = 200 µF in series at 50 Hz have an impedance of 18.4462 Ω, inductive because X_L (31.4 Ω) exceeds X_C (15.9 Ω).
Enter 0 for a component that is not in the circuit.
18.4462299458393 Ω
Full answer, then cut to fewer decimals (not rounded):
- 18.4462299458393 Ω
- 18.446229945839 Ω
- 18.44622994583 Ω
- 18.4462299458 Ω
- 18.446229945 Ω
- 18.44622994 Ω
- 18.4462299 Ω
- 18.446229 Ω
- 18.44622 Ω
- 18.4462 Ω
- 18.446 Ω
- 18.44 Ω
- 18.4 Ω
- Rectangular form
- 10 + j15.5004 Ω
- Phase angle φ
- 57.17218603 °
- Power factor cos φ
- 0.5421161955
- Circuit is
- inductive (current lags)
- Admittance |Y|
- 0.05421161955 S
- Current I = V/|Z|
- 12.4686725 A
Step-by-step solution
- X_L = 2πfL = 31.41592654 Ω; X_C = 1/(2πfC) = 15.91549431 Ω
- Z = R + j(X_L − X_C) = 10 + j15.5004 Ω
- |Z| = √(R² + X²) = 18.44622995 Ω
Impedance Formula
Z = R + j(ωL − 1/ωC) (series)
parallel: 1/Z = 1/R + j(ωC − 1/ωL); ω = 2πf; φ = arctan(X/R)
Worked Example
R = 10 Ω, L = 100 mH and C = 200 µF in series at 50 Hz:
- X_L = 2πfL = 31.41592654 Ω; X_C = 1/(2πfC) = 15.91549431 Ω
- Z = R + j(X_L − X_C) = 10 + j15.5004 Ω
- |Z| = √(R² + X²) = 18.44622995 Ω
Phase angle φ: 57.17218603 ° · Power factor cos φ: 0.5421161955 · Circuit is: inductive (current lags) · Admittance |Y|: 0.05421161955 S · Current I = V/|Z|: 12.4686725 A
GATE tip
For mixed networks, convert each element to its complex impedance, combine series parts by adding Z and parallel parts by adding Y = 1/Z. Keep everything in rectangular form while adding and in polar form while multiplying.
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Frequently asked questions
How do I leave out a component?
Enter 0. In series a missing capacitor is treated as a short (no reactance); in parallel a missing branch is open.
What does a negative phase angle mean?
The circuit is capacitive: current leads voltage. Positive means inductive, with current lagging.
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). Impedance Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/impedance-calculator/
IEEE
Scientific Converters, "Impedance Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/impedance-calculator/