Skip to main content

Rlccircuit Impedance Calculator

Calculate rlccircuit impedance accurately for your build. Get material quantities, waste allowances, and project cost breakdowns.

Skip to calculator
Engineering

Rlccircuit Impedance Calculator

Calculate impedance, phase angle, resonant frequency, Q factor, and power for series and parallel RLC circuits at any frequency.

Last updated: December 2025

Calculator

Adjust values & calculate
100 ohm
10 mH
100 uF
1000 Hz
12 V
Total Impedance (series)
117.26 ohm
Inductive (XL > XC) | Phase: 31.48 deg
XL (Inductive)
62.83 ohm
XC (Capacitive)
1.59 ohm
Current
102.33 mA
Resonant Frequency
159.15 Hz
Quality Factor (Q)
0.10
Real Power
1047.24 mW
Reactive Power
641.34 mVAR
Power Factor
0.8528
V across R
10.233 V
V across L
6.430 V
V across C
0.163 V
Note: Calculations assume ideal components with no parasitic resistance in the inductor or capacitor. Real-world components have additional losses that affect the actual impedance and Q factor.
Your Result
Z: 117.26 ohm | Phase: 31.48 deg | I: 102.33 mA | f0: 159.15 Hz
Share Your Result
Understand the Math

Formula

Z = sqrt(R^2 + (XL - XC)^2); XL = 2*pi*f*L; XC = 1/(2*pi*f*C)

Where Z is impedance in ohms, R is resistance, XL is inductive reactance (proportional to frequency), XC is capacitive reactance (inversely proportional to frequency), f is frequency in Hz, L is inductance in henries, and C is capacitance in farads. Resonant frequency f0 = 1/(2*pi*sqrt(LC)).

Last reviewed: December 2025

Worked Examples

Example 1: Audio Bandpass Filter Design

A series RLC circuit has R = 100 ohm, L = 10 mH, C = 100 uF, driven at 1000 Hz with 12V. Calculate the impedance, current, and resonant frequency.
Solution:
XL = 2*pi*1000*0.01 = 62.83 ohm XC = 1/(2*pi*1000*0.0001) = 1.59 ohm Net reactance = 62.83 - 1.59 = 61.24 ohm (inductive) Z = sqrt(100^2 + 61.24^2) = 117.26 ohm Current = 12 / 117.26 = 0.1023 A = 102.3 mA Phase = arctan(61.24/100) = 31.47 degrees Resonant freq = 1/(2*pi*sqrt(0.01*0.0001)) = 159.15 Hz
Result: Z: 117.26 ohm | I: 102.3 mA | Phase: 31.47 deg | f0: 159.15 Hz

Example 2: Resonance Analysis

Find the resonant frequency and Q factor for a series RLC with R = 50 ohm, L = 5 mH, C = 10 uF. What is the impedance at resonance?
Solution:
f0 = 1/(2*pi*sqrt(0.005*0.00001)) = 711.8 Hz XL at resonance = 2*pi*711.8*0.005 = 22.36 ohm Q = XL/R = 22.36/50 = 0.447 Bandwidth = f0/Q = 711.8/0.447 = 1592 Hz At resonance: Z = R = 50 ohm (XL = XC, they cancel) Current at resonance = V/R (maximum)
Result: f0: 711.8 Hz | Q: 0.447 | BW: 1592 Hz | Z at resonance: 50 ohm (purely resistive)
Expert Insights

Background & Theory

The Rlccircuit Impedance Calculator applies the following established principles and formulas. Structural and construction engineering is governed by fundamental load analysis, material science, and regulatory standards that ensure the safety and durability of built structures. The primary distinction in load analysis is between dead loads โ€” the permanent self-weight of structural elements, finishes, and fixed equipment โ€” and live loads, which represent variable occupancy, furniture, and environmental forces such as wind and snow. These are combined using factored load equations, such as the ASCE 7 formula U = 1.2D + 1.6L, where D is dead load and L is live load. Concrete mix design is governed by the water-cement (w/c) ratio, which is the primary determinant of compressive strength and durability. A w/c ratio of 0.40โ€“0.45 typically yields concrete with 28-day compressive strengths of 30โ€“40 MPa. Common mix ratios by weight for structural concrete are approximately 1 part cement : 1.5โ€“2 parts sand : 3 parts coarse aggregate. Structural steel is characterized by its yield strength (the stress at which permanent deformation begins, typically 250โ€“350 MPa for mild steel) and ultimate tensile strength (typically 400โ€“500 MPa). Mid-span deflection of a simply supported beam under a central point load is given by ฮด = FLยณ / (48EI), where F is force, L is span length, E is Young's modulus, and I is the second moment of area. Building insulation is rated by R-value, a measure of thermal resistance in units of mยฒยทK/W (SI) or ftยฒยทยฐFยทh/BTU (imperial). Higher R-values indicate greater resistance to heat flow. Foundation design depends on the allowable bearing capacity of the underlying soil, which ranges from approximately 75 kPa for soft clay to over 10,000 kPa for bedrock. Drainage gradients for surface water are typically specified as a minimum of 1โ€“2% slope away from building foundations to prevent hydrostatic pressure and water infiltration.

History

The history behind the Rlccircuit Impedance Calculator traces back through the following developments. The history of construction engineering spans thousands of years of accumulated empirical knowledge and, more recently, rigorous scientific analysis. The ancient Egyptians built the Great Pyramid of Giza around 2560 BCE using an estimated 2.3 million stone blocks, demonstrating sophisticated logistics, geometry, and workforce organization. Roman engineers advanced the field dramatically through the use of pozzolanic concrete โ€” a mixture of volcanic ash, lime, and seawater โ€” enabling the construction of the Pantheon dome (43.3 m diameter, completed around 125 CE) and a vast network of aqueducts and roads across the empire. Cast iron emerged as a structural material during the Industrial Revolution, first used prominently in the Iron Bridge at Coalbrookdale, England, completed in 1779. Wrought iron and later steel allowed far greater spans and heights. The Eiffel Tower, completed in 1889, demonstrated the structural possibilities of wrought iron at scale and influenced the development of steel-frame skyscraper construction in Chicago and New York. Reinforced concrete was systematically developed by Joseph Monier, a French gardener, who patented iron-reinforced concrete pots and panels in the 1860s, and later by engineers including Franรงois Hennebique who created the first comprehensive reinforced concrete framing system in the 1890s. The 1906 San Francisco earthquake caused widespread devastation and galvanized the engineering profession to develop seismic design provisions. Subsequent earthquakes โ€” including the 1971 San Fernando and 1994 Northridge events โ€” drove successive improvements in seismic codes, base isolation technology, and ductile detailing of reinforced concrete and steel frames. Building codes became increasingly standardized in the twentieth century, with the International Building Code (IBC) first published in 2000 providing a unified model code adopted across much of the United States. Building Information Modeling (BIM) emerged in the 2000s as a digital workflow integrating architectural, structural, and MEP design into a unified three-dimensional model, fundamentally changing coordination practices across the industry.

Share this calculator

Explore More

Frequently Asked Questions

Impedance is the total opposition to alternating current flow in a circuit containing resistance, inductance, and capacitance. Unlike simple DC resistance, impedance is a complex quantity that accounts for both energy dissipation through resistance and energy storage through reactive components. For a series RLC circuit, the impedance magnitude is calculated as Z equals the square root of R squared plus the quantity XL minus XC squared, where XL is the inductive reactance equal to 2 times pi times frequency times inductance, and XC is the capacitive reactance equal to 1 divided by 2 times pi times frequency times capacitance. The phase angle between voltage and current is the arctangent of the net reactance divided by the resistance. Impedance is measured in ohms and varies with frequency, reaching a minimum at the resonant frequency in series circuits.
Resistance opposes DC current and is purely real. Impedance opposes AC current and includes resistance plus reactance (from capacitors and inductors). Impedance is a complex number: Z = R + jX, measured in ohms. Capacitive reactance decreases with frequency while inductive reactance increases with frequency.
You may use the results for reference and educational purposes. For professional reports, academic papers, or critical decisions, we recommend verifying outputs against peer-reviewed sources or consulting a qualified expert in the relevant field.
All calculations use established mathematical formulas and are performed with high-precision arithmetic. Results are accurate to the precision shown. For critical decisions in finance, medicine, or engineering, always verify results with a qualified professional.
No. All calculations run entirely in your browser using JavaScript. No data you enter is ever transmitted to any server or stored anywhere. Your inputs remain completely private.
The Formula section on this page shows the equation used. You can reproduce the calculation manually or in a spreadsheet using those steps. Compare your answer against the worked examples in the Examples section, which use known reference values so you can confirm the calculator is behaving as expected.
Educational Note: This calculator is provided for educational and informational purposes. Results are based on the formulas and inputs provided. Always verify important calculations independently. NovaCalculator processes calculator inputs client-side; optional analytics follow visitor consent settings. ยฉ 2024โ€“2026 NovaCalculator.

Share this calculator

Formula

Z = sqrt(R^2 + (XL - XC)^2); XL = 2*pi*f*L; XC = 1/(2*pi*f*C)

Where Z is impedance in ohms, R is resistance, XL is inductive reactance (proportional to frequency), XC is capacitive reactance (inversely proportional to frequency), f is frequency in Hz, L is inductance in henries, and C is capacitance in farads. Resonant frequency f0 = 1/(2*pi*sqrt(LC)).

Worked Examples

Example 1: Audio Bandpass Filter Design

Problem: A series RLC circuit has R = 100 ohm, L = 10 mH, C = 100 uF, driven at 1000 Hz with 12V. Calculate the impedance, current, and resonant frequency.

Solution: XL = 2*pi*1000*0.01 = 62.83 ohm\nXC = 1/(2*pi*1000*0.0001) = 1.59 ohm\nNet reactance = 62.83 - 1.59 = 61.24 ohm (inductive)\nZ = sqrt(100^2 + 61.24^2) = 117.26 ohm\nCurrent = 12 / 117.26 = 0.1023 A = 102.3 mA\nPhase = arctan(61.24/100) = 31.47 degrees\nResonant freq = 1/(2*pi*sqrt(0.01*0.0001)) = 159.15 Hz

Result: Z: 117.26 ohm | I: 102.3 mA | Phase: 31.47 deg | f0: 159.15 Hz

Example 2: Resonance Analysis

Problem: Find the resonant frequency and Q factor for a series RLC with R = 50 ohm, L = 5 mH, C = 10 uF. What is the impedance at resonance?

Solution: f0 = 1/(2*pi*sqrt(0.005*0.00001)) = 711.8 Hz\nXL at resonance = 2*pi*711.8*0.005 = 22.36 ohm\nQ = XL/R = 22.36/50 = 0.447\nBandwidth = f0/Q = 711.8/0.447 = 1592 Hz\nAt resonance: Z = R = 50 ohm (XL = XC, they cancel)\nCurrent at resonance = V/R (maximum)

Result: f0: 711.8 Hz | Q: 0.447 | BW: 1592 Hz | Z at resonance: 50 ohm (purely resistive)

Frequently Asked Questions

What is impedance in an RLC circuit and how is it calculated?

Impedance is the total opposition to alternating current flow in a circuit containing resistance, inductance, and capacitance. Unlike simple DC resistance, impedance is a complex quantity that accounts for both energy dissipation through resistance and energy storage through reactive components. For a series RLC circuit, the impedance magnitude is calculated as Z equals the square root of R squared plus the quantity XL minus XC squared, where XL is the inductive reactance equal to 2 times pi times frequency times inductance, and XC is the capacitive reactance equal to 1 divided by 2 times pi times frequency times capacitance. The phase angle between voltage and current is the arctangent of the net reactance divided by the resistance. Impedance is measured in ohms and varies with frequency, reaching a minimum at the resonant frequency in series circuits.

What is impedance and how does it differ from resistance?

Resistance opposes DC current and is purely real. Impedance opposes AC current and includes resistance plus reactance (from capacitors and inductors). Impedance is a complex number: Z = R + jX, measured in ohms. Capacitive reactance decreases with frequency while inductive reactance increases with frequency.

Is my data stored or sent to a server?

No. All calculations run entirely in your browser using JavaScript. No data you enter is ever transmitted to any server or stored anywhere. Your inputs remain completely private.

How do I verify Rlccircuit Impedance Calculator's result independently?

The Formula section on this page shows the equation used. You can reproduce the calculation manually or in a spreadsheet using those steps. Compare your answer against the worked examples in the Examples section, which use known reference values so you can confirm the calculator is behaving as expected.

Can I use Rlccircuit Impedance Calculator on a mobile device?

Yes. All calculators on NovaCalculator are fully responsive and work on smartphones, tablets, and desktops. The layout adapts automatically to your screen size.

Why might my result differ from another tool or reference?

Differences typically arise from rounding conventions, the specific version of a formula (for example, simple vs compound interest), or unit inconsistencies between inputs. Check that both tools are using the same formula variant and the same units. The References section links to the authoritative source behind the formula used here.

References

Reviewed by Daniel Agrici, Founder & Lead Developer ยท Editorial policy