The RLC impedance calculator above evaluates a resistor, inductor and capacitor network at a frequency you choose, rather than only at resonance. It returns the impedance magnitude in ohms, the phase angle between voltage and current, the two individual reactances, the current the network draws from a given voltage, and the power factor that follows from the phase. It works for the series arrangement and the ideal parallel arrangement, whose impedance curves are opposites of one another.
Arb Digital builds free calculators that let you probe a system rather than read one fixed answer. Impedance is a function of frequency, and the interesting engineering lives in how it changes as you sweep across the band — a coupling capacitor that looks like a short at 10 kHz can look like an open at 10 Hz. This page makes that sweep easy by keeping the frequency in its own field with its own unit selector, and it names the character of the load in plain words rather than leaving a signed angle to interpret.
What This RLC Impedance Calculator Does
It treats impedance as a complex quantity with a resistive part and a reactive part, and reports its polar form. The hero shows the magnitude, the number an impedance meter would display. Underneath it, the rectangular form is spelled out as a resistance plus or minus a reactance, because that is the form you need when combining this network with anything else.
The grid separates the two reactances instead of showing only their difference. That separation is what tells you which component is dominating and by how much. At a frequency well below resonance the capacitive reactance is enormous and the inductor is almost irrelevant; well above resonance the reverse holds; at resonance the two are equal and cancel exactly. Seeing both numbers makes the crossover obvious in a way that a single net reactance never does.
The phase angle uses the standard sign convention: positive when the network is inductive and the current lags the voltage, negative when it is capacitive and the current leads. Current is computed from the applied RMS voltage and the impedance magnitude, and the note reports real power, apparent power and power factor, which are the quantities that decide what a supply actually has to deliver.
How to Use It
- Set the topology and the frequency. These two together decide everything else, and the frequency unit selector saves counting zeros in the radio bands.
- Enter the component values. Use the unit selectors rather than typing exponents, and remember that a zero in the L or C field removes that component instead of shorting or opening it.
- Read the two reactances first. Their relative size tells you immediately whether you are below, at or above resonance, before you look at the magnitude at all.
- Use the resonance button to anchor yourself. It sets the frequency to the exact resonant value so you can see the impedance extreme, then step away in either direction.
- Check the power factor. A phase angle near ninety degrees means almost all the apparent power is reactive and very little real work is being done.
The Formula: How RLC Impedance Is Calculated
Inductive reactance is XL = 2πfL and rises with frequency. Capacitive reactance is XC = 1 ÷ (2πfC) and falls with frequency. For the series network the two subtract because they are in antiphase, so the net reactance is X = XL − XC and the magnitude is Z = √(R² + X²) with phase φ = arctan(X ÷ R). Section 15.3 of OpenStax University Physics Volume 2, RLC Series Circuits with AC, derives this from the phasor diagram and defines impedance as the AC analogue of resistance.
The parallel case is done in admittance rather than impedance, because parallel elements add their admittances. Conductance is G = 1 ÷ R, and the net susceptance is B = 2πfC − 1 ÷ (2πfL). Magnitude is then 1 ÷ √(G² + B²) and the phase is the negative of arctan(B ÷ G). The sign flip is why a parallel network is inductive below resonance and capacitive above it — exactly the opposite of the series case. The individual reactance definitions come from section 15.2, Simple AC Circuits.
Work the defaults. At 1 kHz with L = 10 mH, XL = 2π × 1,000 × 0.01 = 62.83 Ω. With C = 100 nF, XC = 1 ÷ (2π × 1,000 × 10−7) = 1,591.55 Ω. Net reactance is −1,528.72 Ω, strongly capacitive, and with R = 50 Ω the magnitude is √(2,500 + 2,336,984) = 1,529.54 Ω. The phase is arctan(−1,528.72 ÷ 50) = −88.13°, and 10 V RMS drives 6.54 mA. Power factor is cos(−88.13°) = 0.0327, so of 65.4 mVA apparent, only about 2.1 mW is real power.
Why Reactances Subtract Instead of Adding
Both reactances are measured in ohms, so the instinct is to add them like resistors in series. They subtract because the voltage across an inductor leads the current by ninety degrees while the voltage across a capacitor lags it by ninety degrees, putting the two voltages exactly one hundred and eighty degrees apart. Two equal-magnitude, opposite-phase voltages cancel.
This is what makes resonance possible and what makes reactive components fundamentally different from resistors. Resistors always add and always dissipate; reactances can cancel and never dissipate at all. In the default circuit the inductor and capacitor between them account for 1,528.72 Ω of the 1,529.54 Ω total, yet they consume no power. All 2.1 mW of real power is dissipated in the 50 Ω resistor, a point made explicitly in section 15.4 of OpenStax University Physics Volume 2, Power in an AC Circuit.
The right-angle relationship also explains why the magnitude uses Pythagoras rather than a plain sum. Resistance and net reactance are perpendicular in the complex plane, so a network with 50 Ω of resistance and 50 Ω of reactance has an impedance of 70.7 Ω, not 100 Ω, and a phase angle of exactly forty-five degrees.
Reading the Impedance Curve Without Plotting It
Three frequencies define the whole shape of a series RLC response, and you can find them with this tool in under a minute. Far below resonance, XC dominates, impedance falls as frequency rises, and the phase sits near minus ninety degrees. At resonance the reactances cancel, impedance collapses to R alone and the phase is exactly zero. Far above resonance, XL dominates, impedance rises with frequency and the phase approaches plus ninety degrees.
The parallel network does the mirror image. Its impedance peaks at resonance rather than dipping, and its phase runs from plus ninety degrees below resonance through zero at resonance to minus ninety degrees above it. That is why a parallel tank is used to select a frequency by presenting a high impedance to it, while a series network is used to shunt a frequency to ground by presenting a low one.
A useful shortcut: the phase angle passes through forty-five degrees exactly at the half-power frequencies of the resonant response, so if you sweep until the phase reads ±45° you have found the edges of the passband without needing a magnitude measurement. The RLC circuit calculator reports those two frequencies directly if you would rather not hunt for them.
Impedance Is Not Resistance, and Meters Know the Difference
A common source of confusion is that a multimeter set to ohms will not measure any of the numbers on this page. It applies a DC test current, and at DC the inductor is a short and the capacitor an open, so a series RLC reads as an open circuit and a parallel one reads as the coil's winding resistance. Neither result has any bearing on how the network behaves at its working frequency.
Impedance meters and LCR bridges avoid this by driving the network with a small AC signal at a stated test frequency, which is why every honest LCR measurement is quoted with the frequency it was taken at. It also explains why the same capacitor can be specified with different equivalent series resistance figures in different data sheets — they were tested at different frequencies. If you need to compare a calculated result with a measurement, match the frequencies first.
One more practical note: the voltage field here is RMS, and mixing RMS with peak values is a routine error when working from an oscilloscope trace rather than a meter. The RMS voltage calculator converts between RMS, peak and peak-to-peak for the common waveforms, and the current figure this tool reports will be RMS whenever the voltage you entered was.
How This Differs From the Site's Other Circuit Tools
The boundary in one sentence: this page gives impedance and phase at whatever frequency you specify, while the RLC circuit calculator describes the resonance itself — the peak frequency, the Q factor, the bandwidth and the damping regime — and says nothing about behaviour away from that peak.
The reactance calculator handles a single inductor or a single capacitor and returns one reactance, which is a component-level question rather than a network-level one. The LC resonant frequency calculator solves for the resonant frequency or for a component value with no losses involved. The filter cutoff calculator covers first-order RC and RL corners, the Ohm's law calculator covers DC, and the capacitance converter and inductance converter rescale component values. Work on mains circuits belongs with the breaker size calculator and a licensed electrician rather than with any of these.
Arb Digital builds free tools like this one because useful pages earn attention. If you want tools, calculators or content built for your own audience, we can help.
Browse All Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Adding the reactances — they are in antiphase and subtract. Adding them gives an impedance that can be wildly too large near resonance.
- Adding resistance and reactance arithmetically — they are perpendicular, so the magnitude is the hypotenuse. 50 and 50 give 70.7, not 100.
- Measuring impedance with a DC ohmmeter — at zero hertz the inductor is a short and the capacitor an open, so the reading has nothing to do with the working frequency.
- Mixing RMS and peak voltages — an oscilloscope shows peak or peak-to-peak, a meter shows RMS, and the resulting current figures differ by a factor of about 1.41 or 2.83.
- Using the series phase convention on a parallel network — the sign reverses, so a parallel network below resonance is inductive where a series one is capacitive.
Related Free Tools From Arb Digital
For the resonance itself, use the RLC circuit calculator; for a single component, the reactance calculator. The LC resonant frequency calculator sizes components for a target frequency, the filter cutoff calculator handles first-order corners, and the RMS voltage calculator keeps your voltage conventions straight. The Ohm's law calculator, capacitance converter and inductance converter cover the supporting arithmetic, and the breaker size calculator is the right starting point for anything mains-connected. The full free online tools hub lists everything.
Frequently Asked Questions
Because the three are not in phase with one another. The reactances are one hundred and eighty degrees apart so they subtract, and the result is ninety degrees from the resistance, so the magnitude is found with Pythagoras rather than addition.
That the network is capacitive and the current leads the applied voltage. A positive angle means inductive behaviour with the current lagging, and zero means the reactances have cancelled and the network looks purely resistive.
Not on the ohms range. A multimeter uses a DC test current, which sees the inductor as a short and the capacitor as an open. Impedance needs an AC measurement at a stated test frequency, which is what an LCR meter provides.
Because parallel elements add admittances rather than impedances, which inverts the sign of the reactive term. A parallel network is therefore inductive below resonance and capacitive above it, the reverse of the series case.
In a series network the reactances cancel and the impedance falls to the resistance alone, with zero phase angle. In a parallel network the impedance rises to a maximum instead, which is why parallel tanks are used to select frequencies.
No. Ideal reactive components store energy and return it each cycle, so all real power is dissipated in the resistance. That is why a network can have a large impedance and still draw almost no real power.
It removes that component from the network rather than treating it as a short or an open, which turns a series RLC into a plain RC or RL circuit. That makes it easy to compare a second-order network with its first-order relative.
This tool is provided for educational and study use. It models ideal lumped components with no parasitics, no source impedance and a single sinusoidal frequency, so treat its output as a design starting point rather than a verified result. Any circuit connected to mains electricity must be designed, installed and signed off by a qualified electrician working to the applicable wiring rules.
