Is series resonance the same as parallel resonance?

The frequency is the same and the behaviour is opposite. At resonance a series LC presents its minimum impedance, so it lets that frequency through and is used to pass or to shunt one; a parallel LC presents its maximum, so it blocks that frequency and is used to reject or to select one. Which of the two a design needs depends on whether the tuned element sits in the signal path or across it, and putting the right formula on the wrong topology produces a circuit that does exactly the opposite of the intention at precisely the right frequency.

Why do the units in the formula look inconsistent?

They are not, once everything is in base units. The formula wants henries and farads, and the fields here take millihenries and microfarads because those are the values printed on real components — a 10 mH inductor is 0.01 H and a 100 µF capacitor is 0.0001 F, and their product is a millionth. Anyone checking by hand should convert first and only then take the square root; converting afterwards is where the answers a thousand times out come from, and a thousandfold error in a frequency is easy to miss when the result is still a plausible-looking number of hertz.

Doubling the Capacitor Lowers the Frequency by 29 %, Not 50 %

Published 10/8/2026 · 3 min read · Everyday calculators

Daniel Okonkwo — Front-end developer and tech writer at OneKitly

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In short

The resonant frequency is one divided by two pi times the square root of L times C, which for 10 mH and 100 µF gives 159.2 Hz. The square root is what makes tuning frustrating in practice. Doubling the capacitance to 200 µF divides the frequency by the square root of two, so it lands at 112.5 Hz — a fall of 29.3 %, not the half that the doubled component suggests. Reaching half the frequency, 79.6 Hz, needs four times the capacitance or four times the inductance, and the two are interchangeable: 40 mH with the original 100 µF gives exactly the same answer. Anyone tuning by swapping parts should expect to move in factors of four, and anyone estimating in their head should take the square root before being surprised.

10 mH with 100 µF resonates at 159.2 Hz. Double the capacitance and it falls to 112.5 Hz; to halve the frequency you have to quadruple a component, because both sit under a square root.

The formula gives the centre and says nothing about the width

Two circuits can resonate at the same frequency and behave completely differently, because this expression contains no resistance. Resistance sets the quality factor, and the quality factor sets how sharply the circuit selects: a high-Q tuned circuit responds to a narrow band around 159.2 Hz, a low-Q one responds broadly and rings only briefly when struck. Whether that is good depends on the job — a radio front end wants sharpness so it can reject the station next door, while a power supply output filter wants damping so it does not oscillate when the load changes. Compute the centre here and then ask what the resistance in the loop is doing.

The nominal value is not what is in the circuit

Tolerance propagates through the square root and halves as it goes, which is the one piece of good news here: ten per cent on the capacitance moves the frequency by about five. Everything else works the other way. Stray capacitance between windings and tracks adds to whatever the design intended, an inductor's value shifts with the current through it as its core approaches saturation, and both drift with temperature. For a circuit that has to sit on a frequency rather than near one, the practical route is a trimmer and a measurement, not a longer calculation.

Frequency

Starting from 10 mH and 100 µF
Change	Frequency
none	159.2 Hz
capacitance ×2	112.5 Hz
capacitance ×4	79.6 Hz
inductance ×4	79.6 Hz

Worked with our own calculator

LC resonant frequency calculator

Given

Inductance (mH): 10
Capacitance (µF): 100

Result

Resonant frequency (Hz): 159.155

These figures are produced by the calculator below, not typed in by hand — they are recomputed whenever the tool changes.

Run it on your own figures →

Frequently asked questions

Is series resonance the same as parallel resonance?: The frequency is the same and the behaviour is opposite. At resonance a series LC presents its minimum impedance, so it lets that frequency through and is used to pass or to shunt one; a parallel LC presents its maximum, so it blocks that frequency and is used to reject or to select one. Which of the two a design needs depends on whether the tuned element sits in the signal path or across it, and putting the right formula on the wrong topology produces a circuit that does exactly the opposite of the intention at precisely the right frequency.
Why do the units in the formula look inconsistent?: They are not, once everything is in base units. The formula wants henries and farads, and the fields here take millihenries and microfarads because those are the values printed on real components — a 10 mH inductor is 0.01 H and a 100 µF capacitor is 0.0001 F, and their product is a millionth. Anyone checking by hand should convert first and only then take the square root; converting afterwards is where the answers a thousand times out come from, and a thousandfold error in a frequency is easy to miss when the result is still a plausible-looking number of hertz.

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Sources

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