What is the LC resonance frequency formula?

The resonant frequency of an LC tank is f = 1 / (2π·√(L·C)), with L in henry and C in farad. For a 1 mH inductor and a 1 µF capacitor, √(L·C) = √(1e-9) ≈ 3.162e-5, so f ≈ 1 / (2π·3.162e-5) ≈ 5033 Hz. The angular form is ω = 2π·f = 1 / √(L·C), which for the same parts is about 31623 rad/s. At this frequency the inductive and capacitive reactances cancel.

How do I find the capacitor needed for a target frequency?

Rearrange the formula to C = 1 / ((2π·f)²·L). Say you want a 1 MHz tuned circuit with a 100 µH coil: (2π·1e6)² ≈ 3.948e13, times 100e-6 gives 3.948e9, so C ≈ 1 / 3.948e9 ≈ 253 pF. Pick the mode 'Capacitor for a target frequency', type 1 MHz and 100 µH, and the tool shows that value directly without the arithmetic.

How do I find the inductor needed for a target frequency?

By symmetry L = 1 / ((2π·f)²·C). For a 455 kHz intermediate-frequency stage with a 250 pF capacitor, (2π·455e3)² ≈ 8.17e12, times 250e-12 gives 2.043, so L ≈ 1 / 2.043 ≈ 0.49 H. Use the 'Inductor for a target frequency' mode, enter 455 kHz and 250 pF, and read the required inductance. This is how you size a coil when the capacitor is fixed.

Why are µH and pF the usual units in radio work?

Radio-frequency tanks use tiny components: an FM front-end coil might be 0.1 µH and its trimmer 25 pF, resonating near 100 MHz. Typing those in farad and henry means counting zeros (0.0000001 H, 0.000000000025 F), which invites mistakes. The tool keeps native µH and pF so you enter exactly what is printed on the part, and it converts to SI internally.

What does the angular frequency ω tell me?

Angular frequency ω = 2π·f measures the oscillation in radians per second rather than cycles per second. It is the quantity that shows up directly in the reactance formulas X_L = ω·L and X_C = 1 / (ω·C), and in the time-domain solution cos(ω·t) of an LC oscillator. At resonance X_L = X_C, which is exactly where ω = 1 / √(L·C). Engineers reach for ω when writing the differential equations; f when reading a dial.

Does this account for resistance, Q or losses?

No. This calculator gives the ideal lossless resonant frequency f = 1 / (2π·√(L·C)), which assumes a pure inductor and pure capacitor. Real coils have series resistance and real caps have leakage, so a damped RLC circuit resonates a hair lower and rings with a finite Q. For most tuning and filter design the ideal LC frequency is the right starting number, then you tweak for stray capacitance and component tolerance on the bench.

Tune an AM radio front-end coil and trimmer

You are building a crystal or regenerative AM receiver and need the tank to cover the broadcast band. Enter a 100 µH loop antenna inductance and sweep the trimmer capacitor: at 250 pF the tool reads about 1.007 MHz, right in the middle of the band. Adjust the cap value and watch the frequency move so you know the tuning range your variable capacitor must span from 540 to 1600 kHz.

Size the capacitor for a Colpitts or Hartley oscillator

Your oscillator design fixes the inductor at a value you already have wound, and you need the cap that lands the output on the target frequency. Switch to 'Capacitor for a target frequency', enter the frequency the spec asks for and the inductance on your bench, and read the exact picofarad value. Round to the nearest stock part and you have your starting point before fine-tuning for stray capacitance.

Design a passive LC band-pass or notch filter

A filter's center frequency is set by its LC resonance. Plug in the inductor and capacitor from your filter table and confirm the resonance lands where the passband should be, before you commit to a board layout. If it is off, the inverse modes tell you which component to change and by how much to move the center frequency onto target.

Check a textbook or homework LC problem

Working through circuits coursework, you get an LC pair and must find the natural frequency, or you are given f and asked for the missing component. Type the values, compare the resonant frequency and angular frequency against your hand calculation, and use the inverse mode to verify the back-solved capacitor or inductor. The shareable link lets you send the exact setup to a study partner or grader.

LC Resonance Frequency Calculator — f = 1/(2π√(LC))

f = 1 / (2π·√(L·C)) — frequency from L and C, or solve back for the capacitor or inductor — angular frequency, one-click copy, browser-only

Runs locally
Category Calculator
Best for Getting a realistic range before a purchase, plan, workout, or schedule decision.

Compute the resonant frequency of an LC tank from inductance and capacitance, or work backward: fix a target frequency and one component to find the other.

What to solve

Common circuits

Inductance L

Capacitance C

Result

Resonant frequency

1.0066 MHz

Angular frequency ω

6324600 rad/s

f = 1 / (2π·√(L·C))

What this tool does

Free LC resonance frequency calculator for tuning tank circuits, oscillators and filters. Enter an inductor L in henry, millihenry or microhenry and a capacitor C in farad, microfarad, nanofarad or picofarad, and the tool returns the resonant frequency f from the standard formula f = 1 / (2π·√(L·C)), plus the angular frequency ω = 1 / √(L·C) in radians per second. Need to hit a specific frequency instead? Switch the mode and the tool solves backward: fix a target frequency and a known inductor to get the exact capacitor, or fix the frequency and a known capacitor to get the inductor. Units autoscale on output, so a 100 µH coil with a 250 pF cap reads cleanly as about 1.007 MHz rather than a string of zeros. Everything runs in your browser with no upload, a one-click copy of the result, and a shareable URL that reopens your exact tuning.

Tool details

Input: Numbers; The page exposes text boxes, numeric controls, file pickers, or structured inputs depending on the tool.
Output: Live result + Copy; The result area focuses on usable output, with copy, download, or preview actions when supported.
Privacy: Browser-side processing; The main tool logic does not call an external API, so inputs normally stay in the current tab.
Save / share: Shareable URL state; Key settings are encoded in the URL so another person can reopen the same setup.
Performance budget: Initial JS <= 9 KB; No WASM budget is declared, keeping the tool quick to open on mobile.
Best fit: Calculator · Developer; Category and role tags drive related tools, internal links, and quick fit checks.

How to use

1. Input

Paste or drop your content into the tool panel.
2. Process

Click the button. All processing is local in your browser.
3. Copy / Download

Copy the result or download to disk in one click.

How LC Resonance Frequency Calculator fits into your work

Use it for fast estimates, comparisons, and planning numbers before you make the final call.

Calculation jobs

Getting a realistic range before a purchase, plan, workout, or schedule decision.
Comparing scenarios by changing one input at a time.
Turning rough assumptions into a number you can discuss.

Calculation checks

Double-check units, dates, rates, and rounding assumptions.
Treat health, finance, tax, and legal outputs as planning aids, not professional advice.
Save the inputs that produced an important result so you can reproduce it later.

Good next steps

These links move the current task into a more complete workflow.

Real-world use cases

Tune an AM radio front-end coil and trimmer
You are building a crystal or regenerative AM receiver and need the tank to cover the broadcast band. Enter a 100 µH loop antenna inductance and sweep the trimmer capacitor: at 250 pF the tool reads about 1.007 MHz, right in the middle of the band. Adjust the cap value and watch the frequency move so you know the tuning range your variable capacitor must span from 540 to 1600 kHz.
Size the capacitor for a Colpitts or Hartley oscillator
Your oscillator design fixes the inductor at a value you already have wound, and you need the cap that lands the output on the target frequency. Switch to 'Capacitor for a target frequency', enter the frequency the spec asks for and the inductance on your bench, and read the exact picofarad value. Round to the nearest stock part and you have your starting point before fine-tuning for stray capacitance.
Design a passive LC band-pass or notch filter
A filter's center frequency is set by its LC resonance. Plug in the inductor and capacitor from your filter table and confirm the resonance lands where the passband should be, before you commit to a board layout. If it is off, the inverse modes tell you which component to change and by how much to move the center frequency onto target.
Check a textbook or homework LC problem
Working through circuits coursework, you get an LC pair and must find the natural frequency, or you are given f and asked for the missing component. Type the values, compare the resonant frequency and angular frequency against your hand calculation, and use the inverse mode to verify the back-solved capacitor or inductor. The shareable link lets you send the exact setup to a study partner or grader.

Common pitfalls

Mixing up the prefixes. A 100 µH coil is 1e-4 H, not 1e-6 H; a 250 pF cap is 2.5e-10 F, not 2.5e-9 F. Picking the wrong unit on the dropdown shifts the frequency by orders of magnitude. Read the part marking carefully and match the unit before trusting the answer.
Forgetting the 2π. The formula is f = 1 / (2π·√(L·C)), not 1 / √(L·C); the second expression is the angular frequency ω in rad/s, which is 2π times larger. Reporting ω as if it were f overstates the cyclic frequency by about 6.28×.
Expecting the ideal frequency to match the bench exactly. This is the lossless LC value. Stray capacitance from wiring, the coil's self-resonance and component tolerance all pull the real resonance a little, usually lower. Treat the calculated number as the design center and trim on the bench.

Privacy

Every step here — the resonance formula, the inverse solve for C or L, the angular frequency and the unit conversions — is plain JavaScript running in your browser tab. No component value or frequency ever leaves the page and nothing is logged. The one caveat: the shareable URL encodes your inputs and units in the query string, so a link pasted into chat records those values in the recipient server's access log. For confidential design work, use the copy button and paste the text instead of sharing the URL.

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LC Resonance Frequency Calculator — f = 1/(2π√(LC))

What this tool does

Tool details

How to use

1. Input

2. Process

3. Copy / Download

How LC Resonance Frequency Calculator fits into your work

Calculation jobs

Calculation checks

Good next steps

Real-world use cases

Tune an AM radio front-end coil and trimmer

Size the capacitor for a Colpitts or Hartley oscillator

Design a passive LC band-pass or notch filter

Check a textbook or homework LC problem

Common pitfalls

Privacy

FAQ

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