# LC Resonance Calculator

> Computes the resonant frequency of an inductor–capacitor circuit from L and C, or solves for the inductance or capacitance needed to resonate at a given frequency, plus the angular frequency and characteristic impedance √(L/C).

- Calculator id: `lc-resonance` · Category: Engineering & Automotive (`engineering`) · Tool name: `solve_lc_resonance`
- Canonical page: https://tttkmbb.com/engineering/lc-resonance · This document: https://tttkmbb.com/engineering/lc-resonance.md · JSON definition: https://tttkmbb.com/engineering/lc-resonance.json

## Purpose

Computes the resonant frequency of an inductor–capacitor circuit from L and C, or solves for the inductance or capacitance needed to resonate at a given frequency, plus the angular frequency and characteristic impedance √(L/C).

**Use when:** You are designing or analysing a tuned circuit, oscillator tank, RF filter or antenna trap and know two of inductance, capacitance and frequency.

**Do not use when:** Resistance matters (bandwidth and Q need the series/parallel resistance), or you have only R and C (use rc-time-constant).

## Input

| Parameter | Type | Unit | Required | Description |
| --- | --- | --- | --- | --- |
| `inductance_uh` | number | µH | optional | Inductance in microhenries (1 mH = 1000 µH, 1 nH = 0.001 µH). Omit to solve for it. (> 0) |
| `capacitance_pf` | number | pF | optional | Capacitance in picofarads (1 nF = 1000 pF, 1 µF = 1e6 pF). Omit to solve for it. (> 0) |
| `frequency_hz` | number | Hz | optional | Resonant frequency in hertz (1 kHz = 1000, 1 MHz = 1e6). Omit to solve for it. (> 0) |

## Output

| Field | Type | Unit | Description |
| --- | --- | --- | --- |
| `solved_for` | string |  | Which quantity was computed: frequency_hz, inductance_uh or capacitance_pf. |
| `resonant_frequency_hz` | number | Hz | f₀ = 1 / (2π √(L C)). |
| `resonant_frequency_khz` | number | kHz | f₀ in kilohertz. |
| `resonant_frequency_mhz` | number | MHz | f₀ in megahertz. |
| `angular_frequency_rad_s` | number | rad/s | ω₀ = 2π f₀ = 1 / √(L C). |
| `inductance_uh` | number | µH | L = 1 / ((2π f)² C). |
| `capacitance_pf` | number | pF | C = 1 / ((2π f)² L). |
| `characteristic_impedance_ohm` | number | Ω | √(L / C), the reactance of L and of C at resonance. |

## Formula

`resonant_frequency_hz = 1 / (2π √(L × C)) with L = inductance_uh × 1e-6 H and C = capacitance_pf × 1e-12 F; L = 1 / ((2π f)² C); C = 1 / ((2π f)² L); characteristic_impedance_ohm = √(L / C)`

## Data Sources

- Wikipedia – LC circuit — https://en.wikipedia.org/wiki/LC_circuit (reference, retrieved 2026-09-24)
- HyperPhysics – Series resonance — http://hyperphysics.phy-astr.gsu.edu/hbase/electric/serres.html (reference, retrieved 2026-09-24)

Data freshness: `static`. Deterministic formula with fixed constants; results never go stale. Inputs supplied by the caller determine the output.

## API

- `GET https://tttkmbb.com/api/v1/calculate/lc-resonance?`
- `POST https://tttkmbb.com/api/v1/calculate/lc-resonance` with JSON body `{"inputs": {…}}`
- Response: unified envelope (`success`, `request`, `result.values`, `result.units`, `sources`, `freshness`, `timestamp`, `next_actions`, `links`); see https://tttkmbb.com/docs/response-format.md
- Schema: https://tttkmbb.com/api/v1/calculators/lc-resonance · OpenAPI operationId `solve_lc_resonance` in https://tttkmbb.com/openapi.json
- Authentication: none. Rate limit: fair use, see https://tttkmbb.com/docs/rate-limits.md.

## MCP

- Server: `https://tttkmbb.com/mcp` (Streamable HTTP, JSON-RPC 2.0, no auth)
- Tool:  `run_calculator` with `{"calculator_id": "lc-resonance", "inputs": {…}}`

## Example

- 100 µH with 100 pF: inputs `{"inductance_uh":100,"capacitance_pf":100}` → `{"solved_for":"frequency_hz","resonant_frequency_hz":1591549.43,"resonant_frequency_mhz":1.591549,"angular_frequency_rad_s":10000000,"characteristic_impedance_ohm":1000}`
- Capacitor for 1 MHz with 10 µH: inputs `{"inductance_uh":10,"frequency_hz":1000000}` → `{"solved_for":"capacitance_pf","capacitance_pf":2533.0296,"characteristic_impedance_ohm":62.8319,"resonant_frequency_khz":1000}`

```
GET https://tttkmbb.com/api/v1/calculate/lc-resonance?inductance_uh=100&capacitance_pf=100
```

## Limitations

Resistance matters (bandwidth and Q need the series/parallel resistance), or you have only R and C (use rc-time-constant). All values are computed from the formula above; no measurement or live data is involved.

## FAQ

**Does resistance change the resonant frequency?**

Only slightly for a series RLC (f₀ is unchanged); in a parallel tank with coil resistance the peak shifts down a little. Resistance mainly sets the bandwidth f₀/Q.

**Why does the same L·C product give the same frequency?**

Only the product L·C fixes f₀; the ratio L/C sets the characteristic impedance, which determines the voltages and currents at resonance.

## Related

- [RC Time Constant Calculator](https://tttkmbb.com/engineering/rc-time-constant.md) — Time constant and cutoff of an RC pair.
- [Wavelength & Frequency Calculator](https://tttkmbb.com/physics/wavelength-frequency.md) — Wavelength of the resonant frequency.
- [Frequency Converter](https://tttkmbb.com/conversion/frequency.md) — Convert between Hz, kHz, MHz and GHz.