# Ohmforge Impedance Calculator

> Complex impedance of R, L, C series/parallel networks: |Z|, phase, admittance, resonance. Type a small network such as R100 + (L10m || C1u) and a frequency. The calculator returns the complex impedance (R + jX), magnitude and phase, the admittance G + jB, the equivalent inductance or capacitance at that frequency, Q, every resonance of the network, an |Z| and phase plot over frequency and the reactance of each part – checked against Ohmforge's AC simulator.

Part of usefulweb.app (https://usefulweb.app/). Part of [Ohmforge](https://ohmforge.usefulweb.app/) (ownerApp: ohmforge). Results are deterministic calculations from the inputs and the listed assumptions; the API returns exactly what the web page shows.

## Use it
- Human interface: https://ohmforgeimpedancecalculator.usefulweb.app/ (interactive tool at https://ohmforgeimpedancecalculator.usefulweb.app/tool)
- JSON API: POST https://ohmforgeimpedancecalculator.usefulweb.app/api/v1/calculate with a JSON object of inputs (schema: https://ohmforgeimpedancecalculator.usefulweb.app/api/v1/tool)
- OpenAPI: https://ohmforgeimpedancecalculator.usefulweb.app/openapi.json
- MCP (Streamable HTTP): https://ohmforgeimpedancecalculator.usefulweb.app/mcp - tool `ohmforge_impedance_calculator`

## Inputs
- network (text): Network - Elements R<value>, L<value>, C<value>; + = series, || (or //) = parallel, parentheses group. || binds tighter than +.
- frequency (number): Frequency

## Method
- Each element becomes a complex impedance: Z_R = R, Z_L = jωL, Z_C = 1/(jωC) with ω = 2πf. Series groups add impedances, parallel groups add admittances (Y = 1/Z). Complex division uses Smith's algorithm for numerical robustness.
- Admittance Y = 1/Z = G + jB. The equivalent part at the frequency is L = X/ω for X > 0 or C = −1/(ωX) for X < 0; Q = |X| / R of the series equivalent.
- Resonances are frequencies where the reactance X changes sign (zero phase): found on a 50-points-per-decade scan from 1 mHz to 100 GHz and refined by bisection. A minimum of |Z| (X from − to +) is a series resonance, a maximum (X from + to −) a parallel resonance.
- Cross-check: the network is driven by a 1 A AC current source in Ohmforge's AC analysis, so the simulated node voltage equals Z; the relative difference is reported.

## Limits
- Ideal parts: real inductors have winding resistance and self-resonance, capacitors have ESR and ESL, and both change with frequency, temperature and (for ceramics) DC bias.