LC resonant frequency calculator

Inductance and capacitance must both be strictly positive: zero L or zero C would send the classical formula to infinity, so the API returns a clear invalid_input error instead of inventing Infinity or NaN.

What f0 = 1 / (2 π √(L C)) means for an ideal LC tank

Prefer SI throughout: convert millihenries to henries and microfarads to farads before the call so comparisons stay consistent. The check path recomputes one over two pi square root of L C with the same fixed rounding used for published fields, so a successful response always ships with steps you can assert in tests or worksheets without floating-point ambiguity between the Worker and the browser.

How to call the API and what comes back

Prefer sending numbers rather than pre-formatted strings when you control the client; string numbers are accepted only when they match a strict finite numeric pattern including optional scientific notation. Send a JSON body with two required finite numbers: L (aliases inductance, henry, and henries) for inductance in henries, and C (aliases capacitance, farad, and farads) for capacitance in farads. Absolute values must stay within the published limit of one trillion so intermediate products and roots remain finite in IEEE double precision on the Worker and in the browser. Both L and C must be strictly positive; values whose absolute magnitude is at or below one times ten to the minus fifteen are treated as zero and rejected, and any strictly negative L or C is also invalid_input for this ideal passive tank model. On success the response echoes rounded L and inductance, C and capacitance, sets f0, frequency, and resonant_frequency to the same positive hertz value, omega0 and angular_frequency to one over square root of L C in rad/s, T and period to one over f0 in seconds, formula to the string f0 equals one over two pi square root of L C, equation to a human-readable substitution line, unit_f0 to Hz, unit_omega0 to rad/s, unit_T to s, unit_L to H, unit_C to F, message to a short English summary, and steps to an ordered array of given values, formula, product, square root, omega line, substitution, period, and summary. Failed validation—missing fields, non-numeric strings, non-finite numbers, values outside absolute limits, zero or negative L, zero or negative C, or a non-finite root—returns invalid_input and is never charged. Pricing is a flat $0.002 per successful request with unit item and zero marginal unit price.

Practical tips, limits, and related searches

When teaching, pair examples: L equals zero point zero zero one henry with C equals one times ten to the minus six farad yields about five thousand thirty-three hertz; scaling L or C by four halves f0; setting L to zero demonstrates the hard invalid_input path for zero inductance; and setting C to zero demonstrates the zero-capacitance rejection. This landing targets people searching for an LC resonant frequency calculator, tank circuit frequency, or f0 equals one over two pi square root of L C online; it is not an RLC damped natural-frequency tool, not a quality-factor or bandwidth calculator, not an inductive or capacitive reactance solver, and not a full impedance analyzer. Failed tasks that return invalid_input do not consume prepaid balance, which keeps exploratory scripts cheap when learners deliberately set inductance or capacitance to zero.