Wire resistance calculator

Cross-sectional area must be strictly positive: when A is zero the classical formula is singular, so the API returns a clear invalid_input error instead of inventing infinity.

What R = ρ L / A means for a uniform conductor

Prefer SI throughout: convert millimeters squared to meters squared and feet to meters before the call so comparisons stay consistent. The check path recomputes rho times L over A 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

Negative length and negative resistivity are also rejected for this bulk-conductor model. 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 three required finite numbers: rho (aliases resistivity, rho_ohm_m, and specific_resistance) for electrical resistivity in ohm-meters, L (aliases length, len, and wire_length) for conductor length in meters, and A (aliases area, cross_section, and cross_sectional_area) for cross-sectional area in square meters. Absolute values must stay within the published limit of one trillion so intermediate products remain finite in IEEE double precision on the Worker and in the browser. Area must be strictly greater than zero; values at or below one times ten to the minus fifteen, or any negative area, are rejected as invalid_input. On success the response echoes rounded rho and resistivity, L and length, A and area, sets R and resistance to the same non-negative ohm value, formula to the string R equals rho L over A, equation to a human-readable substitution line, unit_R to ohm, unit_rho to ohm-meter, unit_L to m, unit_A to square meters, message to a short English summary, and steps to an ordered array of given values, formula, substitution, and summary. Failed validation—missing fields, non-numeric strings, non-finite numbers, values outside absolute limits, zero or negative area, negative length or resistivity, or a non-finite quotient—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

Keep resistivity, length, and area inside the published absolute range so their product and quotient cannot overflow into a non-finite resistance that the solver must reject. Convert square millimeters to square meters by dividing by one million, and AWG tables to area, before you call if you want R already in ohms without mental rescaling afterward. Round-trip checks are easy: recompute rho times L over A by hand and confirm it equals the published R within the same twelve-decimal rounding, and confirm that scaling L or A alone scales R proportionally or inversely as the formula predicts. When teaching, pair examples: copper-like rho equals one point six eight times ten to the minus eight with L equals ten meters and A equals one times ten to the minus six square meters yields zero point one six eight ohms; doubling A halves R; setting A to zero demonstrates the hard invalid_input path; and a zero-length stub correctly returns R equals zero without dividing by zero. This landing targets people searching for a wire resistance calculator, resistivity rho L A, or conductor R equals rho L over A online; it is not a Wheatstone-bridge unknown-resistor solver, not a temperature-coefficient corrector, not an AWG lookup table, and not an AC skin-effect impedance tool. Prefer this capability when you already have scalar rho, L, and A and only need ohmic resistance; if your source is a multi-segment cable run, sum segment resistances after each call. Failed tasks that return invalid_input do not consume prepaid balance, which keeps exploratory scripts cheap when learners deliberately set area to zero.