Overhead conductor tension calculator

This overhead conductor tension calculator accepts those three finite positive numbers—span length, weight per unit length, and allowable sag—validates them, and returns horizontal tension together with echoed inputs and fixed formula labels as structured JSON.

What horizontal conductor tension means and when H = wL²/(8d) applies

Returning horizontal_tension, span_length, weight_per_unit_length, sag, formula, approximation, and method as JSON makes the result easy to paste into notes, pin in automated tests, or reuse across programming languages without reimplementing the arithmetic.

How this calculator validates input and applies the parabolic closed form

Span length, weight per unit length, and sag must all be strictly positive so the geometry and loading remain physically meaningful for this product contract—zero or negative sag would divide by zero or reverse the sag direction, and a zero span is not a supported line section. There is no full catenary hyperbolic solver, no unequal-support elevation difference mode, no temperature-change or creep iteration, no built-in conductor catalog table, and no unit conversion table; this capability is the level-span parabolic horizontal-tension case only. Send a JSON body with the three required fields span_length, weight_per_unit_length, and sag. Every field must be a finite number or a numeric string that parses to one; missing fields, empty strings, non-numeric text, NaN, and Infinity all fail immediately with invalid_input before any tension is returned, and failed validation is not charged against prepaid balance. Optional aliases such as L, span, length, w, weight, unit_weight, d, allowable_sag, and dip are accepted when documented so forms and scripts can use textbook symbols without renaming fields. After validation the engine computes horizontal tension as weight_per_unit_length times span_length squared divided by eight times sag, then rounds to a stable precision so the same input always yields the same JSON across JavaScript engines and Worker isolates. The same pure function powers the free in-browser tool and the API path, with no network call, no random seed, and no wall-clock timestamp in the computation path, which keeps goldens and continuous-integration checks reliable.

Practical use, limits, pricing, and delivery channels for span tension checks

Use the browser tool when you want an immediate horizontal tension check while grading power-system homework, comparing a hand calculation of w L squared over eight d, verifying that a proposed sag keeps H below a fraction of rated strength, or teaching how tension rises when span grows or when allowable sag shrinks. There is no language model, no external line-design service, and no randomness, so the capacity is safe to pin in continuous-integration checks and reproducible course materials. When your problem moves to full catenary geometry, unequal supports, or multi-span ruling spans with temperature and creep, switch to a more general line-design tool; this calculator stays focused on the single level-span parabolic horizontal tension so the answer stays transparent and fast. Each successful request is one billable item at $0.002; failed validation does not consume balance. Choose units consistently and stay within the published magnitude bounds so intermediate products remain finite on a Worker isolate. Results are fully deterministic: identical inputs always produce the same horizontal_tension value and the same formula, approximation, and method labels. Wire the endpoint into transmission drills, early-stage clearance worksheets, catalog conductor screeners, or preprocessing steps where you prefer explicit domain errors—such as rejecting zero sag or a zero span—over opaque widgets that cannot explain why a bad input was refused.