DPMO calculator

This calculator takes a non-negative defect count, a positive unit count, and a positive opportunities-per-unit count, returns the DPMO value together with total opportunities, the defect rate, and defects per unit, and rejects zero or negative units or opportunities with invalid_input so callers never see a silent infinity. The arithmetic is fully deterministic, runs free in the browser, and is available over the API at $0.002 per successful request with no language model and no external quality-management service on the hot path.

Input contract, validation, and the JSON you get back

Call the capability with three required finite numbers. Zero or negative units, and zero or negative opportunities per unit, fail with a message that those quantities make DPMO undefined, matching the rule that the calculator must not divide by zero. Negative defects fail as well because a negative count is not a physical inspection result. Failed validation is never charged. Field defects (aliases defect_count and d) is the observed defect count and must be non-negative; zero is allowed and yields DPMO of zero. Field units (aliases unit_count and n) is how many items were inspected and must be strictly greater than zero. Field opportunities_per_unit (aliases opportunities, opu, and opp) is how many independent chances for a defect exist on each unit and must also be strictly greater than zero. Each field may arrive as a JSON number or as a numeric string; missing values, empty strings, NaN, and infinities fail with invalid_input naming the field. On success the body echoes the three inputs, reports total_opportunities as units times opportunities per unit, reports defect_rate as defects over total opportunities, reports dpu as defects per unit, and reports dpmo as the scaled million-opportunity figure, together with a formula string and a short English message. Example: defects twenty-five, units two hundred, opportunities_per_unit five produces total opportunities one thousand and DPMO twenty-five thousand.

Where a DPMO calculator earns its keep

Use the browser tool when you want an immediate DPMO while checking a homework answer, reviewing a first-article inspection, or explaining why opportunity count matters as much as defect count. Results are fully deterministic: the same defects, units, and opportunities always yield the same DPMO, defect rate, and defects-per-unit figures. Prefer this capability when you already have the three counts and only need DPMO; if your source is a word problem, extract defect count, unit count, and opportunities per unit first, then call the solver and compare the published dpmo field to your hand calculation. Each successful request is one billable item at $0.002; failed validation does not consume balance. Keep counts inside ordinary inspection ranges so the product of units and opportunities remains a finite IEEE number; if an input would overflow to Infinity the solver rejects the request rather than returning a non-numeric DPMO. Wire the endpoint into supplier scorecards, process-capability dashboards, coding-interview sandboxes, or preprocessing steps where you already prefer a closed-form DPMO over opaque calculators that hide whether they multiplied by opportunities per unit before scaling to a million. This landing is for people searching for a DPMO calculator or defects-per-million-opportunities tool; it is not a Cpk calculator, not a process-yield converter from chemistry percent yield, and not a parts-per-million concentration converter.