USP <41> repeatability and minimum weight

Check balance repeatability the way USP <41> asks: s from at least 10 weighings, replaced by 0.41d when smaller, and 2s divided by the smallest net weight no more than 0.10 %. Gives the minimum weight (2000·s) and, on a dual-range balance, uses d from the range the test load is in. Rules checked against USP’s July 2014 official text; a revision official February 1, 2026 keeps them but separates minimum weight from smallest net weight. Check against the current USP–NF.

USP <41> repeatability · minimum weight

v0.1.0 · <41> Dec 2013 revision

Repeatability fromMass unitStandard deviation s of ≥ 10 weighingsDual-range balanceScale interval dTest load (optional)Smallest net weight you plan to weigh (optional)

Minimum weight (smallest net weight that passes)82 mg2000 × 0.41d = 2000 × 0.041 mg; s = 0.02, d = 0.1

Repeatability requirement 2s/m ≤ 0.10 %Meets2s/m = 0.08 % (rounded to two decimals) for m = 100 mg

s = 0.02 is below 0.41d = 0.041, so 0.41d is used, as <41> requires.

Based on the <41> text official July 1, 2014 (an interim revision of the December 2013 revision), checked against USP’s own copy. The revision official February 1, 2026 separates minimum weight (2000·s, from balance performance) from the smallest net weight (your requirement, which should exceed the minimum weight by a safety factor). Per USP’s commentary it also asks for a repeatability test weight of at least 100 mg and no more than 5 % of capacity, and tests multiple-range balances in each range used but multi-interval balances in the fine range only; this tool does not yet apply those test-load rules. Confirm against the current USP–NF.

Wording for a record

USP <41> repeatability: s = 0.02 mg; d = 0.1 mg; 0.41d = 0.041 mg used. Smallest net weight that meets 2s/m ≤ 0.10 %: 82 mg. For a smallest net weight of 100 mg, 2s/m = 0.08 % (rounded): meets the 0.10 % requirement.

s_eff = max(s, 0.41d) · 2s_eff/m ≤ 0.10 % · m_min = 2000·s_eff

How this is calculated

Equation: s_eff = max(s, 0.41d); passes if 2·s_eff/m_snw ≤ 0.10 % (rounded to 2 decimals in %); smallest passing net weight m_min = 2·s_eff/0.0010 = 2000·s_eff
Source: USP General Chapter <41> Balances. Rules checked against USP’s free Interim Revision Announcement (official July 1, 2014, uspnf.com), the text current until 2025; minimum weight 2000·s and the rounding example from Mettler Toledo (USP General Chapter <41>, 2015). A revision (Pharmacopeial Forum 50(5), 2024) of <41> and <1251> became official on February 1, 2026 (USP–NF 2026 Issue 1). Per USP’s published commentary it keeps these rules in substance, but its full text was not read (subscription); check the current official text.
Valid range: At least 10 readings (or s ≥ 0); d > 0; test load and net weight > 0 and within the balance’s top range; all in one mass unit
Rounding: Full precision inside; 2s/m is compared with 0.10 % after rounding to two decimals in percent (0.1049 % passes, 0.1050 % fails). Results shown to 6 significant figures.
Version: v0.1.0 · changelog
NCSLI MII taxa: Measure.Mass.Conventional Measure.Mass.True Source.Mass.Conventional Source.Mass.True

Calculated value, not a certified result. Accredited laboratories must validate any software they use (ISO/IEC 17025 clause 7.11).

Test vectors for this tool

The reference cases this calculator is tested against on every change. Use them to check your own software. All test vectors · Download JSON

ID	Inputs	Expected	Tolerance	Source
USP-01	s = 0.041, d = 0.1, unit = mg, output = minimumWeight	82 mg	± 1e-9	USP <41> Interim Revision Announcement, official July 1, 2014 (uspnf.com), repeatability section; minimum weight 2000·s and the rounding example from Mettler Toledo, “USP General Chapter <41>” (D Louvel, 2015, mt.com): s < 0.41d → use 0.41d; 2s/m ≤ 0.10 %; m_min = 2000 × s; rounding table 0.1049 % pass, 0.1050 % fail.
USP-02	s = 0.02, d = 0.1, unit = mg, output = minimumWeight	82 mg	± 1e-9	USP <41> Interim Revision Announcement, official July 1, 2014 (uspnf.com), repeatability section; minimum weight 2000·s and the rounding example from Mettler Toledo, “USP General Chapter <41>” (D Louvel, 2015, mt.com): s < 0.41d → use 0.41d; 2s/m ≤ 0.10 %; m_min = 2000 × s; rounding table 0.1049 % pass, 0.1050 % fail.
USP-03	s = 0.1, d = 0.1, unit = mg, output = minimumWeight	200 mg	± 1e-9	USP <41> Interim Revision Announcement, official July 1, 2014 (uspnf.com), repeatability section; minimum weight 2000·s and the rounding example from Mettler Toledo, “USP General Chapter <41>” (D Louvel, 2015, mt.com): s < 0.41d → use 0.41d; 2s/m ≤ 0.10 %; m_min = 2000 × s; rounding table 0.1049 % pass, 0.1050 % fail.
USP-04	s = 0, d = 0.01, unit = mg, output = minimumWeight	8.2 mg	± 1e-10	USP <41> Interim Revision Announcement, official July 1, 2014 (uspnf.com), repeatability section; minimum weight 2000·s and the rounding example from Mettler Toledo, “USP General Chapter <41>” (D Louvel, 2015, mt.com): s < 0.41d → use 0.41d; 2s/m ≤ 0.10 %; m_min = 2000 × s; rounding table 0.1049 % pass, 0.1050 % fail.
USP-05	s = 0, d = 1, unit = mg, output = minimumWeight	820 mg	± 1e-9	USP <41> Interim Revision Announcement, official July 1, 2014 (uspnf.com), repeatability section; minimum weight 2000·s and the rounding example from Mettler Toledo, “USP General Chapter <41>” (D Louvel, 2015, mt.com): s < 0.41d → use 0.41d; 2s/m ≤ 0.10 %; m_min = 2000 × s; rounding table 0.1049 % pass, 0.1050 % fail.
USP-06	s = 0.041, d = 0.1, smallestNetWeight = 82, unit = mg, output = passes	true	exact	USP <41> Interim Revision Announcement, official July 1, 2014 (uspnf.com), repeatability section; minimum weight 2000·s and the rounding example from Mettler Toledo, “USP General Chapter <41>” (D Louvel, 2015, mt.com): s < 0.41d → use 0.41d; 2s/m ≤ 0.10 %; m_min = 2000 × s; rounding table 0.1049 % pass, 0.1050 % fail.
USP-07	s = 0.05245, d = 0.1, smallestNetWeight = 100, unit = mg, output = passes	true	exact	USP <41> Interim Revision Announcement, official July 1, 2014 (uspnf.com), repeatability section; minimum weight 2000·s and the rounding example from Mettler Toledo, “USP General Chapter <41>” (D Louvel, 2015, mt.com): s < 0.41d → use 0.41d; 2s/m ≤ 0.10 %; m_min = 2000 × s; rounding table 0.1049 % pass, 0.1050 % fail.
USP-08	s = 0.0525, d = 0.1, smallestNetWeight = 100, unit = mg, output = passes	false	exact	USP <41> Interim Revision Announcement, official July 1, 2014 (uspnf.com), repeatability section; minimum weight 2000·s and the rounding example from Mettler Toledo, “USP General Chapter <41>” (D Louvel, 2015, mt.com): s < 0.41d → use 0.41d; 2s/m ≤ 0.10 %; m_min = 2000 × s; rounding table 0.1049 % pass, 0.1050 % fail.
USP-09	readings = [10.00012,10.0001,10.00013,10.00011,10.00012,10.0001,10.00014,10.00011,10.00012,10.00013], d = 0.00001, unit = g, output = s	0.000013165611772087668 g	± 1e-18	Sample standard deviation (n − 1) of the ten readings, exact rational arithmetic (Python fractions): s² = 13/75 000 000 000 g². USP <41> asks for NLT 10 weighings (Mettler Toledo summary).
USP-10	readings = [10.00012,10.0001,10.00013,10.00011,10.00012,10.0001,10.00014,10.00011,10.00012,10.00013], d = 0.00001, unit = g, output = minimumWeight	0.02633122354417533 g	± 1e-15	USP <41> Interim Revision Announcement, official July 1, 2014 (uspnf.com), repeatability section; minimum weight 2000·s and the rounding example from Mettler Toledo, “USP General Chapter <41>” (D Louvel, 2015, mt.com): s < 0.41d → use 0.41d; 2s/m ≤ 0.10 %; m_min = 2000 × s; rounding table 0.1049 % pass, 0.1050 % fail. s from USP-09.
USP-11	s = 0.00002, ranges = [{"d":0.00001,"max":82},{"d":0.0001,"max":220}], testLoad = 100, unit = g, output = minimumWeight	0.082 g	± 1e-15	USP <41> Interim Revision Announcement, official July 1, 2014 (uspnf.com), repeatability section; minimum weight 2000·s and the rounding example from Mettler Toledo, “USP General Chapter <41>” (D Louvel, 2015, mt.com): s < 0.41d → use 0.41d; 2s/m ≤ 0.10 %; m_min = 2000 × s; rounding table 0.1049 % pass, 0.1050 % fail. On a dual-range balance d is the scale interval of the range the test load is in.
USP-12	s = 0.00002, ranges = [{"d":0.00001,"max":82},{"d":0.0001,"max":220}], testLoad = 50, unit = g, output = minimumWeight	0.04 g	± 1e-15	USP <41> Interim Revision Announcement, official July 1, 2014 (uspnf.com), repeatability section; minimum weight 2000·s and the rounding example from Mettler Toledo, “USP General Chapter <41>” (D Louvel, 2015, mt.com): s < 0.41d → use 0.41d; 2s/m ≤ 0.10 %; m_min = 2000 × s; rounding table 0.1049 % pass, 0.1050 % fail. On a dual-range balance d is the scale interval of the range the test load is in.
USP-13	readings = [10.00012,10.0001,10.00013,10.00011,10.00012,10.0001,10.00014,10.00011,10.00012], d = 0.00001, output = s	RangeError	exact	USP <41> Interim Revision Announcement, official July 1, 2014 (uspnf.com), repeatability section; minimum weight 2000·s and the rounding example from Mettler Toledo, “USP General Chapter <41>” (D Louvel, 2015, mt.com): s < 0.41d → use 0.41d; 2s/m ≤ 0.10 %; m_min = 2000 × s; rounding table 0.1049 % pass, 0.1050 % fail. Repeatability is assessed by weighing one test weight NLT 10 times.
USP-14	s = 0.00002, d = 0, output = minimumWeight	RangeError	exact	USP <41> Interim Revision Announcement, official July 1, 2014 (uspnf.com), repeatability section; minimum weight 2000·s and the rounding example from Mettler Toledo, “USP General Chapter <41>” (D Louvel, 2015, mt.com): s < 0.41d → use 0.41d; 2s/m ≤ 0.10 %; m_min = 2000 × s; rounding table 0.1049 % pass, 0.1050 % fail.
USP-15	s = 0.00002, ranges = [{"d":0.00001,"max":82},{"d":0.0001,"max":220}], testLoad = 230, unit = g, output = minimumWeight	OutOfRangeError	exact	A repeatability test load must be within the balance’s capacity (USP <41> test weight “within the balance’s operating range”, Mettler Toledo summary).

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