Certificate rounding and CMC check

Round an expanded uncertainty to two (or one) significant figures, round the result to the same decimal place, and copy a statement with the unit, k and coverage probability. Optionally check U against your scope CMC.

Certificate rounding · CMC check

v0.1.0 · U to 2 sig. fig.

Measured resultExpanded uncertainty UCoverage factor kCoverage probability (%)UnitSignificant figures in URoundingScope CMC

Report12.35 ± 0.10 mV

12.35 mV ± 0.10 mV (expanded uncertainty with coverage factor k = 2, coverage probability approximately 95 %)

How this is calculated

Equation: U rounded to 2 (or 1) significant figures; result rounded to the same decimal place as U; reported U not smaller than the scope CMC.
Source: Reporting policy per ILAC P14:09/2020 (ILAC Policy for Measurement Uncertainty in Calibration) §5.3 (expanded uncertainty to at most two significant digits, usual rounding rules subject to GUM section 7) and §5.5 (reported uncertainty not smaller than the CMC), and JCGM 100:2008 (GUM) §7.2.6 (at most two significant digits; the estimate rounded to match its uncertainty; rounding uncertainty up rather than to nearest is sometimes appropriate). In the superseded ILAC P14:01/2013 these were §6.3 and §6.5. Default rounds U to nearest (half up); rounding U up is an option. Rounding arithmetic is decimal and deterministic.
Valid range: U > 0; k > 0; coverage probability between 0 and 100 %. Refuses a result that would need more than 15 significant digits at U’s decimal place.
Rounding: Half up by default (a negative tie rounds away from zero), half to even as an option, or round U up (U rounded up, result half up). A U below the CMC is replaced by the CMC rounded up.
Version: v0.1.0 · changelog

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
CERT-01	value = 12.3456, U = 0.0234, k = 2, p = 95, unit = mV	12.346 ± 0.023 mV	exact	Hand-derived decimal arithmetic; derivation in "why"
CERT-02	value = 12.3456, U = 0.0995, k = 2, p = 95, unit = mV	12.35 ± 0.10 mV	exact	Hand-derived decimal arithmetic; derivation in "why"
CERT-03	value = 12.3456, U = 0.0994, k = 2, p = 95, unit = mV	12.346 ± 0.099 mV	exact	Hand-derived decimal arithmetic; derivation in "why"
CERT-04	value = 1.2345, U = 0.0125, k = 2, p = 95, unit = mV, mode = half-up	1.235 ± 0.013 mV	exact	Hand-derived decimal arithmetic; derivation in "why"
CERT-05	value = 1.2345, U = 0.0125, k = 2, p = 95, unit = mV, mode = half-even	1.234 ± 0.012 mV	exact	Hand-derived decimal arithmetic; derivation in "why"
CERT-06	value = 1.2355, U = 0.0135, k = 2, p = 95, unit = mV, mode = half-even	1.236 ± 0.014 mV	exact	Hand-derived decimal arithmetic; derivation in "why"
CERT-07	value = 1.2345, U = 0.0121, k = 2, p = 95, unit = mV, mode = round-u-up	1.235 ± 0.013 mV	exact	Hand-derived decimal arithmetic; derivation in "why"
CERT-08	value = 1.2345, U = 0.012, k = 2, p = 95, unit = mV, mode = round-u-up	1.235 ± 0.012 mV	exact	Hand-derived decimal arithmetic; derivation in "why"
CERT-09	value = 12.345, U = 0.30000000000000004, k = 2, p = 95, unit = mV, mode = round-u-up	12.35 ± 0.30 mV	exact	Hand-derived decimal arithmetic; derivation in "why"
CERT-10	value = -4.5678, U = 0.0234, k = 2, p = 95, unit = mV	-4.568 ± 0.023 mV	exact	Hand-derived decimal arithmetic; derivation in "why"
CERT-11	value = -1.2345, U = 0.0125, k = 2, p = 95, unit = mV, mode = half-up	-1.235 ± 0.013 mV	exact	Hand-derived decimal arithmetic; derivation in "why"
CERT-12	value = -1.2345, U = 0.0125, k = 2, p = 95, unit = mV, mode = half-even	-1.234 ± 0.012 mV	exact	Hand-derived decimal arithmetic; derivation in "why"
CERT-13	value = -0.0004, U = 0.012, k = 2, p = 95, unit = mV	0.000 ± 0.012 mV	exact	Hand-derived decimal arithmetic; derivation in "why"
CERT-14	value = 12.3456, U = 0.0234, k = 2, p = 95, unit = mV, sigFigs = 1	12.35 ± 0.02 mV	exact	Hand-derived decimal arithmetic; derivation in "why"
CERT-15	value = 12.3456, U = 0.096, k = 2, p = 95, unit = mV, sigFigs = 1	12.3 ± 0.1 mV	exact	Hand-derived decimal arithmetic; derivation in "why"
CERT-16	value = 12345.6, U = 123, k = 2, p = 95, unit = mV	12350 ± 120 mV	exact	Hand-derived decimal arithmetic; derivation in "why"
CERT-17	value = 1.23456e-7, U = 2.34e-9, k = 2, p = 95, unit = mV	0.0000001235 ± 0.0000000023 mV	exact	Hand-derived decimal arithmetic; derivation in "why"
CERT-18	value = 9.9996, U = 0.012, k = 2, p = 95, unit = mV	10.000 ± 0.012 mV	exact	Hand-derived decimal arithmetic; derivation in "why"
CERT-19	value = 12.3456, U = 0, k = 2, p = 95, unit = mV	RangeError mV	exact	Hand-derived decimal arithmetic; derivation in "why"
CERT-20	value = 12.3456, U = -0.02, k = 2, p = 95, unit = mV	RangeError mV	exact	Hand-derived decimal arithmetic; derivation in "why"
CERT-21	value = 1234567890123.456, U = 0.001, k = 2, p = 95, unit = mV	RangeError mV	exact	Hand-derived decimal arithmetic; derivation in "why"
CERT-22	value = 10, U = 0.01234, k = 2, p = 95, unit = mV, cmc_kind = absolute, cmc_value = 0.0123	10.000 ± 0.013 (CMC) mV	exact	Hand-derived decimal arithmetic; reported U not smaller than the scope CMC (ILAC P14:09/2020 §5.5; §6.5 in P14:01/2013)
CERT-23	value = 10, U = 0.012, k = 2, p = 95, unit = mV, cmc_kind = absolute, cmc_value = 0.012	10.000 ± 0.012 mV	exact	Hand-derived decimal arithmetic; reported U not smaller than the scope CMC (ILAC P14:09/2020 §5.5; §6.5 in P14:01/2013)
CERT-24	value = 10, U = 0.004, k = 2, p = 95, unit = mV, cmc_kind = relative, cmc_value = 0.05, cmc_per = percent	10.0000 ± 0.0050 (CMC) mV	exact	Hand-derived decimal arithmetic; reported U not smaller than the scope CMC (ILAC P14:09/2020 §5.5; §6.5 in P14:01/2013)
CERT-25	value = 10, U = 0.0051, k = 2, p = 95, unit = mV, cmc_kind = relative, cmc_value = 500, cmc_per = ppm	10.0000 ± 0.0051 mV	exact	Hand-derived decimal arithmetic; reported U not smaller than the scope CMC (ILAC P14:09/2020 §5.5; §6.5 in P14:01/2013)
CERT-26	value = 10.00049, U = 0.00041, k = 2, p = 95, unit = mV, cmc_kind = absolute, cmc_value = 0.0123	10.000 ± 0.013 (CMC) mV	exact	Hand-derived decimal arithmetic; reported U not smaller than the scope CMC (ILAC P14:09/2020 §5.5; §6.5 in P14:01/2013)
CERT-27	value = 5.4321, U = 0.995, k = 2, p = 95, unit = mV	5.4 ± 1.0 mV	exact	Hand-derived decimal arithmetic; derivation in "why"
CERT-28	value = 123.456, U = 9.95, k = 2, p = 95, unit = mV	123 ± 10 mV	exact	Hand-derived decimal arithmetic; derivation in "why"
CERT-29	value = 1234.56, U = 99.5, k = 2, p = 95, unit = mV	1230 ± 100 mV	exact	Hand-derived decimal arithmetic; derivation in "why"
CERT-30	value = 12.3456, U = 0.0995, k = 2, p = 95, unit = mV, mode = half-even	12.35 ± 0.10 mV	exact	Hand-derived decimal arithmetic; derivation in "why"
CERT-31	value = 12.3456, U = 0.0991, k = 2, p = 95, unit = mV, mode = round-u-up	12.35 ± 0.10 mV	exact	Hand-derived decimal arithmetic; derivation in "why"
CERT-32	value = 1.2, U = 0.15, k = 2, p = 95, unit = mV	1.20 ± 0.15 mV	exact	Hand-derived decimal arithmetic; derivation in "why"
CERT-33	value = 1.2346, U = 0.02, k = 2, p = 95, unit = mV	1.235 ± 0.020 mV	exact	Hand-derived decimal arithmetic; derivation in "why"
CERT-34	value = 1.2346, U = 0.02, k = 2, p = 95, unit = mV, sigFigs = 1	1.23 ± 0.02 mV	exact	Hand-derived decimal arithmetic; derivation in "why"
CERT-35	value = 2.3445, U = 0.012, k = 2, p = 95, unit = mV, mode = half-up	2.345 ± 0.012 mV	exact	Hand-derived decimal arithmetic; derivation in "why"
CERT-36	value = 2.3445, U = 0.012, k = 2, p = 95, unit = mV, mode = half-even	2.344 ± 0.012 mV	exact	Hand-derived decimal arithmetic; derivation in "why"
CERT-37	value = 123456789.4, U = 9950, k = 2, p = 95, unit = Pa	123457000 ± 10000 Pa	exact	Hand-derived decimal arithmetic; derivation in "why"
CERT-38	value = 0.00000123456, U = 9.95e-8, k = 2, p = 95, unit = mV	0.00000123 ± 0.00000010 mV	exact	Hand-derived decimal arithmetic; derivation in "why"
CERT-39	value = -7.65, U = 0.995, k = 2, p = 95, unit = mV	-7.7 ± 1.0 mV	exact	Hand-derived decimal arithmetic; derivation in "why"

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