Weighing Instrument Calibration Uncertainty Calculator

Calibration data

Mass unit for all inputs and results

Repeatability test (one load)

Enter at least two readings taken at the same load; leave unused boxes empty.

Reading 1 (g)

Reading 2 (g)

Reading 3 (g)

Reading 4 (g)

Reading 5 (g)

Reading 6 (g)

Reading 7 (g)

Reading 8 (g)

Reading 9 (g)

Reading 10 (g)

Scale interval

Scale interval d (g)

Eccentricity test

Centre reading and the readings at the eccentric positions, all at the test load L_ecc; leave unused eccentric boxes empty.

Centre reading (g)

Eccentric reading 1 (g)

Eccentric reading 2 (g)

Eccentric reading 3 (g)

Eccentric reading 4 (g)

Test load L_ecc (g)

Calibration point

Calibration load L (g)

Indication I at load L (g)

Buoyancy correction (g)H1 treats 2.138 × 10⁻⁸ × L as negligible: enter 0 to reproduce it.

Reference standard and environment

Conventional mass standard uncertainty u_c (g)Aggregated value for the weights forming L, from your certificates (H1 row u(δm_c), p. 64).

Certificate coverage factor k_c (unitless)

Drift multiplier k_D (unitless)

Buoyancy standard uncertainty u_b (g)H1 uses L × 3.203 × 10⁻⁸.

Convection standard uncertainty u_v (g)

How the calculation works

Steps

Choose the mass unit (g or mg). Every mass field and every mass result uses it; switching converts from the value exactly as you typed it, so switching back restores your entry.
Enter at least two repeatability readings taken at one load, and the scale interval d.
Enter the centre reading and the eccentric readings obtained at the positive test load L_ecc.
Enter the calibration load L, its indication I and the buoyancy correction (0 to follow H1).
Enter u_c and k_c from your weight certificates, the drift multiplier k_D, and the buoyancy and convection standard uncertainties u_b and u_v, then press Calculate.

Formulas

s: sample standard deviation of the n repeatability readings (divisor n − 1).
e: largest absolute difference between an eccentric reading and the centre reading.
Reference mass: m_ref = L + buoyancy correction; error: E = I − m_ref.
u_i² = s² + d²/12 + d²/12 + (I × e / (2 × L_ecc × √3))², where the second d²/12 term (rounding at load) applies only when L > 0.
Drift: u_D = k_D × k_c × u_c / √3.
u_ref = √(u_c² + u_D² + u_b² + u_v²) and u = √(u_i² + u_ref²).
Effective degrees of freedom (Welch–Satterthwaite, only s carries finite degrees of freedom): ν_full = u⁴ / (s⁴ / (n − 1)), truncated to ν = floor(ν_full). The truncation is computed with exact rational arithmetic on the squared components, so a mathematically whole result stays whole.
k is the two-sided Student t quantile for a central probability of 95.45 % with ν degrees of freedom, and U = k × u.

Sources and assumptions

EURAMET cg-18 B3 (p. 42) allows the coverage factor to be determined from the underlying t-distribution described in GUM Annex C.3.8; GUM (JCGM 100:2008) G.4.1 Note 1 (p. 73) permits truncation of the degrees of freedom to the next lower integer.
Under cg-18 B2, k = 2 applies when a normal distribution can be attributed to the error and the standard uncertainty is sufficiently reliable. This tool uses the B3 calculation instead.
Inputs are treated as uncorrelated, the error as normally distributed, and every contribution other than repeatability as having infinite degrees of freedom, as in H1. The method is not valid when a non-normal component dominates the budget.
At L = 0 the standard and environmental uncertainties u_c, u_b and u_v must be 0. The repeatability readings must not all be equal.

This calculator reproduces a published worked example for guidance. It does not replace a laboratory’s validated calibration procedure, accredited uncertainty budget or the judgement of a qualified metrologist. Check results before using them on a calibration certificate.