Tare mass ($m_{\mathrm{t}}$)

Tare mass is the specified container or packaging mass excluded when reporting net mass. It is also called tare weight in weighing terminology. The intended boundary matters: a jar alone and that jar with its lid have different tare masses. A tare device adjusts a weighing scale's indication with a load present, whereas a zero-setting device establishes zero with the load receptor unloaded.^[ref]

A simple demonstration separates the reading from the physical load. Choose an empty container of mass $m_{\mathrm{t}}=0.120\mathrm{kg}$ and an ideal weighing scale that initially reads zero. After the container is placed on the load receptor, operate the tare device. Its displayed value becomes zero while the container's mass remains $0.120\mathrm{kg}$. In a uniform gravitational field with chosen magnitude $g=9.81\mathrm{m}{\mathrm{s}}^{-2}$, its gravitational weight is stillThe supporting force remains present after the display adjustment.

In an ideal unit-gain measurement model, the tared indication for a complete load of mass $m$ is $I(m)=m-m_{\mathrm{t}}$. Adding $0.300\mathrm{kg}$ of contents gives gross mass $0.420\mathrm{kg}$ and indication $0.300\mathrm{kg}$. Removing the complete load while retaining that reference gives indication $-0.120\mathrm{kg}$. The negative indication expresses the difference from the stored reference; the removed container still has positive mass.

A preset tare device instead uses an introduced preset tare value, which can be recalled or entered without weighing each individual empty container.^[ref] For the same chosen load, using a preset of $0.100\mathrm{kg}$ gives calculated net mass $0.420-0.100=0.320\mathrm{kg}$: the contents are overestimated by 20 g. A persistently low preset produces a systematic error even with otherwise exact readings.

Composite tare mass includes several excluded components, such as all the jars and an outer crate. The gross mass example shows how to account for these components once each. The symbol $m_{\mathrm{t}}$ here denotes a mass; the terminology's use of the word weight does not change the quantity's unit from a kilogram to a unit of force.

A preset tare value is a numerical tare mass entered or recalled for use in subsequent weighings without individually determining each container's tare. The pinned OIML terminology denotes it by $\mathrm{PT}$ and calls the measured gross or net indication minus this value a calculated net value. It can be supplied through a preset tare device rather than obtained by weighing the current empty container.^[ref]

For an original example, a stored container tare is $\mathrm{PT}=250\mathrm{g}$, but the actual empty container has tare mass $T=263\mathrm{g}$. Adding $500\mathrm{g}$ of material gives gross mass $G=763\mathrm{g}$. Applying the stored value givesalthough the actual net mass is $N=G-T=500\mathrm{g}$. Their difference isAn underestimated preset tare therefore overestimates the contents. Repeating the same discrepancy across ten containers produces a $130\mathrm{g}$ total discrepancy; more displayed digits do not remove it.

A useful physical check independently weighs representative empty containers, including the same lids and attachments used during the loaded measurement, and compares them with the stored value. Record which load components the preset represents. If it is subtracted from an indication that has already had those components removed by a tare device, the same tare mass is deducted twice. The stored number's provenance and variability belong in the measurement model and its measurement uncertainty.

A composite tare mass is the combined tare mass of several disjoint container or support components included within the chosen weighing boundary. If component $i$ contributes $m_{\mathrm{t},i}$,The boundary matters: include each unwanted load component once, and exclude everything that is not on the load receptor. OIML's tare and gross/net terminology supplies the underlying weighing distinction; the component sum here is an explicit additive mass model.^[ref]

For an original assembly, three empty crucibles each have mass $80\mathrm{g}$, their three lids each have mass $10\mathrm{g}$, and their common tray has mass $100\mathrm{g}$. The composite tare mass isIf the loaded assembly has gross mass $970\mathrm{g}$, its material has net mass $600\mathrm{g}$. Subtracting the lids again after subtracting the complete $370\mathrm{g}$ tare would incorrectly give $570\mathrm{g}$.

One can weigh the empty assembled system directly or sum separately measured component masses. For independent component standard uncertainties of $0.10\mathrm{g}$ per crucible, $0.02\mathrm{g}$ per lid and $0.20\mathrm{g}$ for the tray, the sum hasShared calibration errors require covariance terms instead of this independent-input calculation.^[ref] A changed lid, retained material or substituted tray changes the assembly and can invalidate a previously stored tare.