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An additive tare device is a tare device that can establish a zero indication with a load present without reducing the weighing range available for net loads.^[ref] The supported container still contributes tare mass; the instrument provides a separate tare allowance rather than obtaining extra capacity simply by changing a displayed number.

Consider a deliberately specified model with maximum weighing capacity $\mathrm{Max}=5\mathrm{kg}$ for net loads and a maximum additive tare allowance $T_{\mathrm{add}}=2\mathrm{kg}$. Assume these ranges are available together for the stated configuration:A container with tare mass $T=1.2\mathrm{kg}$ can then accompany net mass $N=5\mathrm{kg}$, giving gross mass $G=6.2\mathrm{kg}$. The model's full combined boundary is $7\mathrm{kg}$ when both allowances are used. These numbers are chosen examples, not specifications for a particular scale.

By comparison, a subtractive tare device with a $5\mathrm{kg}$ gross-load budget would leave only $3.8\mathrm{kg}$ for net mass after the same $1.2\mathrm{kg}$ container is tared. Both displays can initially read zero; their available net-load capacities differ.

The OIML definition of maximum weighing capacity explicitly omits additive tare capacity, while its maximum-tare-effect terminology records the tare device's capacity separately.^[ref] A complete load description therefore identifies the container's tare mass, the desired net mass and the instrument's declared tare allowance. The load receptor continues to carry their combined physical load.

A calculated net value is the difference between a measured weighing value, gross or net, and a preset tare value. The key distinction is the origin of the subtracted quantity: it is entered or recalled numerically rather than necessarily being a freshly measured tare for that individual container. OIML R76-1:2006 defines these terms separately from an ordinary net indication after operation of a tare device.^[ref]

Write the arithmetic aswhere $PT$ is the stored preset tare value. Here the weighing values are expressed as mass estimates, for example in kilograms; they are not forces expressed in newtons. The instrument determines mass using gravity under its measurement model.^[ref]

For a chosen packaging example, let a loaded container give $2.480\mathrm{kg}$ and let the stored nominal container tare be $0.180\mathrm{kg}$. The calculated net value is then $2.300\mathrm{kg}$. If this particular empty container actually has mass $0.195\mathrm{kg}$, its contents have ideal net mass $2.285\mathrm{kg}$. The calculated indication overestimates that value by $0.015\mathrm{kg}$. The subtraction has been performed correctly; the discrepancy arises because a nominal tare was substituted for an individual one.

More generally, let the true contents' mass be $m$, the actual container mass be $t$, and the measured gross value be $m+t+e$, where $e$ is measurement error. ThenRepeating weighings can assess variation in $e$, but it does not by itself remove an incorrectly chosen $PT$. A useful check therefore weighs representative empty containers as well as repeating loaded measurements. Report the stored tare and what it represents along with the result. This makes the physical assumptions behind a calculated net value visible rather than treating a precise-looking display as evidence that every container has the nominal tare mass.

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.

Gravimetric dilution determines a dilution from measured masses. A measured amount of a stock solution is combined with material containing none of the quantity being diluted. For a closed transfer and a homogeneous mixture, the conserved amount divided by the final mass determines the new mass-based concentration.

Let $m_s$ be the stock's net mass, $m_d$ the added net mass, and $M=m_s+m_d$. Define the stock fraction $f$ and the gravimetric dilution factor $F$ byIf the stock has solute mass fraction $w_s$, thenFor stipulated $m_s=2.000\mathrm{g}$, $m_d=18.000\mathrm{g}$ and $w_s=0.2000$, the final mass is $20.000\mathrm{g}$, $F=10$, and $\boxed{w_f=0.02000}$: 2% by mass. The solute mass is $0.4000\mathrm{g}$ before and after dilution. The net masses exclude their containers. This mass basis does not require an assumption that liquid volumes add.

The uncertainty of a gravimetric dilution depends on which readings share errors. For independently evaluated inputs $w_s,m_s,m_d$, first-order propagation of uncertainty givesHere $u$ denotes standard uncertainty. The sensitivity factors follow from the partial derivatives $\partial f/\partial m_s=m_d/M^2$ and $\partial f/\partial m_d=-m_s/M^2$. With a chosen independent $u(m_s)=u(m_d)=0.001\mathrm{g}$ at the example's nominal masses, the relative mass-ratio contribution is approximately 0.0453%. Adding an independent 0.5% relative stock-value contribution in quadrature gives approximately 0.502%. These are illustrative inputs, rather than a balance specification.^[ref]

If input errors have covariance, their cross terms must be retained. A useful exact check isA common multiplicative mass-scale factor therefore cancels from $f$. Counting it as two independent contributions would lose that correlation. Container subtraction, transfer losses and changes in composition require their own assessment; this cancellation establishes only the common-scale property.

For massic activity, the same conservation argument applies after expressing all activities at a common reference time. A 2000 NIST study compared massic activity ratios inferred from gravimetric dilution with independent liquid scintillation counting. Their agreement within reported uncertainties provided an experimental check on transferring standards through mass ratios.^[ref]

Gross mass is the mass of the complete specified load, including its contents and the packaging counted as tare mass. For that same boundary,The gross indication in OIML's weighing terminology is obtained with neither a tare device nor a preset tare device operating, after an initial zero indication.^[ref] A full crate's gross mass consequently differs from an individual jar's gross mass, because the specified loads differ.

Consider four jars, each containing $0.50\mathrm{kg}$ of material and having an empty-container tare mass of $0.20\mathrm{kg}$. An outer crate adds $0.80\mathrm{kg}$. For the complete load, the net mass of the contents, composite tare mass, and gross mass are respectivelyThese are chosen bookkeeping values, assuming the listed components exhaust the load and each component is counted once.

Subtracting the full composite tare mass from the complete gross mass gives $3.60-1.60=2.00\mathrm{kg}$ of contents. If the jars' $0.80\mathrm{kg}$ has already been removed from an intermediate total, subtracting the same full composite tare mass again gives $1.20\mathrm{kg}$. The missing $0.80\mathrm{kg}$ is precisely the duplicated deduction. Use one load boundary and subtract each packaging component once.

The gross mass also remains relevant to maximum weighing capacity when a subtractive tare device reduces the available net-load range.^[ref] For an illustrative instrument modeled with a $1.000\mathrm{kg}$ gross-load limit, a $0.120\mathrm{kg}$ container leaves $0.880\mathrm{kg}$ for contents. At that limit the complete load still has gross mass $1.000\mathrm{kg}$, even though the tared display reports only its contents.

For a stationary ideal weighing scale, the normal contact force associated with a complete load is related to its gravitational weight. A displayed net mass is a processed indication of that load; it is not the full supported mass. Changes in the gravitational field, measurement calibration, or the load boundary must therefore be distinguished when interpreting a reading.

A load receptor is the part of a weighing scale intended to receive the load, such as the platform supporting a parcel. The instrument can transmit that load's force to a separate measuring element, for example a load cell.^[ref]

A simple static model explains why the physical support path matters. Suppose a $2\mathrm{kg}$ object rests entirely on a horizontal load receptor, with local gravitational acceleration $g=9.8\mathrm{m}{\mathrm{s}}^{-2}$. Neglecting air buoyancy, its gravitational weight is $19.6\mathrm{N}$. The instrument can convert the measured supporting force into a mass indication through its calibration.

Now arrange a separate overhead support to carry $4.9\mathrm{N}$ of the same object's gravitational weight, while the rest still reaches the load receptor. The scale then supports $14.7\mathrm{N}$ and, under the same ideal calibration, indicates $1.5\mathrm{kg}$. The object's mass remains $2\mathrm{kg}$: the indication changed because the support path changed. This is an illustrative static equilibrium experiment, rather than a claim about any instrument's specified error.

A removable container placed on the platform contributes tare mass; it is distinct from the instrument's own load receptor. To measure the net mass of the contents, the tare device changes the indicated reference while the receptor continues to carry both container and contents. Contact with an external support can therefore defeat an otherwise correct subtraction.

The maximum weighing capacity, conventionally $\mathrm{Max}$, specifies the upper capacity of a weighing scale; the OIML definition excludes additional capacity provided by an additive tare device.^[ref] A display reset does not by itself establish a new physical load capacity.

For a chosen model with a subtractive tare device, let $\mathrm{Max}=5\mathrm{kg}$ and suppose the combined gross mass on the load receptor must satisfyA container with tare mass $1.2\mathrm{kg}$ leaves at most $3.8\mathrm{kg}$ for net mass. Pressing the tare device can make the display read zero with that container present, but the container remains part of the supported mass. This calculation assumes the stated subtractive-tare model; it does not assign the same capacity budget to a scale with an additive tare device.

The maximum safe load describes a different boundary: the static load an instrument can carry without permanently changing its metrological qualities. It does not define the upper end of its specified weighing capacity.^[ref] For example, an instrument could have a declared $\mathrm{Max}$ of $5\mathrm{kg}$ and a separately declared maximum safe load of $7\mathrm{kg}$. Those hypothetical markings would not turn a $6\mathrm{kg}$ indication into a measurement within the declared $5\mathrm{kg}$ weighing capacity.

Net mass is the mass attributed to the material of interest after excluding the container or other specified tare mass. For a container-and-contents measurement, the ideal bookkeeping relation iswhere $m_{\mathrm{g}}$ is the gross mass of the complete load and $m_{\mathrm{t}}$ is the mass excluded as tare. State which parts of the load belong to each quantity.^[ref]

For an own weighing example, a container and its contents give a mass estimate of $0.842\mathrm{kg}$, while the corresponding empty container gives $0.217\mathrm{kg}$. Assuming comparable conditions and no change in the container, the contents' estimated net mass isAn instrument's tare operation can instead establish the container reading as its reference before displaying a net indication for the added contents. The recommendation distinguishes this operation from subtracting a stored preset tare value.^[ref]

The physical apparatus is a weighing scale: it determines mass using gravity under its measurement model. The fact that weighing terminology sometimes says weight value does not turn the result in kilograms into a force in newtons.^[ref]

Subtraction also exposes how errors enter. In a simple additive model, let the two estimated masses be $G=m_{\mathrm{g}}+e_g$ and $T=m_{\mathrm{t}}+e_t$. ThenA stable common additive offset cancels when $e_g=e_t$; unequal errors do not. For example, overestimating the tare by $0.005\mathrm{kg}$ while leaving the gross estimate unchanged underestimates net mass by the same amount.

Real measurements additionally involve resolution, drift, measurement uncertainty and the definition of the load. The exact algebraic relation between ideal quantities is not a promise that independently rounded display readings always reproduce the same final digit. Record the relevant tare and measurement conditions along with the net result, rather than treating net mass as a new kind of matter independent of how the excluded mass was defined.

A preset tare device subtracts a preset tare value from a measured gross or net indication and displays the calculated result.^[ref] A stored container value can therefore be reused without weighing each empty container individually.

Suppose a container and its contents have measured gross mass $G=2.30\mathrm{kg}$ and the entered preset tare value is $PT=0.30\mathrm{kg}$. Subtraction gives a calculated net mass of $2.00\mathrm{kg}$. If this particular container actually has tare mass $T=0.34\mathrm{kg}$, however, its contents have mass $1.96\mathrm{kg}$. Even an otherwise exact gross measurement would then overestimate the contents by $0.04\mathrm{kg}$.

The error follows without any instrument-specific assumption:A mismatch in the entered container value passes directly into the result. Reusing one value for nominally identical containers is therefore an assumption about their tare masses, rather than a new measurement of each container.

The starting indication also matters. If an ordinary tare device has already removed a $0.30\mathrm{kg}$ container contribution, the displayed $2.00\mathrm{kg}$ is already net for that reference. Subtracting the same $0.30\mathrm{kg}$ again would give $1.70\mathrm{kg}$. A deliberate second subtraction can represent another distinct component, but applying the same container correction twice is a different calculation from removing its tare mass once.

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 subtractive tare device is a tare device whose operation reduces the weighing range available for net loads.^[ref] Its zero display accounts for a load already present, while that load continues to occupy part of the instrument's capacity.

Consider a chosen model with maximum weighing capacity $\mathrm{Max}=10\mathrm{kg}$ and no additive tare capacity. If a container of tare mass $T$ is supported on the load receptor, the admissible net mass $N$ in this model satisfiesWith $T=2.5\mathrm{kg}$, the largest net load in this capacity budget is $7.5\mathrm{kg}$. Adding $8\mathrm{kg}$ after taring would produce gross mass $10.5\mathrm{kg}$, even though the desired net indication is below $10\mathrm{kg}$.

Changing to a $0.8\mathrm{kg}$ container would leave $9.2\mathrm{kg}$ available for net mass in the same model. This is a physical consequence of reducing the supported tare mass, rather than a benefit obtainable by repeatedly resetting the display.

An additive tare device is defined by retaining the net-load weighing range. Therefore the equation above is a model for subtractive tare and a shared gross-load bound, rather than a universal rule that every scale's printed $\mathrm{Max}$ includes every possible tare allowance. The chosen container, allowed tare range and instrument capacity must describe the same load configuration.

A tare device establishes a zero indication on a weighing scale while a load remains on its load receptor. An additive tare device preserves the weighing range for net loads; a subtractive tare device reduces that range.^[ref]

For example, place an empty $0.40\mathrm{kg}$ container on the load receptor and operate the tare device. The display reads zero even though the scale still supports the container. Adding $1.10\mathrm{kg}$ of material gives gross mass $1.50\mathrm{kg}$ and, ideally, an indicated net mass of $1.10\mathrm{kg}$. Removing both material and container without clearing the tare would ideally give $-0.40\mathrm{kg}$. This negative indication is consistent with the changed reference.

The cancellation can be seen in a linear model. If the unrounded indication before tare is $r(m)=am+b$, and the supported container has tare mass $T$, the indicated result after adding net mass $N$ isThe additive offset $b$ and the container contribution cancel. A response scale factor $a\ne 1$ remains, so taring alone does not establish calibration across the load range.

The container's physical load remains on the scale after taring. Consequently the available maximum weighing capacity depends on the kind of tare device, even when two instruments show the same zero. A preset tare device performs a related numerical subtraction using an entered or recalled value, rather than necessarily measuring this particular empty container.

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.