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## Does gravity or altitude effect weighing? (FAQ - Mass & Density)

Yes, but unless you are making weighings at the very highest level of accuracy, the consequences are probably too small to worry about. Whilst the variation in gravitational attraction with altitude and latitude is otherwise significant (see below) its effect on most weighing procedures largely cancels out provided that your balance (particularly the single-pan variety when used to make direct measurements) is set up properly and calibrated. Before reading the rest of this section, though, it is worth being sure of the differences between comparators, balances, comparative weighing and direct weighing.

### Two-pan balance/comparator

When making comparative weighings using a two-pan balance it is not normally necessary to make corrections for variations in gravitational acceleration provided that the weights are at the same height. This is because a changed level of gravitational attraction influences the weight of the items being compared in exact proportion to their masses and therefore, to within very fine limits, the measured ratio of the two mass values being compared will stay the same. (The mass of one weight is essentially calculated by multiplying the mass value of the other weight by the measured ratio of the mass values.)

The exception to this is when trying to make extremely high accuracy weighings, as typically made in a national measurement institute such as NPL, where it can be necessary to correct for differences in height between the centres of gravity of a pair of weights. Typically, for every 1 mm height difference (yes, one millimetre) between the centres of gravity of two 1 kg weights a correction of approximately 0.3 µg has to be applied. In practice it is not uncommon to have to compare, say, a 10 kg standard with a 10 kg slab weight where the centres of gravity are 70 mm or so apart vertically and this means that a correction of around 0.2 mg has to be applied to allow for this.

### Single-pan balance - used as a mass comparator

Similarly, when making comparative weighings using a single-pan balance it is not normally necessary to make corrections for variations in gravitational acceleration - provided again that the weights being compared are at the same height. The force-sensing element in the balance will undoubtedly be affected by the changes in g but provided the balance's sensitivity is properly re-determined at its new location (by the use of weights with known mass values), it will not be necessary to know the local value of g.

### Single-pan balance - used for direct measurement.

In direct measurement mode (as opposed to comparative mode) - where a mass value is essentially determined by reading a previously calibrated scale - a change in gravitational acceleration will cause a directly proportional effect on the readings. The variation in g, at ground level across the UK, is around 1 part in 2 000 so it is clear that single-pan balances used for accurate weighing will have to be compensated in some way. Again this can be achieved by calibrating the balance with known weights. To some degree it is possible to calculate the correction by knowing the difference in values of g between the location at which the balance was calibrated and its new location but this is not good practice and it is not recommended.

Last Updated: 25 Mar 2010
Created: 9 Aug 2007

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