An Introduction to Mass Measurements

Records dating back to 4000 B.C. on the development of trade around the Euphrates, Tigris and Indus rivers refer to mass and length measurements, making them the oldest types of measurements in the world. The first weighing instruments were discovered in the areas of ancient Mesopotamia and were made of limestone, linen ropes and wood. Several of the European museums of weighing instruments display similar weighing equipment, made up of a beam with two ropes on either side of it.

Over the last 6000 years, the design of beam balances have not changed much from this initial concept - they are still based on the same physical property connected with gravitational acceleration.

New Technologies

Revolutionary change came about in the design and operation of the weighing instruments with the development of electronics and, as such, the traditional beam balance is now only seen in museums. New technologies have opened the door for cheaper and more user-friendly weighing equipment. Electronic scales and balances are most commonly used today, whereby the mass of weighed load is compensated by a magnetoelectric converter.

It uses the feedback between gravitational force exerting an impact on the load and the force generated by the magnetoelectric converter. The weighing pan remains at state of equilibrium as the forces compensate one another.

Example of different RADWAG-manufactured mechanical designs using feedback. Own work

Example of different RADWAG-manufactured mechanical designs using feedback. Own work. Image Credit: Radwag Balances & Scales

Gravitational Force and Effect of Buoyancy Force

During mass measurement, two physical phenomena occur - gravitational force [FG] (the force with which sample mass is attracted by Earth), and the effect of buoyancy force [FW] (which is opposite to the direction of gravitational force).

There is a relationship between the measurement and a certain resultant force [6]. Converter's systems convert this force into an electrical signal, which is then presented as the measurement result. As a measuring element, a converter features its characteristics in terms of stability over time, resistance to temperature changes etc. A complex relationship, presented in numerous publications, can be obtained by compiling all weighing factors.


      RD - indicated result

Section A*: FCAL - balance adjustment coefficient
  f - force converter coefficient (electrical quantity)


  CZ - temperature coefficient of force converter sensitivity
  T - temperature coefficient of force converter sensitivity
  Δmcz - indication of force converter sensitivity drift as a function of time
  t - time interval since the latest sensitivity adjustment

* Section A is constant, results from the mass comparator design.


Section B: g - gravity force at the workstation (constant)


Section C: ρa - air density at the workstation
  ρ - the tested object density


During standard weighing, there is an insignificant influence of air buoyancy on the result. However, it is important for comparison processes when resolutions are very high. Function of mass correction is featured on some balances, such as RADWAG-manufactured XA.4Y series, dependent on air and object density.

Section D: m - tested object mass (specific feature, usually constant)


Section E: δD - readability component (constant)
  δR - balance repeatability component (dependent on the external conditions and the object)
  δL - balance non-linearity component (constant)
  δECC - eccentricity component (constant)


Section F: FZERO - coefficient of force converter zero point
  CZZERO - coefficient of force converter zero point drift as a function of time


Most of the above variables are insignificant for traditional weighing instruments. However, comparison process Section C (influence of air buoyancy) and Section F (influence of ambient conditions on mass comparator stability) are hugely important.

Magnetoelectric Converters

Magnetoelectric converters are incorporated on analytical (ultra and microanalytical) and precision balances. The equation used for mass measurement with such converters is given below. High resolutions can be obtained as they operate as a feedback loop. This is of great importance for applications such as analytical chemistry, biotechnology and high-accuracy mass measurements of small loads.

Load cells can also be used on weighing instruments. An electric signal is produced when loading the weighing pan that is proportional to the weight of the loaded object. The prices of these are relatively low as they are manufactured on a large scale. The principle of their operation is based on the deformation of the measuring element (strain gauge). Change of strain gauge's resistance, DR, is proportional to mechanical stress.


  R - strain gauge's resistance without stresses;
  k - strain gauge constant;

  e - relative elongation;
  σ - stress;
  E - Young's modulus.

Aside from the price, one advantage of such a solution is the possibility to design balances of high maximum capacities. However, it does have a rather low measuring accuracy. A standard resolution of load cells is around 3000 ÷ 6000 units.

Load cell attached to the base with a weighing pan support

Load cell attached to the base with a weighing pan support. Image Credit: Radwag Balances & Scales

Weighing Equipment

It is possible to design weighing equipment of resolution of 60,000 units through selection, optimization and program correction.

A comparison between the measuring signal and a suitable mass standard, scaled and expressed in mass units is always made regardless of the converter solution used [6]. This so-called adjustment is periodically carried out during normal use of the weighing instrument.

Principle of adjustment.

Figure 1. Principle of adjustment. Image Credit: Radwag Balances & Scales

In the past, mechanical balances and scales were common solutions that carried out the mass measurement by comparing the object mass with a weight, the mass of which was determined to suitable accuracy. This method of measurement was replaced by electronic weighing equipment.

Legal Metrology

However, users still required reassurance that the electronic instrument would always indicate the correct value of the measured load mass. For specific measuring equipment and in determined applications, legal metrology is crucial and defined by relevant legal acts. In respect to the measuring equipment, legal metrology ensures the fulfillment of specific requirements, such as conformity assessment and re-verification.

Industrial Metrology

A different evaluation criterion, usually a calibration or other approved procedure, needs to be adopted to use measuring equipment for purposes that do not require conformity with the legal system.

Industrial metrology uses the methodology determined by legal metrology in terms of calibration of the measuring instrument, i.e. comparing it with an international reference standard and specifying its uncertainty. National and international legislative acts both outline the recommendations and guidelines regarding metrological activities.

Both the testing methods and the requirements need to be optimized to take into account their specific demands. In addition to these two areas, there is also Scientific Metrology. This handles the maintenance and development of mass standards and related values.


[1] Bettin H., Physikalisch-Technische Bundesanstalt (PTB), S Schlamminger, National Institute of Standards and Technology (NIST), “Realization, maintenance and dissemination of the kilogram in the revised SI”, Metrologia 53 (2016) A1–A5.

[2] Chung J., Ryu K., Davis R., “Uncertainty analysis of the BIPM susceptometer”, Metrologia 38 (2001), pp. 535-541.

[3] Davis R., “New method to measure magnetic susceptibility”, Meas. Sci. Technol. 4, 141–147 (1993).

[4] Davis R., “Determining the magnetic properties of 1 kg mass standards”, J. Res. Natl. Inst. Stand. Technol. 100, 209 (1995).

[5] Guidelines on the Calibration of Non-Automatic Weighing Instruments EURAMET/cg-18/v.02, January 2009.

[6] Janas S., “Metrology in laboratory – measurement mass and derived values” Radwag, 2015.

[7] Janas S., “Micro scale measurements”, Radwag 2014.

[8] Fujii K., Bettin H., Becker P., Massa E., Rienitz O., Pramann A., Nicolaus A., Kuramoto N., Busch I. , Borys M., “Realization of the kilogram by the XRCD method”, Metrologia 53 (2016) A19–A45.

[9] Lu H., Chang C., “Evaluating the magnetic property of one kilogram mass standard in Center for Measurement”, APMF'2003 Proceedings, pp. 57-60.

[10] Mohr P. J., Newell D. B. and Taylor B. N., 2016 CODATA recommended values of the fundamental physical constants: 2014 Rev. Mod. Phys. (arXiv:1507.07956).

[11] Myklebust T. 1997, “Intercomparison: Measurement of the volume magnetic susceptibility and magnetization of two cylindrical (kg) weights. EUROMET project 324”, Justervesenet (NO).

[12] Myklebust T., Davis R., “Comparison between JV and BIPM to determine the volume susceptibility of one 20 g weight and two 1 g weights”, Justervesenet (1996).

[13] Myklebust T., Källgren H., Lau P., Nielsen L., Riski K., “Testing of weights: Part 3 - Magnetism and convection”, OIML Bulletin, Vol. XXXVIII, No. 4 (1997) 5.

[14] OIML D 28, “Conventional value of the result of weighing in air” Edition 2004 (E).

[15] OIML R 111-1, “Weights of classes E1, E2, F1, F2, M1, M1–2, M2, M2–3 and M3, Part 1: Metrological and technical requirements”.

[16] Pan Sheau-shi, Lu H., Chang C., “Instruments used for measuring the magnetic properties of one kilogram mass standard in Center for Measurement Standards (CMS)”, TC3 IMEKO’2005 Proceedings, pp. 1-7.

[17] Robinson I., Schlamminger S., “The Watt or Kibble balance: a technique for implementing the new SI definition of the unit of mass”, Metrologia 53 (2016) A46–A74.

[18] Richard P., Fang H., Davis R., “Foundation for the redefinition of the kilogram”, Metrologia 53 (2016) A6–A11.

[19] Stock M., “The Watt balance: determination of the Planck constant and redefinition of the kilogram”, Bureau International des Poids et Mesures (BIPM), Pavillon de Breteuil, Downloaded from on March 13, 2017.

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Last updated: Nov 29, 2019 at 9:53 AM


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