In everyday language, mass and weight are the same thing: a bag of sugar weighs a kilo. In metrology they are two different quantities, and force is the link between them. Anyone who understands that difference also understands why a scale is calibrated with weights, a force transducer on a force calibration bench, and why a crane scale can be calibrated either way. This article explains the chain, from mass via weighing to force.
Mass: how much matter
Mass is the amount of matter in an object, expressed in kilograms (kg). Mass is a property of the object itself and does not change with location: a 1 kg weight has the same mass in Geldermalsen, on Mont Blanc and in a space station. That is why weights, despite their name, are mass standards: a calibrated 1 kg weight embodies a known mass, traceable to the national and international mass standard. What is actually calibrated is the conventional mass; you can read up on that concept in conventional mass and air buoyancy.
Weight: the force of gravity
In physics, weight is the force with which the earth pulls on a mass. That force follows from Newton's second law: force is mass times acceleration, in this case the gravitational acceleration g.
F = m × g
Force is expressed in newtons (N). A mass of 1 kg experiences a gravitational force of about 9.81 N on earth; a mass of 100 kg about 981 N, almost 1 kN. The gravitational acceleration is not the same everywhere. At sea level at the equator g is about 9.78 m/s², at the poles about 9.83 m/s². In the Netherlands g is around 9.81 m/s² and differs from place to place only in the order of a hundredth of a percent, but for accurate scales and for legally verified instruments that is already relevant. In our force laboratory we work with the local value g = 9.8129296 m/s².
Measuring force: the load cell
A load cell or force transducer does not measure mass but force. Under load, the measuring body deforms slightly, strain gauges convert that deformation into an electrical signal and the electronics convert that into a figure. Whether that figure is displayed in newtons or in kilograms is only a matter of converting with g. A force transducer in a press, a dynamometer on a crane and the load cell under the platform of a scale essentially do the same thing: they measure a force.
The scale: from force back to mass
A scale is therefore a force gauge that converts back to mass. It measures the gravitational force on the load and divides it, implicitly, by g. That works as long as g is known. That is why a scale is calibrated with calibrated weights at the place of use: the weight introduces a known mass, the local g is automatically included in the measurement, and the indication is compared directly with the mass. If you move an accurate scale to another location, g changes and a new calibration or adjustment is required. How that calibration is carried out is explained at scale calibration.
The chain in one picture
- Mass (kg): a calibrated weight embodies a known mass.
- Gravity: the earth pulls on that mass with a force F = m × g.
- Force (N): a load cell or force transducer measures that force.
- Readout: the electronics display the force in N or kN, or use g to convert back to a mass in kg or tonnes.
Each link can be calibrated: the mass of the weight in the mass laboratory, the complete scale with weights on site, and the force transducer against a reference force transducer on the force calibration bench. See calibrating a force transducer or load cell.
Converting: kN, kg and tonnes
Force measuring instruments in lifting applications often display kilograms or tonnes, while a force calibration bench works in kilonewtons. The conversion is done with g. With g = 9.81 m/s²:
| Force | Corresponds to a mass of |
|---|---|
| 1 kN | approx. 102 kg |
| 10 kN | approx. 1,019 kg (approx. 1 t) |
| 50 kN | approx. 5,097 kg (approx. 5.1 t) |
| 100 kN | approx. 10,194 kg (approx. 10.2 t) |
| 500 kN | approx. 50,968 kg (approx. 51 t) |
| 4,000 kN | approx. 407,747 kg (approx. 408 t) |
The exact value depends on the g used; a certificate therefore always states which gravitational acceleration was applied. A kilogram-force (kgf) is the force exerted by 1 kg under the standard gravitational acceleration of 9.80665 m/s² and is still used on older force gauges.
Crane scale: weights or tensile test bench?
A crane scale shows how close weighing and force measurement are to each other. Up to a few tonnes it is calibrated by hanging calibrated weights from it: mass in, indication in kg out. Heavier crane scales we hang in the tensile test bench, where a reference force transducer measures the actual tensile force; we convert this with the local g to the indication in kg or tonnes. Both routes are traceable, one to the mass standard, the other to the force standard. Read more at crane scale calibration.
In summary
Mass is a property of the object and is measured in kilograms. Weight is the gravitational force on that mass, a force in newtons, dependent on the local gravitational acceleration. A load cell measures force; a scale converts that force back to mass. That is why we calibrate weights in the mass laboratory, scales with weights on site and force measuring instruments on the tensile and compression test bench. Three disciplines, one metrological chain.