The article focuses on designing methods for quantitative assessment of the postural stability in a quiet stance by measuring segments of the appendicular skeleton, namely upper and forearms by inertial measurement units (IMU). Although an array of quantitative analysis methods assessing data of postural stability in the quiet stance exist by measuring the head and trunk movement, these methods have not been used to date to assess the behaviour of appendicular skeleton segments, namely the upper limbs. The applicability of methods assessing arm movement during the quiet stance has been verified by comparing the values of healthy subjects performing various stance tasks. The tests determined the quantitative evaluation of acceleration measured on individual anatomical axes. The quantities included: the volume of a convex polyhedron (PV), the volume of confidence ellipsoid (EV) and average velocity (AV) obtained by plotting three accelerations against each other. The most important findings in this study concern significant differences of PV and AV between dominant and non-dominant upper extremities and significant differences of EV, PV and AV between the data measured with a subject's eyes closed and open. Higher values of indicators were in the non-dominant extremities when subjects were measured with closed eyes. Interestingly, statistically significant differences between dominant and non-dominant arm movements were documented in PV and AV cases. This is due to the PV calculation being more sensitive to random deviations, i.e. the range of measured data, since the polyhedron bounds all the measured data, as opposed to the method, where the ellipse bounds only 95% of the measured data. In the case of the AV method, it is due to higher sensitivity to movements corresponding with arm tremors; the AV calculation relates not only to the range of measured data but, above all, to the intensity of data changes in the segment measured in a particular space and time interval. These conclusions demonstrate that it is possible to apply the proposed methods in the assessment of arm movement during a quiet stance since the differences between individual stance tasks and the dominant and non-dominant arms in specific cases of quiet stance have been identified. These conclusions also indicate a potentially more extensive medical application of the proposed quantitative data evaluation obtained from IMU, for example, within the rehabilitation process of injured appendicular skeleton segments. The use of cheaper IMU methods in mobile phones or watches can be of significant benefit in measuring the segmental movement of the appendicular skeleton in quiet stance. The methods outlined in this paper have remarkable potential in the field of telemedicine.