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INTERNATIONAL ISO
STANDARD 80000-3
Second edition
2019-10
Quantities and units —
Part 3:
Space and time
Grandeurs et unités —
Partie 3: Espace et temps
Reference number
©
ISO 2019
© ISO 2019
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ii © ISO 2019 – All rights reserved
Contents Page
Foreword .iv
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
Bibliography .10
Index .11
Foreword
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iso/ foreword .html.
This document was prepared by Technical Committee ISO/TC 12, Quantities and units, in collaboration
with Technical Committee IEC/TC 25, Quantities and units.
This second edition cancels and replaces the first edition (ISO 80000-3:2006), which has been
technically revised.
The main changes compared to the previous edition are as follows:
— the table giving the quantities and units has been simplified;
— some definitions and the remarks have been stated physically more precisely.
A list of all parts in the ISO 80000 and IEC 80000 series can be found on the ISO and IEC websites.
Any feedback or questions on this document should be directed to the user’s national standards body. A
complete listing of these bodies can be found at www .iso .org/ members .html.
iv © ISO 2019 – All rights reserved
INTERNATIONAL STANDARD ISO 80000-3:2019(E)
Quantities and units —
Part 3:
Space and time
1 Scope
This document gives names, symbols, definitions and units for quantities of space and time. Where
appropriate, conversion factors are also given.
2 Normative references
There are no normative references in this document.
3 Terms and definitions
Names, symbols, definitions and units for quantities of space and time are given in Table 1.
ISO and IEC maintain terminological databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at http:// www .electropedia .org/
2 © ISO 2019 – All rights reserved
Table 1 — Quantities and units of space and time
Item No. Quantity Unit Remarks
Name Symbol Definition
3-1.1 length l, L linear extent in space between any two points m Length does not need to be measured along a
straight line.
Length is one of the seven base quantities in the Inter-
national System of Units (ISO 80000-1).
3-1.2 width, b, B minimum length of a straight line segment m This quantity is non-negative.
between two parallel straight lines (in two
breadth
dimensions) or planes (in three dimensions)
that enclose a given geometrical shape
3-1.3 height, h, H minimum length of a straight line segment m This quantity is usually signed. The sign expresses
between a point and a reference line or refer- the position of the particular point with respect to the
depth,
ence surface reference line or surface and is chosen by convention.
altitude
The symbol H is often used to denote altitude, i.e.
height above sea level.
3-1.4 thickness d, δ width (item 3-1.2) m This quantity is non-negative.
3-1.5 diameter d, D width (item 3-1.2) of a circle, cylinder or sphere m This quantity is non-negative.
3-1.6 radius r, R half of a diameter (item 3-1.5) m This quantity is non-negative.
3-1.7 path length, s length of a rectifiable curve between two of m The differential path length at a given point of a
its points curve is:
arc length
ddsx= + ddyz+
() () ()
where x, y, and z denote the Cartesian coordinates
(ISO 80000-2) of the particular point.
There are curves which are not rectifiable, for exam-
ple fractal curves.
3-1.8 distance d, r shortest path length (item 3-1.7) between two m A metric space might be curved. An example of a
points in a metric space curved metric space is the surface of the Earth.
In this case, distances are measured along great
circles.
A metric is not necessarily Euclidean.
Table 1 (continued)
Item No. Quantity Unit Remarks
Name Symbol Definition
3-1.9 radial distance r , ρ distance (item 3-1.8), where one point is locat- m The subscript Q denotes the point from which the
Q
ed on an axis or within a closed non self-inter- radial distance is measured.
secting curve or surface
Examples of closed non self-intersecting curves are
circles or ellipses.
Examples of closed non self-intersecting surfaces are
surfaces of spheres or egg-shaped objects.
3-1.10 position vector r vector (ISO 80000-2) quantity from the origin m Position vectors are so-called bounded vectors, i.e.
of a coordinate system to a point in space their magnitude (ISO 80000-2) and direction depend
on the particular coordinate system used.
3-1.11 displacement Δr vector (ISO 80000-2) quantity between any m Displacement vectors are so-called free vectors, i.e.
two points in space their magnitude (ISO 80000-2) and direction do not
depend on a particular coordinate system.
The magnitude of this vector is also called displace-
ment.
3-1.12 radius of curvature ρ radius (item 3-1.6) of the osculating circle of a m The radius of curvature is only defined for curves
planar curve at a particular point of the curve which are at least twice continuously differentiable.
−1
κ
3-2 curvature inverse of the radius of curvature (item 3-1.12) m The curvature is given by:
κ=
ρ
where ρ denotes the radius of curvature (item 3-1.12).
3-3 area A, S extent of a two-dimensional geometrical shape m The surface element at a given point of a surface is
given by:
dA = g du dv
where u and v denote the Gaussian surface coordi-
nates and g denotes the determinant of the metric
tensor (ISO 80000-2) at the particular point.
The symbol dσ is also used for the surface element.
4 © ISO 2019 – All rights reserved
Table 1 (continued)
Item No. Quantity Unit Remarks
Name Symbol Definition
3-4 volume V, (S) extent of a three-dimensional geometrical m The volume element in Euclidean space is given by:
shape
dV = dx dy dz
where dx, dy, and dz denote the differentials of the
Cartesian coordinates (ISO 80000-2).
The symbol dτ is also used for the volume element.
3-5 angular measure α, β, γ measure of a geometric figure, called plane rad The angular measure is given by:
angle, formed by two rays, called
...