Multiplicity
Numbers at the end of a line, such as 1, 0..1 or 0..*, are a multiplicity: how many objects at that end can take part for each object at the other end. A star (*) means "many", with no upper limit.
How to read it
A UML multiplicity is written as a lower bound, two dots and an upper bound. The star stands for an unlimited upper bound, so 0..* is zero or more and 1..* is one or more. When the two bounds are the same, one number is enough: 1 means the same as 1..1. A star on its own is shorthand for 0..*. On an association the multiplicity is written near the end it applies to, without brackets; on an attribute written inside a class box it goes in square brackets, as in phone : String[0..*]. (UML 2.5.1, clause 7.5.) The University of Wisconsin–La Crosse's course notes give the reading: with n..m at the B end of a line from class A to class B, each A goes with between n and m Bs at the same time.
Also searched as: 0..*, multiplicity symbol, uml cardinality, uml multiplicity.
Common multiplicities
| Multiplicity | Read as |
|---|---|
| 1 | exactly one |
| 0..1 | zero or one (optional) |
| * or 0..* | zero or more |
| 1..* | one or more |
| 2..4 | from two to four |
| 3..* | three or more |
The readings are those of Virginia Tech's OpenDSA notes and the University of Washington's course slides.
When no multiplicity is shown
On an association end, a missing multiplicity means nothing at all: UML 2.5.1 says no conclusion may be drawn about it. On an attribute written as text, leaving the multiplicity out means exactly one.
Multiplicity, cardinality and crow's feet
Some course notes call it cardinality (OpenDSA; Wisconsin–La Crosse). Entity-relationship diagrams in crow's foot notation draw the same kind of limit with marks instead of numbers: compare zero or many and one or many.
Read next
- Next in UML diagram symbolsActorA stick figure on a use case diagram is an actor: a role played by someone or something outside the system that interacts with it. An actor can be a person, another computer system or a piece of hardware.
- In ER diagram symbolsZero or manyZero or more: optional, with no upper limit. On a crow’s foot ER diagram, a circle and a three-pronged crow’s foot at the end of a relationship line mean each record at the other end may have none, one or many matching records in the entity beside them.
More UML diagram symbols
The same shape elsewhere
Browse symbols drawn with letters and numbers, lines or squares and rectangles.
Sources
- OMG Unified Modeling Language (OMG UML), Version 2.5.1, OMG document formal/17-12-05, December 2017, Object Management Group, 7.5.4 Notation; 9.5.4 Notation; 11.5.4 Notation
- The Unified Modeling Language (OpenDSA Complete Catalog, 3.2), Chapter 3, Object-Oriented Programming, OpenDSA Project, Virginia Tech, 3.2.1.2 Class Diagrams, Multiplicity
- UML Class Diagrams (CSE 403 lecture slides), Emina Torlak, CSE 403: Software Engineering, Fall 2016, University of Washington, Paul G. Allen School of Computer Science & Engineering (Internet Archive), Slide 20
- Informal Semantics for UML Class Diagrams, CS 743, Software Verification and Validation, Fall 2019, University of Wisconsin–La Crosse, Department of Computer Science, Association, rule ASSO.6
- UML (CIS 400 Textbook: Object-Oriented Design, Implementation, and Testing), Chapter 5, UML, Kansas State University, Department of Computer Science, Multiplicity
Researched, edited and approved by Rory Hansen before publishing. Last reviewed October 9, 2026. How we research
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