People are considered employed if they do any paid work which contributes to production in the economy. For practical purposes, this means people who work for at least one hour a week are considered employed. This is consistent with approaches used internationally.
People who do paid work, even if it's only a small number of hours a week, have a job. Given the work in their job contributes to economic production, it is important that all paid work is included when measuring employment (the labour 'input' to the economic 'output'). Any work that people do is important - for the individual, the labour market, and the economy.
The purpose of official employment statistics is to provide an objective and comprehensive measure of whether people are working in a job or not. The headline estimates don't provide a view of the adequacy of an individual's work situation or an individual's family or household circumstances, for example, whether anyone else in the household has a paid job, whether they have other sources of income (welfare payments, investment or pension income), etc.
There's a variety of monthly and quarterly data available from the Labour Force Survey on people whose hours are insufficient. In addition, there are two annual sources that can help understand and monitor the extent of insufficient or inadequate work:
While some people working one hour a week may want to work more hours, or may want a different or better job, the majority of people working only a few hours a week are happy with the hours they have. They may not need, or be able to, work additional hours.