Bruce Silver's blog post - Calendar Arithmetic in DMN
Bruce Silver

Calendar Arithmetic in DMN

By Bruce Silver

Read Time: 4 Minutes

Often in decision models you need to calculate a date or duration. For example, an application must be submitted within 90 days of some event, or a vaccine should not be administered within 120 days of a previous dose. DMN has powerful calendar arithmetic features. This post will illustrate how to use them.

ISO 8601 Format

The FEEL expressions for dates, times, and durations may look strange, but don’t blame DMN for that. They are based on the formats defined by ISO 8601, the international standard for dates and times in many computer languages. In FEEL expressions, dates and times can be specified by using a constructor function, e.g. date(), applied to a literal string value in ISO format, as seen below. For input and output data values, the constructor function is omitted.

A date is a 4-digit year, hyphen, 2-digit month, hyphen, 2-digit day. For example, to express May 3, 2017 as an input data value, just write 2015-05-03. But in a FEEL expression you must write date(2017-05-03).

Time is based on a 24-hour clock, no am/pm. The format is a 2-digit hour, 2-digit minute, 2-digit second, with optional fractional seconds after the decimal point. There is also an optional time offset field, representing the time zone expressed as an offset from UTC, what they used to call Greenwich Mean Time. For example, to specify 1:10 pm and 30 seconds Pacific Daylight Time, which is UTC 7 hours, you would enter 13:10:30-07:00 as an input data value, or time(13:10:30-07:00) in a FEEL expression. To specify the time as UTC, you can either use 00:00 as the time offset, or the letter Z, which stands for Zulu, which is the military symbol for UTC. DateTime values concatenate the date and time formats with a capital T separating them, as you see here. In a FEEL expression, you must use the proper constructor function with the ISO text string enclosed in quotes.

Date and Time Components

It is possible in FEEL to extract the year, month, or day component from a date, time, or dateTime using a dot followed by the component name: year, month, day, hour, minute, second, or time offset. For example, the expression date(“2017-05-03”).year returns the number 2017. All of these extractions return a number except for the time offset component, which returns not a number but a duration, with a format well discuss shortly.

DMN also provides an attribute, weekday not really a component but also extracted via dot notation returning an integer from 1 to 7, with 1 meaning Monday and 7 meaning Sunday.


The interval between two dates, times, or dateTimes defines a duration. DMN, like ISO, defines two kinds of duration: days and time duration, and years and months duration. Days and time duration is equivalent to the number of seconds in the duration. The ISO format is PdDThHmMsS, where the lower case d,h,m, and s are integers indicating the days, hours, minutes, and seconds in the duration. If any of them is zero, they are omitted along with the corresponding uppercase D, H, M, or S. And they are supposed to be normalized so that the sum of the component values is minimized.

For example a duration of 61 seconds could be written P0DT61S, but we can omit the 0D, and the normalized form is 1 minute 1 second, so the correct value is PT1M1S. In a FEEL expression, you need to enclose that in quotes and make it the argument of the duration constructor function: duration(“PT1M1S”).

Days and time duration is the one normally used in calendar arithmetic, but for long durations the alternative years and months duration is available, equivalent to the number of whole months included in the duration. The ISO format is PyYmM, where lower case y and m are again numbers representing number of years and months in the duration, and again the normalized form minimizes the sum of those component values. So a duration of 14 months would be written in normalized form as P1Y2M, and in FEEL, duration(P1Y2M). Since months contain varying numbers of days, the precise value of years and months duration is the number of months in between the start date and the end date, plus 1 if the day of the end month is greater than or equal to the day of the start month, or plus 0 otherwise.

As with dates and times, you can extract the components of a duration using a dot notation. For days and time duration, the components are days, hours, minutes, and seconds. For years and months duration, the components are years and months.

Arithmetic Expressions

The point of all this is to be able to do calendar arithmetic.

Lets start with addition of a duration.

  • You can add a days and time duration to a dateTime or a date, returning a dateTime.
  • You can add a years and months duration to a date, giving a date, or to a dateTime, giving another dateTime.
  • You can add a days and time duration to a time, giving another time.
  • And you can add two durations of the same type days and time or years and months to get another duration of that type.

A common use of calendar arithmetic is finding the difference between two dates or dateTimes.

  • Subtracting a start date or dateTime from an end date or dateTime always returns a days and time duration, even if this spans a multi-year period.
  • To get the years and months duration value between the start date and end date, use the FEEL function years and months duration(start dateTime, end dateTime).

You can multiply a duration times a number to get another duration of the same type, either days and time duration or years and months duration.

You can divide a duration by a number to get another duration of the same type.But the really useful one is dividing a duration by a duration, giving a number. For example, to find the number of seconds in a year, the expression duration(“P365D”)/duration(“PT1S”) returns the correct value, number 31536000. Note this is not the result returned by extracting the seconds component. The expression duration(P365D).seconds returns 0.

Refund Eligibility

Here is a simple example of calendar arithmetic from the DMN training. Given the purchase date and the timestamp of item return, determine the eligibility for a refund, based on simple rules.

The solution, using calendar arithmetic, is shown below:

Here we use a context in which the first context entry computes a days and time duration by subtracting the two dateTimes. The second context entry is a decision table that applies the rules. Note we can use durations like any other FEEL type in the decision table input entries.

Unix Timestamp

A second example comes from the Low-Code Business Automation training. It is common for databases and REST services to express dateTime values as a simple number. One common format used is the Unix timestamp, defined as the number of seconds since January 1, 1970, midnight UTC. To convert a Unix timestamp to a FEEL dateTime, you can use the BKM below:

The BKM multiplies the duration of one second by timestamp, a number, returning a days and time duration, and then adds that to the dateTime of January 1, 1970 midnight UTC, giving a dateTime. And you can perform the reverse mapping with the BKM below:

This time we subtract January 1, 1970 midnight UTC from the FEEL dateTime, giving a days and time duration, and then divide that by the duration one second, giving a number.

Calendar arithmetic is used all the time in both decision models and Low-Code business automation models. While the formats are unfamiliar at first, FEEL makes calendar arithmetic very easy. It’s all explained in the training. Both the DMN Method and Style course and the Low-Code Business Automation course provide 60-day use of the Trisotech platform and include post-class certification. Check out!

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