Day Into Year Calculator
Day of the Year Calculator works out Day of the week and ISO weekday number (Monday = 1) from Date. The default figures on this page give day of the year of 201; change any entry and the result, the working and the sources update together.
Your figures
Updates as you typeHow this is worked out
3 steps
- Zeller's congruence for 1969-07-20: q=20, m=7, K=69, J=19: (20 + floor(13*(7+1)/5)=20 + 69 + floor(69/4)=17 + floor(19/4)=4 + 5*19=95) mod 7 = 1, and h = 1 counts from Saturday, so the day is Sunday.
- Day of the year: 201 of 365 (1969 is not a leap year), leaving 164 days.
- ISO week date: 1969-W29-7. The week belongs to 1969 because that is the year holding its Thursday.
Its 5 worked examples are re-run on every release, last on 15 September 2026. What changed
Sources and references
3 sources
What the Day of the Year Calculator calculates
The weekday any date falls on, with the hand working (Zeller’s congruence), the day of the year, the days left in the year, the quarter, the ISO week and the ISO week-numbering year, which is not always the calendar year. In birth-date mode it also lists the weekday of the coming anniversaries.
How to use this Day of the Year Calculator
Enter Date. Day of the week updates as you type. Change one figure at a time to see what drives the result.
How the result is worked out
Open “How this is worked out” beside the result for the step-by-step calculation behind Day of the week, ISO weekday number (Monday = 1) and US weekday number (Sunday = 1).
The method follows ISO 8601-1:2019, Date and time - Representations for information interchange, Christian Zeller, "Kalender-Formeln", Acta Mathematica 9 (1887), 131-136 and Howard Hinnant, chrono-Compatible Low-Level Date Algorithms.
What you can compare
Change one input at a time to see how it affects Day of the week, ISO weekday number (Monday = 1) and US weekday number (Sunday = 1). The inputs you can vary are Date.
Results are general information, not financial, tax, legal, medical or engineering advice. Check any decision that matters with a qualified professional.
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Frequently asked questions
What information do I need for the Day of the Year Calculator?
You need Date. The page opens with default figures that give day of the year of 201, so you can see the scale before entering your own.
What does this Day of the Year Calculator show?
It shows Day of the week, ISO weekday number (Monday = 1), US weekday number (Sunday = 1), Day of the year, Days left in the year, Days in that year, ISO week number and ISO week-numbering year, with the working and any warnings for your entries.
Can I check how the Day of the Year Calculator result was calculated?
Yes. The “How this is worked out” section shows the calculation steps, and the sources section identifies the references used for the method.