What is the formula for the Day of the Week Calculator?
Day of the Week Calculator: weekday = Gregorian calendar date modulo seven-day cycle. Input definitions: date = Calendar date. Use the selected convention throughout the calculation.
Dates & time
Day of the Week Calculator
Look up a Gregorian calendar weekday or ISO 8601 week number. ISO weeks begin on Monday, and the first week contains January 4; the ISO week-year can differ from the calendar year.
- Explicit formulas and worked examples
- Check your inputs, then calculate
- Data is calculated in this browser only
Check the stated input format, calculation convention and limits before using the result.
Check the example inputs, then calculate. Your values stay in this browser.
This tool uses the proleptic Gregorian calendar, not historical local calendar reforms.
Calculation notes
Understand the Day of the Week Calculator
Day of the Week Calculator validates calendar date before applying the displayed equation. This tool uses the proleptic Gregorian calendar, not historical local calendar reforms.
How can I reproduce the Day of the Week Calculator example?
Day of the Week Calculator baseline input: Calendar date: 2026-01-01. Output: Weekday = Thursday. Substitute these values into the displayed equation to reproduce the result.
How should I interpret the Day of the Week Calculator result?
- Read weekday with its stated unit and convention. The default example and the independent worked scenario use different inputs, so compare the assumptions before comparing the numbers.
- Change one input at a time and use the equation to explain the result; do not mix unit, grade-scale, time-zone or rounding conventions across comparisons.
What limits apply to the Day of the Week Calculator?
- This tool uses the proleptic Gregorian calendar, not historical local calendar reforms.
- ISO weeks are not Sunday-start or locale-specific week numbering.
- Calendar-date inputs and calculated calendar dates must stay within years 0001–9999.
Content and calculation reviewed:
Understand the calculation
How to use it and the math behind it
Four steps to check your inputs and results
- Look up a Gregorian calendar weekday or ISO 8601 week number. ISO weeks begin on Monday, and the first week contains January 4; the ISO week-year can differ from the calendar year.
- Enter Calendar date in the stated format. Baseline values are for reproduction.
- Check the output unit and convention: Read weekday with its stated unit and convention. The default example and the independent worked scenario use different inputs, so compare the assumptions before comparing the numbers.
- Change one input and compare the result. This tool uses the proleptic Gregorian calendar, not historical local calendar reforms. ISO weeks are not Sunday-start or locale-specific week numbering. Calendar-date inputs and calculated calendar dates must stay within years 0001–9999.
Day of the Week Calculator: calendar conventions
The seven-day cycle repeats continuously across month and year boundaries. January 1, 2021 was a Friday; advancing by seven calendar days preserves Friday. Leap days alter the offset between the same month/day in successive years. The tool applies the proleptic Gregorian calendar, rather than reconstructing a region’s historical change from the Julian calendar.
weekday = Gregorian calendar date modulo seven-day cycle
The detailed guide adds variable definitions, a reproducible example, a practice question and model limitations.
From question to result