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HomedateDay of the Week Calculator

Day of the Week Calculator

Determine the exact day of the week for any past, present, or future date with Zeller's congruence and planetary etymology.

Day of the Week Calculator & Calendar History

Zeller's congruence algorithm • ISO 8601 week solver • Planetary etymology & trivia

Select Target Date
Calculated Day of the Week
Sunday

September 20, 2026

Day 263 of 365ISO Week 38102 Days Left in YearGregorian

Month Calendar View (Gregorian)

September 202630 days
SuMoTuWeThFrSa

Sunday Trivia & Etymology

• Celestial Body: The Sun (Sol / Helios)
• Roman / Norse Deity: Sol (Sun God) / Sunna (Goddess of the Sun)
• Sanskrit: Ravivara (रविवार) (Ravi (Sun God, vitality and life))
• Japanese: Nichiyōbi (日曜日) (Sun Day (日 = Sun))

• In traditional Christian, Jewish, and Islamic week structures, Sunday is the first day of the weekly cycle.

• Recognized globally as a traditional day of rest and communal worship in Western cultures.

Zeller's Congruence Step-by-Step Mathematical Derivation

Day of the Week Calculator

Authoritative Date Calculation & Calendar Analysis Report • Generated on

Calculated Result
Sunday
September 20, 2026
Calendar System: Gregorian
Day of Year: Day 263 of 365
ISO 8601 Week: Week 38
Days Remaining: 102 days
Month Calendar View (September 2026 • Gregorian)
SuMoTuWeThFrSa
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2
3
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5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
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30
Zeller's Congruence Derivation:
Formula: h = (q + ⌊13(m+1)/5⌋ + K + ⌊K/4⌋ + ⌊J/4⌋ - 2J) mod 7
Parameters: q = 20, m = 9, K = 26, J = 20
Computed h = 1 → Sunday (Gregorian)
CalcPlatform Educational Reference • Deterministic calendar modular arithmetic • https://calcplatform.com/calculators/day-of-the-week-calculator
RELATED CALCULATORS:
Date Calculator|Day Counter Calculator|Age Calculator|Time Calculator|Hours Calculator

Find the Day of the Week for Any Date

The Day of the Week Calculator tells you which weekday falls on any valid date you enter. It can be used for a birthday, anniversary, historical event, future deadline, calendar check, or simply to answer questions such as:

  • What day of the week was I born?
  • What day was July 20, 1969?
  • What day of the week was July 4, 1776?
  • What day will a future date fall on?

The calculator goes beyond returning only Monday through Sunday. It can also show the day of the year, ISO week number, leap-year status, days remaining in the year, a monthly calendar view, and the mathematical steps behind the weekday calculation. It also supports batch date checking and a separate proleptic Julian-calendar mode.

What Day of the Week Is Today?

The calculator's Today function uses the current local calendar date rather than relying on a fixed example date. It can also calculate Yesterday with one click.

Because a weekday is determined from the calendar date itself, a date such as September 15, 2026 has a fixed Gregorian weekday: Tuesday. The calculator independently verifies this result against an additional weekday algorithm.

What Is a Day of the Week Calculator?

A day-of-the-week calculator is a calendar algorithm that maps a valid date to one of the seven weekdays: Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday.

Unlike a date-duration calculator, it does not primarily ask how much time passed between two dates. Instead, it answers: “Which weekday corresponds to this calendar date?” That can be calculated mathematically without counting every date one by one.

What Day Was I Born?

One of the most common uses of a weekday calculator is finding your birth weekday. Enter your month, day, and year, and the calculator returns the corresponding weekday. For example, entering July 20, 1969 returns Sunday. The calculator also reports the date's day-of-year position, leap-year status and ISO week information. For detailed age calculation in years, months, and days from your birth date, explore our Age Calculator.

How Does the Day of the Week Calculator Work?

The Gregorian calculation uses Zeller's Congruence. Instead of moving through every date from a reference point, the formula transforms the date into a small set of arithmetic values.

h = ( q + ⌊13(m + 1) / 5⌋ + K + ⌊K / 4⌋ + ⌊J / 4⌋ - 2J ) mod 7

The calculator maps the modular result as follows:

Result (h)Weekday
0Saturday
1Sunday
2Monday
3Tuesday
4Wednesday
5Thursday
6Friday

January and February are treated as months 13 and 14 of the preceding year, which is an important part of the algorithm. The calculator also provides a Show Steps feature so you can inspect the arithmetic rather than relying on a hidden result.

What Is Zeller's Congruence?

Zeller's Congruence is a closed-form calendar algorithm for finding the weekday of a date. The key variables are:

  • q — day of the month
  • m — adjusted month number (March = 3, April = 4, …, December = 12, January = 13, February = 14)
  • K — year within the century (year mod 100)
  • J — zero-based century (⌊year / 100⌋)

For January and February, the year is treated as the previous year for the calculation. This allows the weekday to be obtained using modular arithmetic rather than iterating through every preceding calendar day.

Step-by-Step Example: September 15, 2026

Date: September 15, 2026 (Gregorian)

  • q = 15, m = 9, year = 2026
  • K = 2026 mod 100 = 26, J = ⌊2026 / 100⌋ = 20
  • ⌊13(9 + 1) / 5⌋ = ⌊130 / 5⌋ = 26
  • ⌊K / 4⌋ = ⌊26 / 4⌋ = 6, ⌊J / 4⌋ = ⌊20 / 4⌋ = 5, 2J = 40
  • h = (15 + 26 + 26 + 6 + 5 - 40) mod 7 = 38 mod 7 = 3

The validated result is Tuesday (h = 3). The calculator's Gregorian engine has been independently tested against another weekday algorithm, including this specific date. That means the visible result, the calendar grid and the mathematical derivation all use the same authoritative calendar calculation rather than separate approximations.

What Is the Day of the Year?

The day of the year, also called an ordinal date, tells you the numerical position of a date within its calendar year. January 1 is Day 1. In a common year, December 31 is Day 365. In a leap year, December 31 is Day 366.

For example: September 15, 2026 = Day 258, and February 29, 2024 = Day 60. Both values are independently verified by the calculator.

How Many Days Are Left in the Year?

The calculator defines days remaining as: Days in Year − Day of Year, excluding the current date.

For September 15, 2026: 365 − 258 = 107 days remaining.

For December 31: 365 − 365 = 0 days remaining.

For February 29, 2024: 366 − 60 = 306 days remaining.

This definition matters because “days left” can otherwise be ambiguous if the current date is included.

What Is an ISO Week Number?

An ISO week number identifies a date's position within the ISO week calendar. ISO week dates are part of the ISO 8601 family of standards. ISO defines week dates alongside calendar and ordinal dates.

For ISO week numbering: Monday is Day 1 of the week. The first ISO week is the week containing the year's first Thursday. This means January 1 does not always belong to ISO Week 1 of its own calendar year. For example, December 30, 2024 belongs to ISO Week 1 of 2025. The calculator verifies this boundary case.

Why Can January 1 Belong to the Previous ISO Year?

ISO week numbering is based on complete Monday-to-Sunday week boundaries rather than simply starting a new week on January 1. Consider a January 1 that falls near the end of an ISO week. It may belong to Week 52 or Week 53 of the previous ISO year.

This is why a date can have Calendar year = 2025 but ISO week-year = 2024. The distinction becomes especially important in business reporting, financial reporting, logistics, payroll systems and software that groups data by ISO week.

How Does the Calculator Handle Leap Years?

The Gregorian leap-year rule is:

  • Divisible by 4 → normally a leap year;
  • Divisible by 100 → not a leap year;
  • Divisible by 400 → leap year again.

Therefore: 2000 = leap year, 2024 = leap year, 2028 = leap year, while 2100, 2200, and 2300 = common years, and 2400 = leap year.

The U.S. Naval Observatory describes the same Gregorian rule and notes that the calendar contains 146,097 days in 400 years, averaging 365.2425 days per year. The calculator independently validates these century boundaries.

Why Does a Leap Year Have 366 Days?

The Gregorian calendar normally has 365 days. A leap day is added approximately every four years to keep the civil calendar aligned with the seasonal year. Without leap-year corrections, the calendar would gradually drift relative to the seasons. The Gregorian system improves this by using the century and 400-year exceptions described above. That extra day is why February 29, 2024 exists while February 29, 2025 does not.

Why February 29 Can Change Calendar Calculations

A leap day affects day of year, days remaining, weekday calculations, date arithmetic, and ISO week boundaries. For example, February 29, 2024 is Thursday and Day 60 of 366. The following day, March 1, 2024, is Day 61. The calculator independently verifies these values.

Does the First Day of the Week Setting Change the Answer?

No. The calculator allows Sunday-start or Monday-start for the visual calendar layout. Changing that setting changes how the month grid is displayed, but it does not change the actual weekday of the selected date. For example, September 15, 2026 remains Tuesday whether the calendar grid starts on Sunday or Monday. This distinction is important: week display convention ≠ calculated weekday.

Gregorian Calendar vs Julian Calendar

The calculator supports both the Gregorian Calendar and the Proleptic Julian Calendar. These are different calendar systems with different leap-year rules. The Gregorian calendar uses the 400-year century rule. The Julian calendar treats every fourth year as a leap year, without the Gregorian century exception. As a result, the same nominal date can produce a different weekday under the two systems.

What Is a Proleptic Julian Calendar?

A proleptic Julian calendar applies Julian calendar rules mathematically to a date even when that date falls outside the period in which the Julian calendar was historically in civil use.

This calculator intentionally describes its mode as Proleptic Julian Calendar (Historical / Astronomical) rather than implying that every location historically used the Julian calendar until one universal switch date. That distinction is important when researching historical dates.

Why Can a Historical Date Have Two Different Weekdays?

The same written date can produce different results depending on which calendar system is being used. For example, the calculator verifies:

September 15, 2026: Tuesday — Gregorian

September 15, 2026: Monday — Proleptic Julian

Those are not contradictory results once the calendar system is explicitly identified. The key is to know which calendar your source used.

Why Historical Dates Need Extra Care

The Gregorian calendar was introduced in 1582, but adoption was not simultaneous worldwide. Different regions adopted Gregorian dating at different times (e.g., Britain and the American colonies in 1752, Russia in 1918, Greece in 1923).

Therefore, there is a difference between the mathematically calculated proleptic Gregorian weekday and the weekday actually used in a particular historical location at that time. For historical research, the local calendar and historical convention should be checked rather than assuming that every country used the same system. The calculator explicitly presents its Julian mode as a mathematical/proleptic system rather than a universal reconstruction of every historical civil calendar.

Benchmark Historical Dates

What Day Was July 20, 1969?

July 20, 1969 was Sunday. This is the date associated with the Apollo 11 lunar landing. The calculator uses this date as a preset and independently verifies its weekday.

What Day Was July 4, 1776?

July 4, 1776 was Thursday under the Gregorian calculation used by the calculator. It is available as the US Independence (1776) preset and is independently validated.

What Day Was January 1, 2000?

January 1, 2000 was Saturday. This is one of the calculator's regression reference dates and is independently verified.

How Does the Batch Date Parser Work?

The Batch Multi-Date Parser lets you enter multiple dates, typically one per line, and calculate them together. For example:

1969-07-20
1776-07-04
2000-01-01
2026-08-18

The calculator returns the weekday and additional date information for each valid input. The batch parser uses strict YYYY-MM-DD parsing and validates each date before calculating it. This prevents malformed dates from being silently converted into different valid dates.

Strict Date Validation: What Happens If I Enter February 30?

February 30 is not a valid Gregorian date. The calculator rejects impossible dates such as:

  • 2026-02-30 (February has at most 28 or 29 days)
  • 2026-02-31
  • 2026-04-31 (April has 30 days)
  • 2025-02-29 (2025 is a common year)

Calendar software can accidentally normalize impossible dates if it relies directly on native date constructors (for example, overflowing February 30 into March 2). A reliable date calculator should first ask: Does this calendar date actually exist? Only after that validation should the weekday calculation begin. This calculator explicitly validates the year, month and day and reports an accessible error state for invalid dates.

Does the Calculator Work for Very Old Years?

The supported range is Year 1 through Year 9999. The calculator also specifically protects against the common JavaScript Date behavior that can reinterpret years from 0–99 as 1900–1999. For example, 0033 remains 0033 rather than incorrectly becoming 1933. That makes the historical mode considerably safer for ancient-date calculations than a naive JavaScript-date implementation.

Day of Year vs. ISO Week vs. Weekday

They measure different calendar properties:

  • Day of Year: Counts the date's position from January 1 (e.g., September 15, 2026 = Day 258).
  • ISO Week: Places the date into an ISO Monday-to-Sunday week (e.g., September 15, 2026 = ISO Week 38).
  • Weekday vs Weekend: Weekday is Monday through Friday; Weekend is Saturday and Sunday. The actual calculated weekday itself does not depend on this classification.

Using the Calculator for Future and Historical Events

A weekday is mathematically determined for any valid date within the calculator's supported range. You can use it for future deadlines, anniversaries, planned events, recurring dates, and scheduling checks.

When researching historical events, always identify whether the source recorded the date in the Gregorian calendar, Julian calendar, or another local convention. The one-day difference for September 15, 2026 (Tuesday in Gregorian vs. Monday in Julian) is not an arithmetic mistake; it is the consequence of applying two different calendar systems to the same nominal date.

Day of the Week Calculator vs. Day Counter vs. Date Calculator

These calculators answer different questions:

QuestionBest Tool
What day of the week is this date?Day of the Week Calculator
What day was I born?Day of the Week Calculator / Age Calculator
How many days are between two dates?Day Counter Calculator
How many working days are in a period?Day Counter Calculator
What date is 30 days after another date?Date Calculator

For elapsed date calculations, use the Day Counter Calculator rather than trying to infer duration from weekday information. For date arithmetic like adding or subtracting days, our Date Calculator is specifically designed for calendar math.

Calendar Grid: Synchronized Month View

The calculator includes a monthly calendar view around the selected date. The grid is generated from the same active calendar engine used for the main weekday result. This prevents a confusing failure mode where the headline could say one weekday while the selected date appeared under another weekday in the calendar.

The calendar remains seven columns wide and supports both Sunday-first and Monday-first presentation. Changing the calendar system changes both the result and the grid consistently.

Copy, Share, History, CSV and Print Architecture

The calculator supports several practical output options:

  • Copy Summary: Copies the selected date, weekday, calendar system, day-of-year information, ISO week and related details.
  • Share URL: Preserves the complete calculation state (date, calendar system, week start) so recipients see the identical result.
  • History: Valid calculations can be saved locally in your browser, while invalid dates are blocked from saving.
  • CSV Export: Structured CSV export is provided for both single-date and batch multi-date results.
  • PDF / Print: A dedicated print-report stylesheet preserves a clean 7-column calendar and calculation summary while hiding web-only buttons and navigation.
  • Client-Side Execution: All calculations execute locally in your browser with zero outbound network requests.

How to Calculate the Weekday Manually & The 400-Year Cycle

To calculate the weekday by hand using Zeller's Congruence:

  1. Take the day of the month (q).
  2. Adjust January and February to months 13 and 14 of the previous year.
  3. Split the year into century (J) and within-century (K) parts.
  4. Substitute the values into the formula and evaluate integer divisions.
  5. Take the resulting sum modulo 7.
  6. Map the result (0 = Saturday, 1 = Sunday, …, 6 = Friday).

Because there are 7 weekdays, advancing 7 days returns to the same weekday. The Gregorian calendar contains exactly 146,097 days in 400 years, and 146,097 = 20,871 × 7. The complete 400-year Gregorian cycle contains an exact whole number of weeks, meaning the calendar repeats its exact pattern of days every 400 years.

Common Day-of-the-Week Calculation Mistakes

Mistake 1: Treating invalid dates as validFebruary 30 or April 31 do not exist in the calendar and must be rejected.
Mistake 2: Ignoring leap yearsWeekdays shift differently around February and March in leap years vs. common years.
Mistake 3: Confusing ISO week with calendar weekISO week numbering follows its own standard where Week 1 has the year's first Thursday.
Mistake 4: Ignoring the calendar systemGregorian and Julian calculations produce different historical weekdays.
Mistake 5: Assuming display week changes the weekdaySunday-start or Monday-start display setting only rearranges the calendar columns.
Mistake 6: Assuming global 1582 adoptionHistorical calendar adoption varied widely between regions across four centuries.

Quick Reference: Verified Reference Dates

DateGregorian WeekdayDay of YearLeap Year
January 1, 2000Saturday1Yes
July 4, 1776Thursday186No (Julian 1776 was leap)
July 20, 1969Sunday201No
February 29, 2024Thursday60Yes
January 1, 2025Wednesday1No
September 13, 2026Sunday256No
September 14, 2026Monday257No
September 15, 2026Tuesday258No
December 31, 2026Thursday365No

Methodology and Sources

Gregorian Weekday Calculation

The calculator uses Zeller's Congruence for Gregorian weekday calculation, including the standard January/February adjustment and modulo mapping. Its implementation has been independently checked against another weekday algorithm across 1,000 randomized Gregorian dates.

Proleptic Julian Calculation

The historical mode uses pure proleptic Julian arithmetic and applies the Julian leap-year rule. It has been independently checked against an astronomical Julian-day-based calculation across 1,000 randomized dates.

ISO 8601 Week Dates & Day of Year

ISO 8601 defines Gregorian calendar dates, ordinal dates and week dates. The calculator's ISO-week implementation follows Monday-based ISO week numbering and has been independently tested against the ISO definition.

Gregorian Leap Years & Date Validation

The Gregorian calendar uses the 4-year rule with the century exception and 400-year correction. The U.S. Naval Observatory states that 97 leap days occur every 400 years and the average Gregorian calendar year is 365.2425 days. The calculator validates year, month and day combinations before performing calculations, rejecting non-existent dates.

Useful Related Calculators

Explore complementary tools across our date and time suite:

  • For date arithmetic rather than weekday lookup, the Day Counter Calculator can calculate elapsed calendar days, working days and related durations.
  • For age-specific calculations and chronological milestones, use the Age Calculator.
  • For general date addition and subtraction operations, the Date Calculator provides calendar math.
  • For sub-day intervals and clock calculations, the Time Calculator and Hours Calculator are better suited to hour-level and minute-level duration.

Final Takeaway

The answer to “What day of the week is this date?” may look simple, but a reliable calculator must handle much more than a seven-item lookup table. It must correctly understand valid calendar dates, leap years, century rules, Gregorian arithmetic, Julian arithmetic, ISO week numbering, historical calendar interpretation, and the distinction between calendar presentation and weekday calculation.

The Day of the Week Calculator combines those capabilities in one interface. It can calculate a single date, process batches of dates, show the mathematical Zeller derivation, display day-of-year and ISO-week information, compare Gregorian and proleptic Julian systems, preserve calculation state for sharing, save valid history entries, export CSV data and generate a dedicated printable report.

For an ordinary modern date, the Gregorian result is the appropriate starting point. For a historical date, always check the calendar system behind the source. Enter a date above to find its weekday instantly.

Frequently Asked Questions

Enter your birth date into the Day of the Week Calculator. It returns the corresponding weekday and can also show the day of year, ISO week and leap-year status.
It uses calendar arithmetic to map a valid date to one of seven weekdays. This calculator uses Zeller's Congruence for its Gregorian weekday calculation and exposes the mathematical steps.
Zeller's Congruence is a modular-arithmetic formula for calculating the weekday of a calendar date. January and February are treated as months 13 and 14 of the preceding year in the standard formulation.
July 20, 1969 was Sunday. The date is also available as an Apollo 11 preset in the calculator.
July 4, 1776 was Thursday under the Gregorian calculation used by the calculator.
January 1, 2000 was Saturday.
An ISO week number identifies a date's week under ISO 8601 week-date rules. ISO weeks start on Monday and Week 1 is the week containing the first Thursday.
Because ISO week numbering is based on Monday-to-Sunday weeks and the week containing the year's first Thursday. Therefore, the first days of January can fall in the final ISO week of the previous year.
It is the ordinal position of a date within its calendar year. January 1 is Day 1; December 31 is Day 365 in a common year and Day 366 in a leap year.
This calculator defines days remaining as the number of days after the selected date. For September 15, 2026, Day 258 of 365 leaves 107 days remaining.
No. Sunday-start or Monday-start only changes the arrangement of the calendar grid. The calculated weekday stays the same.
They are different calendar systems with different leap-year rules. Gregorian uses century exceptions; the Julian system treats every fourth year as a leap year.
It applies Julian calendar rules mathematically to dates regardless of whether that calendar was historically used in that place and period. This calculator explicitly labels the mode as proleptic Julian.
Because the two calendar systems use different rules for leap years and calendar dates. For September 15, 2026, this calculator gives Tuesday in Gregorian mode and Monday in proleptic Julian mode.
Yes. It correctly handles Gregorian leap-year rules, including the special century cases such as 2000 and 2100.
Yes, within the supported year range of 1–9999. Historical results should be interpreted with the selected calendar system in mind.
The calculator rejects impossible dates such as February 30 rather than silently normalizing them. An accessible validation message is shown.
Yes. The Batch Multi-Date Parser accepts multiple dates and returns the calculated results for valid entries.
Yes. Valid calculations can be stored in the browser's local history. Invalid dates cannot be saved.
Yes. The share state includes the relevant date and calendar parameters so the recipient can reproduce the calculation.
Yes. CSV export is implemented for both single-date and batch results.
Yes. The calculator uses a dedicated print report designed to keep the calculation separate from the interactive webpage interface.
The post-fix audit verified client-side calculation with no external outbound requests during testing.
They may use different calendar systems, date conventions, historical interpretations, or algorithms. Always check whether both tools are using Gregorian, Julian or another calendar framework.