calendata — a calendar maker's toolkit

Leap-cycle wizard L/C search

Leap unit

Max cycle (yr)

Max wobble (±d)

7 | cycle days

Best L-per-C cycles vs the target year, ranked by error. ±W = within-cycle wobble. CF ★ = continued-fraction convergent (best possible at that size). Click a row twice to generate it as a fresh calendar.

Leap-month cycles (lunisolar)

Max cycle (yr)

k leap months per n years vs the solar target and synodic month (Metonic = 7/19). Click a row twice to generate a lunisolar scaffold — 30/29 alternating months + smooth-spread 13-month years; fine-tune lengths by hand.

Calendar def

Name

Weekday names (comma-separated)

Days / week

Epoch year

…starts on weekday

The epoch fixes the weekday of day 1 of the epoch year (its first in-week day); every other date is counted from it.

Target year

days

Target month (synodic) track

days

Eras

Intercalation rules ↓ first match

Read top-down; the first rule a year satisfies sets its type. mod: year mod N = R. smooth: (L·y+K) mod C < L spreads L matches per C years as evenly as possible. interval: divisor list, “!” excludes and passes to the next rule — Gregorian is the single rule 400,!100,4.

Convert ↔ Gregorian

Convert with

This calendar → Gregorian

Day

Month

Year

—

Gregorian → this calendar

Day

Month

Year

—

Show year

Months to display

Day numbers Mark intercalary days

Cycle & drift analysis

design-space & accuracy

Drift vs. true day count

from span

drift — year shorter than target, calendar falls behind snap-back — intercalary day overshoots, calendar catches up mean trend true day count (zero drift) ±W wobble envelope

Per-year error spikes — the texture the sawtooth integrates

Each year's length − target, coloured by year type. Shares the drift window above.

Leap rhythm — one cell per year, wrapped by cycle row

Year wheel & weekday alignment

Wheel: the displayed year, 12 o'clock = day 1; ticks = week starts; red dots = out-of-week days; rim dots = solstices & equinoxes (hollow = extrapolated).

Mean-year convergence — running mean vs horizon

Average year length over the first N years (log N). Settles onto the exact mean (gold) each full cycle P; distance from the target line is the drift rate.

Season drift — the March equinox in this calendar

Day-of-year of the March equinox. Solid dots: AstroPixels data 2000–2060; hollow: extrapolated at the mean vernal-equinox year (365.2424 d) — shaded region. Violet band: ±W wobble.

Moon-phase drift — day 1 of every month

Phase age of each month's first day, from the displayed year (anchor new moon: 6 Jan 2000 18:14 UTC). A lunisolar calendar holds a flat band; a solar one wanders through the whole cycle. Shown while a synodic target is tracked (Calendar tab).

Named systems — side by side

All against the current target year. Click a column to sort. ±W = within-cycle wobble; the dot marks weekly-clean systems.

month-length heatmap · all year types

Calendar definition (JSON) — export / import

The leap lab — design-space explorer

d = 365 + a + Σ b/n · one b-day correction every n years · coinciding levels stack