Computing the sky…
Every other wheel here spends its angle on time. This one spends it on position along the ecliptic, so the planets can be read against the zodiac directly. Outside are the twelve signs, equal thirty-degree cuts from the equinox, as a birth chart uses them. Inside is the sky itself: the thirteen constellations the ecliptic really crosses, at their real and very unequal widths.
The wheel above is the ring laid out flat. This is that same ring seen from underneath, which is where we live. The rim is your horizon and the middle is straight up. The ecliptic crosses as an arc rather than a circle because you only ever get half of it: from where it rises in the east, over the meridian, down to where it sets in the west. The other half is under your feet.
North is at the top and east is on the left, which looks wrong on paper and is right in the sky. This is a picture of what is above you, so it is handed like a map held over your head rather than laid on a table.
The cycle here is not the calendar year. It starts on the day of the winter solstice and runs to the day before the next winter solstice. Because the tropical year is about 365.2422 days long, that count comes out to 365 days in most cycles and 366 in some, roughly one in four, but not on a fixed rule. Nothing in this site adds a leap day; the length is simply the number of sunrises between one solstice and the next.
Look closely where day 365 meets day 1 and there is a small discontinuity. That is not a drawing error, it is the honest edge of the metaphor. A circle has to close, so the wheel lays the last day of one cycle right beside the first day of the same cycle, but those two days are a whole year apart. The Moon is at a different phase and a different distance; nothing about them actually continues into each other. The Moon's orbit line is deliberately left unjoined there rather than drawing a link that isn't real.
What actually happens is that day 365 hands off to the next cycle's day 1. So this is a helix, not a ring: it never closes, it only comes back round to the same place a turn further along. See the years as a spiral unrolls it: one coil per cycle, climbing toward the summer solstice and falling back to winter, with each coil's real length printed underneath. That is also the clearest way to see where the extra day in a 366-day cycle goes.
Above the months sits a ring that divides the year the way the sky does rather than the way the calendar does: cut at the four solstices and equinoxes, and cut again halfway between each pair. The cardinal cuts are drawn stronger, since one opens a season and the other only halves it.
Those midpoints are the cross-quarter days, the oldest festival dates in the northern year, and they fall where they fall rather than on any month's edge. That is exactly why they want a layer of their own: laid over the months you can see that they answer to nothing in the calendar.
Four are astronomical: the two solstices and the two equinoxes. Four are the midpoints between them, labelled by which season they're the midpoint of (Winter Midseason, Spring Midseason, and so on) rather than by one tradition's name for them. Those same four points are also the Gaelic cross-quarter fire festivals (Imbolc, Beltane, Lughnasadh, Samhain), kept as the alt line under each label, and they are the same instants as the four Chinese solar terms that open the seasons. This site places them where the Sun actually reaches 315°, 45°, 135° and 225° of apparent longitude. Turn on Traditional festival dates to also mark the fixed calendar dates (1 February, 1 May, 1 August, 1 November) that the folk calendar settled on; they drift a few days from the astronomical midpoints.
Solstices and equinoxes are defined by the Sun's position, not by any star, but the Big Dipper is a real, checkable consequence of the same orbital motion: because it circles Polaris once a year in addition to once a night, its orientation at a fixed clock time drifts through the seasons. Each station carries a small sketch of the Dipper's bowl and handle exactly as they stand facing north at nightfall (nautical twilight) on that date, computed for your place, not a generic diagram. Go outside after dark near one of those dates and it should match. Below the latitude where the Dipper never clears the horizon, the circle is left empty instead of guessing.
The bright cross in each circle is Polaris, and the dashed line is the oldest trick in the sky: the two stars on the outer edge of the Dipper's bowl point straight at it. Polaris sits almost exactly on the axis Earth spins around, so it barely moves all night or all year, and its height above your horizon is simply your latitude. Having it fixed in every circle is what makes the rotation legible: the Dipper is what swings, Polaris is the hinge it swings on.
These sketches are drawn on an azimuthal-equidistant projection about the group's centre, which keeps angular distances honest across the roughly 50° of sky the Dipper and Polaris span together, with up in the picture matching up in the sky.
The seasons are not caused by the equator, and not by distance from the Sun either. They are caused by Earth's axis being tilted 23.44° from the plane of its orbit, which keeps that axis pointing the same way in space all year while Earth goes around. So one hemisphere leans sunward for half the orbit and away for the other half.
What the equator gives us is the ruler. Extend Earth's equator outward onto the sky and you get the celestial equator, and the Sun's angle north or south of it is called its declination. That single number is what the four days are defined by: the equinoxes are the exact moments the Sun's declination passes through 0°, and the solstices the moments it reaches its extremes of +23.44° and −23.44°, the tilt itself. Turn on the declination layer and the inner ring draws that number directly: gold where the Sun stands north of the celestial equator, blue where it stands south, against a dashed circle at 0°. The curve crosses that circle exactly where the equinox spokes are and reaches furthest out and in exactly at the solstices, which is the definition made visible rather than asserted.
A synodic month, new moon to new moon, is 29.53 days. A solar cycle is about 365.24. Divide one by the other and you get 12.37 lunations per year, which is not a whole number and never will be, so the two calendars cannot be made to agree. Twelve lunar months run 354.4 days and fall about eleven days short of the year; thirteen run 383.9 and overshoot it. This is the oldest problem in calendar-making, and every culture that tried to run both at once had to invent something to paper over the difference.
This wheel does not try. The chain of lunar months is computed on its own terms, new moon to new moon, running without end in both directions, and the solar year is consulted only afterwards to give each month a name. Nothing is cut at a solstice. A month that opens before one and closes after it keeps all 29 or 30 of its days, and the days at its ends simply belong to the neighbouring solar cycle, which the readout says outright.
There are two numbers on a lunar month here and they are counting different things. Confusing them is easy, so the wheel names each.
Lunation 9 of 12 counts whole cycles of the moon through the solar year. A lunation belongs to the year holding its full moon: every lunation has exactly one full moon, and every full moon falls in exactly one year, so each month goes to exactly one year with none left over. That is what makes the count come out clean at the boundary, where Lunation 12 of one year is followed by Lunation 1 of the next. Some years carry 13, which is why the total is shown rather than assumed.
Summer Full Moon 3 counts something else: full moons falling inside a season. These are not the same tally. A lunation can open in spring and close in summer, so the lunation holding the third full moon of summer need not be the third lunation of summer. The seasonal label names a moon, and now says which kind, so the two readings cannot be taken for one another.
Inside a lunation the count is in lunar days, the unit Hindu calendars call the tithi. A lunar day is not a calendar day. It is the time the moon takes to gain 12 degrees of elongation from the sun, which is the angle between the moon and the sun as seen from here, and the same quantity that decides how much of the moon is lit.
A lunation is one full circuit of that angle: 360 degrees, new moon back to new moon. Thirty steps of twelve degrees make 360. So a lunation holds exactly thirty lunar days, always, the way a foot holds twelve inches. It is a definition rather than a measurement, and no arrangement of the sky can make it come out twenty-nine.
The twenty-nine you may be thinking of is the calendar day count, which is a different thing and does wobble. A calendar day is a rigid 24 hours and a lunation is 29.53 of them, which will not divide evenly, so a lunation lands across 29 or 30 dates depending on where it starts. That number is still on the wheel, as the date span in the heading.
For the moon, yes. But two different things get called accuracy here, and the lunar day wins one and loses the other.
It is exact in angle. Every tithi is precisely twelve degrees, and thirty of them close the circle with nothing left over: no rounding, no leap day, no remainder. It is not constant in time. The moon's orbit is an ellipse, so it runs faster near perigee and slower near apogee, and one tithi lasts anywhere from about 20 to 27 hours. If what you want is something to set a clock by, the tithi is the worse of the two.
| Divides the moon's cycle | Constant length | |
|---|---|---|
| Lunar day | exactly, thirty every time | no, 20 to 27 hours |
| Calendar day | no, 29.53 will not fit | yes, 24 hours by definition |
Each is exact for its own cycle and awkward for the other, which is not a fault in either. The moon's phase cycle and the Earth's rotation are unrelated motions, so no unit can be clean in both. It is the same incommensurability that runs through the whole wheel: 12.37 lunations to a year, so no lunar calendar closes on a solar one; 365.2422 days to a year, hence leap years; 29.53 days to a lunation, hence months of 29 or 30. Only the thirty comes out whole, and it manages that by being defined in angle instead of in time.
There is a mean tithi as well as a true one, exactly parallel to the mean and apparent solar time behind daylight saving. The mean tithi is the synodic month divided by thirty, a flat 23 hours 37 minutes, used where simplicity matters more than precision. The true tithi is twelve real degrees of the real moon. This wheel computes the true one, which is why the lengths you see vary, and it is the same choice made for the sun.
Going round the circle is time passing, one whole lunation. That means the thirty lunar days are not drawn equal: each takes the width its real duration earns, so a 21-hour lunar day is visibly pinched and a 26-hour one broad. The moon covers the same twelve degrees either way; it just takes longer over some of them.
Each segment carries the number of hours it runs, so the width can be read as well as seen.
The face itself moves with the moon's distance, twice over: it swells when the moon is near and shrinks when it is far, and it rides nearer the centre when near and further out when far, the same way the year wheel draws it. That is the same quantity that makes the segment narrow or wide, since the moon runs faster when it is closer, so the widest segments carry the smallest, outermost faces and the narrowest carry the biggest and innermost. Cause and effect sit beside each other. The real change in the moon's apparent width between perigee and apogee is about 14 per cent, which at this size would be a pixel and a half, so it is drawn at roughly four times that to make it legible.
Two marks name the turning points of that distance: perigee where the moon is nearest and apogee where it is furthest. They sit wherever they fall, which is not the same phase from month to month. Distance runs on a third clock again, the anomalistic month of 27.55 days, perigee to perigee, against the lunation's 29.53. The two do not match, so the pair walks backwards through the month by about two lunar days each time and wraps round roughly every fifteen months. That drift is the whole reason a supermoon is an event: a perigee has to land near a full moon, and usually it does not.
The perigee distance is not fixed either, running from about 356,500 km to 370,000 km depending on where the sun is pulling. Both marks print the real figure for that month.
The outermost band is the solar reckoning, cut into a wedge for every day and divided at every local midnight: the day of the solar cycle on the rim, the ordinary date beneath it. It is laid on the same clock face as the lunar days, and because both are drawn to real elapsed time they line up in the only way two incommensurable things can, by the hour. The sliding between them is there to see. A short lunar day that opens and closes without crossing a midnight is the kshaya case, and on this ring you can watch it happen.
The band of light takes its radius from the lit fraction, so it thins to nothing at the new moon and swells to full at the far side. The turning points fall where the definition puts them: the new moon opens lunar day 1 and the full moon opens lunar day 16, so the first fifteen are the waxing half and the second fifteen the waning, the division Hindu calendars call shukla and krishna paksha. The two quarters sit at the exact midpoints of lunar days 8 and 23, which is why the centre reads exactly 50 per cent there.
A season averages 91.3 days and a lunar month 29.53, so 3.09 months fit inside one. In practice a season carries three full moons, and sometimes four. Counted over 3,204 seasons from 1600 to 2400: 2,903 held three, 298 held four, and three held only two.
Those three are worth knowing about, because they show how fine the margins are. All of them fall in winter, which at 88.9 days is the shortest season: Earth is near perihelion then and moving fastest through its orbit, so the sun crosses that quarter of the sky quicker. Summer, at the far end of the ellipse, runs 93.7 days, which is also why four-moon seasons turn up there most often.
Winter 1961 is the clearest case, and it misses at both ends. A full moon fell at 00:41 on 22 December, and the solstice came at 02:19 the same morning: 98 minutes too early, so that moon counts as autumn's. Two more followed, in January and February. The next arrived at 07:55 on 21 March, and the equinox had already passed at 02:29: five and a half hours too late, so that one counts as spring's. It happens roughly once in 270 years, and only ever in winter.
The third full moon of a four-moon season is the original blue moon, which is where the phrase comes from, and the wheel marks it when one turns up.
Each day carries the Moon's real lit shape for that date, not a dimmed dot, so the waxing and waning rhythm is legible directly. The ring's radius is the Moon's actual distance from Earth, which is not constant: its orbit is an ellipse, carrying it from roughly 356,500 km at perigee out to about 406,700 km at apogee and back roughly every 27.5 days. Drawn nearer the centre when it is nearer to us, that becomes a visible wave, about thirteen of them around the year. A full moon landing near perigee is what gets called a supermoon.
Turn this layer on and a ring appears directly beneath the seasons, which is where it belongs: both cut the year by the Sun's own longitude, the seasons into eight and the terms into twenty-four. The months sit further in, answering to nothing celestial.
Each term is 15° of that longitude, so each runs 14 to 16 days: longest around the June solstice, when the Earth is near aphelion and the Sun creeps through the sky, shortest around December near perihelion when it hurries. Every day carries which term it is in and how far into it, counted from one at the term's opening day.
The divisions are real and precise. The traditional Chinese names for them are not shown, and that is deliberate: names of the sort that mean "Rain Water" or "Frost Descends" describe a climate calendar built for one particular part of China, and putting them on your wheel makes them look like a forecast for wherever you happen to be, which they are not. The number is the honest part. What actually happens on that day where you are is worth finding out and writing down yourself, which is what notes are for.
Conventionally the twenty-four are listed beginning with Start of Spring, around 4 February, because that opened the agricultural and civil year. But the system was not built outward from there. The winter solstice was the anchor: it is the one moment in the year a gnomon can fix precisely, by the longest noon shadow it casts, and Chinese calendrical astronomy reckoned from it for centuries. The solstices and equinoxes were determined first, then the eight nodes between them, and the full twenty-four appear complete in the Huainanzi of 139 BCE.
So this wheel counts from the winter solstice, and term 1 is the solstice itself, falling on day 1. That agrees with the wheel's own anchor and with where the system was measured from, at the cost of disagreeing with the order the terms are usually recited in. Start of Spring is term 22 here.
South of the equator the wheel anchors on your own winter solstice in June, and the seasonal festival names move with the season, as southern practice generally does. The Chinese solar terms are tied to solar longitude itself, so those stay fixed to the sky and do not flip.
First and last frost are the only things here that are not astronomy. They depend on elevation, slope, water, soil and the particular hollow you are standing in, far more than on latitude. The dates shown until you change them are a coarse latitude-band estimate and are labelled as such. Type your own; they are saved in this browser.
Either way it is a single guess, not a forecast, so the wheel shades it as a fade rather than a hard line: light green for roughly a month either side of each date, where frost is still plausible, deepening into a solid dark green for the stretch safely between the two, the actual growing season. Nowhere close to either latitude, the wheel doesn't expect frost at all, in which case the whole ring is filled dark green as a year-round growing season.
Open any day and there is a small pencil below the sun and moon figures. Click it to write down what actually happened there: the morning the tomatoes got hit, the first robin, when the corn went knee-high, when it got harvested, whatever you'd otherwise trust to memory. Each note is tied to that exact calendar date, and the wheel marks any day that has one with a small dot near the frost band, so a year of noticing is visible at a glance.
Written the same date the year before, or the year before that, shows up right alongside the box as you write, so "when did it actually last frost here" stops being a guess after a season or two. Notes stay on this device, in this browser, the same as your frost dates; there is no account and nothing is sent anywhere.
Solar positions come from a truncated VSOP87 series and agree with reference values to well under an arcsecond; solstice and equinox instants land within about a minute. Lunar positions use the Meeus ch. 47 series, good to roughly ten arcseconds. Rise and set times account for refraction at the standard horizon (−0.833° for the Sun, and the Moon's own parallax) and assume a flat sea horizon. Real hills and buildings will move them by minutes. All times are shown in the selected place's own time zone, including its daylight-saving shifts, so a spring-forward day is genuinely 23 hours long here.
Zoom into a day and the small globe in the middle is a real orthographic projection, the same kind used for maps of a hemisphere, not an illustration standing in for one: it is genuinely centred on your place, so you sit at the exact middle of the visible disc, with the gold line marking the actual day/night terminator at that instant. On today it tracks the live moment (the same one the radial "now" marker points to); on any other day it shows local solar noon, since there is no "now" to anchor to.
Algorithms after Jean Meeus, Astronomical Algorithms, and the VSOP87 theory of Bretagnon & Francou. Everything runs in your browser; the page makes no network requests and stores only your place and frost dates, locally.
The sun's height above the horizon, hour by hour, on each of the four cardinal days of this cycle. Same clock, four very different arcs.
A circle has to close, so on the wheel day 365 lands back beside day 1 and leaves a visible seam. Time doesn't close: that day hands off to the next cycle's day 1, one turn further along. Here the same stretch is unrolled, one coil per cycle, so what looks like a jump on the wheel is just the line carrying on.