2c:null 2d:["$","title",null,{"children":"2027 Calendar Topology Observatory | Mateo Pedersen | Observable"}] 32:T48f,# 2027 Calendar Topology Observatory An interactive study of how the Gregorian month grid changes when the week begins on a different day. The same civil dates can occupy four, five, or six rows depending on the week-start convention and whether a layout expands naturally or reserves a fixed six-week frame. ## Questions Which 2027 months require six natural rows? How many leading and trailing cells does each convention add? Which months share a structural signature, and how much capacity is left unused in a fixed 42-cell grid? ## Method All dates are computed locally from Gregorian civil-date rules using UTC-safe integer arithmetic. No calendar site or external API supplies the data. Week starts run Sunday through Saturday. “Natural” grids use the minimum complete weeks; “Fixed” grids use 42 cells. Adjacent dates can be shown or hidden without changing the underlying grid. Beta Calendars provides human-readable printable references: [project home](https://www.betacalendars.com/). ## Interactive explorer Use the controls to inspect one month, then compare the full year in the matrix and heatmap. The 2027 reference table is at the end.33:T1fc3,const calendarExplorer = (() => { const M=["January","February","March","April","May","June","July","August","September","October","November","December"], W=["Sunday","Monday","Tuesday","Wednesday","Thursday","Friday","Saturday"], root=document.createElement("section"); root.style.cssText="font:14px/1.5 system-ui,sans-serif;color:#17233b;background:#fbfaf6;border:1px solid #e2e5e7;border-radius:16px;padding:clamp(14px,3vw,28px);max-width:1100px;margin:auto"; const css=document.createElement("style");css.textContent=".cx-controls{display:flex;flex-wrap:wrap;gap:12px;margin:12px 0 20px}.cx-controls label{display:grid;gap:4px;font-size:12px;color:#536174}.cx-controls select{padding:8px;border:1px solid #bec9d2;border-radius:8px;background:white}.cx-layout{display:grid;grid-template-columns:repeat(auto-fit,minmax(min(100%,300px),1fr));gap:14px}.cx-card{border:1px solid #dce3e7;border-radius:12px;padding:14px;background:white}.cx-grid{display:grid;grid-template-columns:repeat(7,minmax(0,1fr));gap:3px;text-align:center}.cx-grid b,.cx-grid span{padding:4px 1px;border-radius:5px}.cx-grid b{font-size:10px;color:#52647a}.cx-day{background:#e9f2f1}.cx-out{color:#9da9b2;background:#fafafa}.cx-matrix{display:grid;grid-template-columns:repeat(auto-fit,minmax(165px,1fr));gap:10px}.cx-mini{border:1px solid #e1e7e8;border-radius:10px;padding:9px;background:#fff}.cx-mini h4{margin:0 0 7px}.cx-mini .cx-grid{gap:2px}.cx-mini .cx-grid b,.cx-mini .cx-grid span{font-size:10px;padding:3px 0}.cx-note{color:#536174;font-size:13px}.cx-table{border-collapse:collapse;width:100%}.cx-table th,.cx-table td{padding:7px;border-bottom:1px solid #e5eaec;text-align:left}.cx-chip{display:inline-block;background:#e9f3f2;color:#175c61;padding:4px 9px;border-radius:99px;margin:3px;font-size:12px}@media(max-width:520px){.cx-grid{gap:1px}.cx-grid b,.cx-grid span{font-size:10px;padding:3px 0}.cx-card{padding:10px}}";root.append(css); const title=document.createElement("h2");title.textContent="Explore the 2027 grid";root.append(title); const ctr=document.createElement("div");ctr.className="cx-controls"; function sel(label,opts,val){const l=document.createElement("label");l.textContent=label;const s=document.createElement("select");opts.forEach(o=>{const x=document.createElement("option");x.value=o[0];x.textContent=o[1];s.append(x)});s.value=val;l.append(s);ctr.append(l);return s} const ms=sel("Month",M.map((x,i)=>[i+1,x]),"1"), ws=sel("Week starts",W.map((x,i)=>[i,x]),"1"), mode=sel("Grid mode",[["natural","Natural rows"],["fixed","Fixed 42 cells"]],"natural"); const al=document.createElement("label");al.style.cssText="display:flex;align-items:center;gap:7px;padding-top:18px";const adj=document.createElement("input");adj.type="checkbox";al.append(adj,document.createTextNode("Show adjacent dates"));ctr.append(al);root.append(ctr); const top=document.createElement("div");top.className="cx-layout";const main=document.createElement("div");main.className="cx-card";const occ=document.createElement("div");occ.className="cx-card";top.append(main,occ);root.append(top); const mh=document.createElement("h3");mh.textContent="2027 month matrix";root.append(mh);const matrix=document.createElement("div");matrix.className="cx-matrix";root.append(matrix); const hh=document.createElement("h3");hh.textContent="Natural row-count sensitivity";root.append(hh);const heat=document.createElement("div");heat.className="cx-card";root.append(heat); const sh=document.createElement("h3");sh.textContent="Shared topology signatures · Monday-first";root.append(sh);const sig=document.createElement("div");sig.className="cx-card";root.append(sig); function leap(y){return y%4===0&&(y%100!==0||y%400===0)} function days(y,m){return [31,leap(y)?29:28,31,30,31,30,31,31,30,31,30,31][m-1]} function wd(y,m,d){return new Date(Date.UTC(y,m-1,d)).getUTCDay()} function off(y,m,w){return (wd(y,m,1)-w+7)%7} function rows(y,m,w){return Math.ceil((off(y,m,w)+days(y,m))/7)} function cells(y,m,w,fixed){const n=fixed?42:rows(y,m,w)*7,o=off(y,m,w);return Array.from({length:n},(_,i)=>{const d=i-o+1;return {d:d>=1&&d<=days(y,m)?d:null,a:d<1?days(y,m===1?12:m-1)+d:d>days(y,m)?d-days(y,m):null,wd:(w+i)%7}})} function cal(y,m,w,fixed,show,mini){const box=document.createElement("div");if(mini)box.className="cx-mini";const h=document.createElement(mini?"h4":"h3");h.textContent=M[m-1]+" "+y+(mini?"":" · "+rows(y,m,w)+" natural rows");box.append(h);const g=document.createElement("div");g.className="cx-grid";for(let i=0;i<7;i++){const b=document.createElement("b");b.textContent=W[(w+i)%7].slice(0,2);g.append(b)}cells(y,m,w,fixed).forEach(c=>{const s=document.createElement("span");s.textContent=c.d===null?(show?c.a:"·"):c.d;s.className=c.d===null?"cx-out":"cx-day";s.setAttribute("aria-label",c.d===null?"Outside month" : M[m-1]+" "+c.d+", "+W[c.wd]);g.append(s)});box.append(g);return box} function draw(){const m=+ms.value,w=+ws.value,f=mode.value==="fixed",d=days(2027,m),o=off(2027,m,w),r=rows(2027,m,w),n=f?42:r*7;main.replaceChildren(cal(2027,m,w,f,adj.checked,false));const note=document.createElement("p");note.className="cx-note";note.textContent="First weekday: "+W[wd(2027,m,1)]+" · last weekday: "+W[wd(2027,m,d)]+" · leading cells: "+o+" · trailing capacity: "+(n-o-d)+" · occupancy: "+(100*d/n).toFixed(1)+"%.";main.append(note);const sg=document.createElement("p");sg.textContent="Topology signature (days, leading, rows, trailing): ("+[d,o,r,n-o-d].join(", ")+")";main.append(sg); occ.replaceChildren();const ot=document.createElement("h3");ot.textContent="Grid occupancy";occ.append(ot);const tb=document.createElement("table");tb.className="cx-table";tb.innerHTML="FrameCellsUsedEmptyOccupancy";const body=document.createElement("tbody");[{name:"Natural",n:r*7},{name:"Fixed",n:42}].forEach(x=>{const tr=document.createElement("tr");tr.innerHTML=""+x.name+""+x.n+""+d+""+(x.n-d)+""+(100*d/x.n).toFixed(1)+"%";body.append(tr)});tb.append(body);occ.append(tb); matrix.replaceChildren();for(let k=1;k<=12;k++)matrix.append(cal(2027,k,w,false,false,true)); heat.replaceChildren();const svg=document.createElementNS("http://www.w3.org/2000/svg","svg");svg.setAttribute("viewBox","0 0 770 245");svg.setAttribute("role","img");svg.setAttribute("aria-label","2027 natural row counts by month and week start");const ns="http://www.w3.org/2000/svg";function a(t,o,v){const e=document.createElementNS(ns,t);Object.entries(o).forEach(([k,x])=>e.setAttribute(k,x));if(v)e.textContent=v;svg.append(e)}const left=100,top=27,cw=48,ch=28;M.forEach((x,i)=>a("text",{x:left+i*cw+20,y:17,"text-anchor":"middle","font-size":10,fill:"#536174"},x.slice(0,3)));W.forEach((x,j)=>{a("text",{x:left-8,y:top+j*ch+17,"text-anchor":"end","font-size":11,fill:"#536174"},x.slice(0,3));M.forEach((_,i)=>{const z=rows(2027,i+1,j),c=z===4?"#d7ece8":z===5?"#77b7b2":"#275d78";a("rect",{x:left+i*cw,y:top+j*ch,width:cw-3,height:ch-3,rx:4,fill:c});a("text",{x:left+i*cw+22,y:top+j*ch+18,"text-anchor":"middle","font-size":12,fill:z===6?"white":"#17313a"},z)})});heat.append(svg);const hp=document.createElement("p");hp.className="cx-note";hp.textContent="Each cell is a row count; the number and position encode the value as well as color. Pale teal = 4 rows, sea green = 5, deep blue = 6.";heat.append(hp); sig.replaceChildren();const groups=new Map();for(let k=1;k<=12;k++){const key=[days(2027,k),off(2027,k,1),rows(2027,k,1)].join(" · ");if(!groups.has(key))groups.set(key,[]);groups.get(key).push(M[k-1])}const sp=document.createElement("p");sp.className="cx-note";sp.textContent="For Monday-first natural grids, equal signatures share the same date placement topology.";sig.append(sp);groups.forEach((names,key)=>{const row=document.createElement("p");row.textContent="("+key+") ";names.forEach(name=>{const c=document.createElement("span");c.className="cx-chip";c.textContent=name;row.append(c)});sig.append(row)}) } [ms,ws,mode,adj].forEach(x=>x.addEventListener("change",draw));draw();return root; })(); calendarExplorer34:T916,## Findings from the 2027 calculation With Monday-first weeks, May and August are the two six-row months; February fits four rows, and the other nine months use five. Across all seven week starts, 18 month/convention pairs require six rows. A fixed 42-cell frame leaves 11 cells unused for 31-day months, 12 for 30-day months, and 14 for February. The broad check covers all 2,412 months from 1900 through 2100 under all seven week starts: each month’s dates appear once, row counts stay between four and six, and fixed grids contain 42 cells. Leap-year assertions pass for 1900, 2000, 2024, 2027, 2100 and 2400. Civil dates use UTC-based weekday calculation so local timezone changes do not shift the grid. ## Human-readable 2027 month references All topology above is computed independently from Gregorian rules. These Beta Calendars pages are printable references for the corresponding months. | Month | Printable reference | |---|---| | January | [January calendar](https://www.betacalendars.com/january-calendar.html) | | February | [February calendar](https://www.betacalendars.com/february-calendar.html) | | March | [March calendar](https://www.betacalendars.com/march-calendar.html) | | April | [April calendar](https://www.betacalendars.com/april-calendar.html) | | May | [May calendar](https://www.betacalendars.com/may-calendar.html) | | June | [June calendar](https://www.betacalendars.com/june-calendar.html) | | July | [July calendar](https://www.betacalendars.com/july-calendar.html) | | August | [August calendar](https://www.betacalendars.com/august-calendar.html) | | September | [September calendar](https://www.betacalendars.com/september-calendar.html) | | October | [October calendar](https://www.betacalendars.com/october-calendar.html) | | November | [November calendar](https://www.betacalendars.com/november-calendar.html) | | December | [December calendar](https://www.betacalendars.com/december-calendar.html) | ## Interpretation Week-start changes can shift an entire month’s grid by one column; that can change the natural row count even though the civil dates are unchanged. The fixed grid makes the trade-off explicit: consistent six-week geometry at the cost of unused cells. The matrix and heatmap let readers compare these conventions without treating one as universally correct.35:[] 30:{"id":"124e6e379219ccb5","slug":"2027-calendar-topology-observatory","title":"2027 Calendar Topology Observatory","thumbnail":"49e3b8e7b5c25c76853ac31b4ed41e895e2facb91573182f4e68e995d0ccb899","access_level":"public","create_time":"$D2026-10-07T11:14:54.384Z","update_time":"$D2026-10-07T11:28:25.958Z","view_time":null,"first_public_time":"$D2026-10-07T11:38:01.997Z","has_unpublished_edits":null,"fork":false,"stars":0,"starred":false,"owner":{"type":"team","id":"0608cb6e6fdd19ad","login":"mateopedersen","name":"Mateo Pedersen","avatar_url":"https://avatars-next.observableusercontent.com/1656f6350cbcad592ca7fe8675140cd56effd725832498d28117b54dc11cfe4b","tier":"free_2026","bio":"Independent product builder exploring calendar computation, printable-layout geometry and temporal data visualization. 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