Minutes as a share of a time budget

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<!doctype html><html lang="en-US"><head><meta charset="utf-8"><meta name="viewport" content="width=device-width,initial-scale=1"><title>Minutes as a share of a time budget</title><style>*{box-sizing:border-box}:root{--ink:#26353e;--muted:#526771;--accent:#285f77;--line:#d0dade;--soft:#edf3f5;color-scheme:light}body{margin:0;background:#f2f5f5;color:var(--ink);font:16px/1.5 system-ui,-apple-system,"Segoe UI",sans-serif}main{max-width:1120px;margin:auto;padding:28px 32px 64px}header{margin-bottom:20px}h1{font-size:clamp(1.5rem,3vw,2.1rem);line-height:1.2;letter-spacing:-.035em;margin:0 0 8px}header p{margin:0}h2{font-size:1.2rem;line-height:1.3;margin:0 0 16px}h3{font-size:1rem;margin:0 0 8px}p{margin:9px 0 16px}.panel{background:white;border:1px solid var(--line);border-radius:10px;padding:24px}.grid{display:grid;grid-template-columns:minmax(0,1fr) minmax(0,1fr);gap:24px}.fields{display:grid;grid-template-columns:repeat(2,minmax(0,1fr));gap:16px}.below{margin-top:24px}.muted,small{color:var(--muted)}.big{font-size:clamp(2rem,5vw,3.6rem);font-weight:750;line-height:1.14;letter-spacing:-.04em;margin:9px 0;font-variant-numeric:tabular-nums;overflow-wrap:anywhere}.subresult{font-size:1.2rem;font-weight:700}.formula{font-family:ui-monospace,SFMono-Regular,Consolas,monospace;overflow-wrap:anywhere}label{display:block;font-size:.9rem;font-weight:650}input,select,textarea,button{font:inherit}input,select,textarea{display:block;width:100%;min-width:0;margin-top:6px;padding:10px 12px;border:1px solid #879da8;border-radius:6px;background:white;color:var(--ink)}input,select{min-height:46px}textarea{line-height:1.6;resize:vertical}button{min-height:44px;padding:9px 15px;border:1px solid var(--accent);border-radius:6px;background:var(--accent);color:white;font-weight:650;cursor:pointer}button.secondary{background:white;color:var(--accent)}button:disabled{opacity:.5;cursor:not-allowed}:focus-visible{outline:3px solid #bf6a22;outline-offset:3px}.actions{display:flex;flex-wrap:wrap;gap:10px;margin-top:16px}.check{display:flex;align-items:flex-start;gap:10px;font-weight:500}.check input{width:20px;height:20px;min-height:20px;margin:2px 0 0;flex:none;accent-color:var(--accent)}.badge{display:inline-block;background:var(--soft);color:var(--accent);font-size:.78rem;font-weight:700;padding:4px 9px;border-radius:24px}.error{min-height:24px;color:#a52f29;font-weight:650;margin:8px 0 0}.status{font-size:.88rem;color:var(--muted)}.note{background:#fff3de;border-left:3px solid #b47e3d;padding:12px 16px;color:#63491f}.rule{border-top:1px solid var(--line);margin:18px 0}table{border-collapse:collapse;width:100%;font-size:.92rem}th{font-size:.82rem;color:var(--muted);text-align:left}th,td{border-bottom:1px solid var(--line);padding:10px 8px;vertical-align:top}th:first-child,td:first-child{padding-left:0}details{border-top:1px solid var(--line);padding:16px 0}summary{font-weight:650;cursor:pointer}svg{display:block;width:100%;height:auto}figure{margin:0}figcaption{font-size:.84rem;color:var(--muted);margin-top:10px}pre{white-space:pre-wrap;overflow-wrap:anywhere;font:.86rem/1.6 ui-monospace,Consolas,monospace;background:#eaf0f3;border-radius:6px;padding:18px}ol{padding-left:24px}li{margin:7px 0}[hidden]{display:none!important}@media(max-width:720px){main{padding:22px 20px 44px}.grid{grid-template-columns:1fr;gap:18px}.panel{padding:20px}}@media(max-width:400px){main{padding:18px 16px 36px}.panel{padding:16px}.big{font-size:2.3rem}.fields{gap:12px}th,td{padding:8px 5px}}@media print{body{background:white}main{padding:0;max-width:none}.actions,button{display:none}.panel{break-inside:avoid}details>*{display:block}}:root{--accent:#77523e}body{background:#f5f0e9}.time-answer{border-top:5px solid #ac855c;border-bottom:1px solid #d8cbb8;background:#fffdf9;padding:25px 28px}.time-answer .big{color:#805934}.time-answer p:last-child:empty{display:none}.basis-comparison{display:grid;grid-template-columns:1fr 1fr;gap:24px}.basis-comparison b{display:block;font-size:1.7rem;color:#765739}.basis-comparison span{color:var(--muted);font-size:.87rem}@media(max-width:400px){.time-answer{padding:20px}.basis-comparison{gap:14px}}</style></head><body><main><header><h1>Minutes as a share of a time budget</h1><p>Keep the total beside the answer in both conversion directions.</p></header>
<section class="time-answer" aria-live="polite"><div id="result" class="big">44.44%</div><div id="caption" class="subresult">of the 45-minute workshop</div><p id="derive" class="formula">20 ÷ 45 × 100 ≈ 44.44%</p><p id="exceeds"></p></section>
<section class="panel below"><div class="fields"><label for="mode">Convert<select id="mode"><option value="forward">Minutes → percentage</option><option value="reverse">Percentage → minutes</option></select></label><label for="basis">Reference basis<select id="basis"><option value="custom">Custom positive total</option><option value="hour">One 60-minute hour</option></select></label><label for="part">Part duration (minutes)<input id="part" value="20" inputmode="decimal" aria-describedby="error"></label><label for="total">Total time budget (minutes)<input id="total" value="45" inputmode="decimal" aria-describedby="error"></label><label for="name">Budget name<input id="name" value="workshop" ></label></div><div class="actions"><button type="button" id="calculate">Calculate</button><button type="button" id="reset" class="secondary">Clear all inputs</button></div><p id="error" class="error" role="status"></p></section>
<section class="below panel"><h2>Same 20 minutes, different totals</h2><div class="basis-comparison"><div><b>44.44%</b><span>20 of 45 minutes · workshop</span></div><div><b>33.33%</b><span>20 of 60 minutes · hour</span></div></div><p>Fictional planning examples. A ratio of durations is not work completion, productivity, or a time record.</p></section><details class="below"><summary>Precision and input notes</summary><p>Forward: part ÷ total × 100. Reverse: percentage ÷ 100 × total. Exact decimal fractions are retained; displayed answers round to two places. Literal 33.33% of 60 is 19.998 minutes, not an exact return to 20. Values above 100% are allowed and are never clamped.</p><p>Main entries are minutes, not hours or colon notation. Explicitly normalize 1.5 hours to 90 minutes; 30/90 is 33.33% rounded. A blank value is missing, zero total is invalid, and zero part is valid. This bounded helper accepts nonnegative dot decimals up to 1 million with six places. No exponents, network, autosave, imports, or official timesheet replacement.</p></details></main><script>const $=id=>document.getElementById(id),put=(id,s)=>{$(id).textContent=s};
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function exact(a){let d=a.d;while(d%2n===0n)d/=2n;while(d%5n===0n)d/=5n;if(d!==1n)return a.n+'/'+a.d;let places=0,p=1n;while(p%a.d!==0n&&places<40){p*=10n;places++}return format(a,places).text;}
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function timeShare(part,total,mode){const p=parse(part),t=parse(total,{positive:true});if(!['forward','reverse'].includes(mode))throw Error('Choose a supported conversion direction.');return {p,t,out:mode==='forward'?div(mul(p,R(100n)),t):div(mul(p,t),R(100n)),above:mode==='forward'?cmp(p,t)>0:cmp(p,R(100n))>0};}
function update(){const hour=$('basis').value==='hour',reverse=$('mode').value==='reverse';if(hour)$('total').value='60';$('total').disabled=hour;document.querySelector('label[for="part"]').firstChild.textContent=reverse?'Percentage of total (%)':'Part duration (minutes)';try{const r=timeShare($('part').value,$('total').value,$('mode').value),f=format(r.out,2),total=exact(r.t),name=hour?'one 60-minute hour':total+'-minute '+($('name').value.trim()||'time budget');put('result',f.text+(reverse?' minutes':'%'));put('caption',reverse?'from '+exact(r.p)+'% of '+name:'of '+name);put('derive',exact(r.p)+(reverse?' ÷ 100 × '+total:' ÷ '+total+' × 100')+(f.approx?' ≈ ':' = ')+f.text+(reverse?' minutes':'%'));put('exceeds',r.above?'Duration exceeds the reference budget; this is not a success score.':'');put('error','');}catch(e){put('result','—');['caption','derive','exceeds'].forEach(id=>put(id,''));put('error',e.message);}}
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