Density conversion

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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>Density conversion</title><style>*{box-sizing:border-box}:root{--ink:#24333d;--muted:#586872;--line:#cfd9de;--accent:#27627b;--soft:#edf3f5;--paper:white;color-scheme:light}body{margin:0;background:#f2f4f4;color:var(--ink);font:16px/1.5 system-ui,-apple-system,"Segoe UI",sans-serif}main{max-width:1100px;padding:28px 32px 64px;margin:auto}header{margin-bottom:20px}h1{font-size:clamp(1.5rem,3vw,2.1rem);letter-spacing:-.035em;line-height:1.18;margin:0 0 9px}h2{font-size:1.2rem;line-height:1.3;margin:0 0 15px}h3{font-size:1rem;margin:0 0 8px}p{margin:9px 0 16px}header p{margin-bottom:0}.eyebrow{font-size:.75rem;font-weight:750;text-transform:uppercase;letter-spacing:.12em;color:var(--accent);margin-bottom:8px}.muted,small{color:var(--muted)}.panel{background:var(--paper);border:1px solid var(--line);padding:24px;border-radius:12px}.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:15px}.triple{display:grid;grid-template-columns:2fr 1fr 1fr;gap:16px}.below{margin-top:24px}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{resize:vertical;line-height:1.6}button{min-height:44px;border:1px solid var(--accent);border-radius:6px;padding:9px 15px;background:var(--accent);color:white;font-weight:650;cursor:pointer}button.secondary{background:white;color:var(--accent)}button:disabled{opacity:.5;cursor:not-allowed}button:hover:enabled{filter:brightness(.95)}:focus-visible{outline:3px solid #bb6b22;outline-offset:3px}.actions{display:flex;flex-wrap:wrap;gap:10px;margin-top:18px}.result{padding:26px;background:var(--ink);color:white;border-radius:12px}.result .muted{color:#d1e0e7}.big{font-size:clamp(2rem,5vw,3.5rem);line-height:1.15;letter-spacing:-.04em;font-weight:750;font-variant-numeric:tabular-nums;margin:10px 0;overflow-wrap:anywhere}.formula{font-family:ui-monospace,SFMono-Regular,Consolas,monospace;overflow-wrap:anywhere}.error{min-height:24px;color:#a33028;font-weight:650;margin:9px 0 0}.status{font-size:.9rem;color:var(--muted)}.note{padding:12px 16px;background:#fff3de;border-left:3px solid #b67e38;color:#65481d}table{width:100%;border-collapse:collapse;font-size:.92rem}th{text-align:left;color:var(--muted);font-size:.83rem}th,td{padding:10px 8px;border-bottom:1px solid var(--line);vertical-align:top}th:first-child,td:first-child{padding-left:0}details{padding:16px 0;border-top:1px solid var(--line)}summary{font-weight:650;cursor:pointer}pre{white-space:pre-wrap;overflow-wrap:anywhere;font:.87rem/1.6 ui-monospace,Consolas,monospace;background:#edf1f3;border:1px solid #d7e0e4;padding:18px;border-radius:7px}svg{display:block;width:100%;height:auto}.badge{display:inline-block;padding:3px 9px;background:var(--soft);color:var(--accent);font-size:.78rem;font-weight:700;border-radius:25px}.rule{height:1px;background:var(--line);margin:18px 0}[hidden]{display:none!important}a{color:var(--accent)}@media(max-width:720px){main{padding:22px 20px 45px}.grid{grid-template-columns:1fr;gap:18px}.panel{padding:20px}.triple{grid-template-columns:1fr 1fr}.triple>label:first-child{grid-column:1/-1}}@media(max-width:400px){main{padding:18px 16px 36px}.panel{padding:16px}.fields{gap:12px}.result{padding:20px}.big{font-size:2.2rem}th,td{padding:9px 5px}}.density-strip{display:grid;grid-template-columns:1fr auto 1.6fr;gap:26px;align-items:center;background:#e9f1f3;padding:26px;border-top:5px solid #547b90}.density-strip>span:first-child{font-size:1.45rem}.density-strip .big{color:#23566f}.unit-arrow{font-size:2rem;color:#6b8c9d}.dimensional{display:flex;align-items:center;gap:24px;flex-wrap:wrap}.dimensional span{display:block;color:var(--muted);font-size:.88rem}.division{font-size:2rem}@media(max-width:600px){.density-strip{grid-template-columns:1fr;gap:4px;padding:20px}.unit-arrow{display:none}.dimensional{gap:12px}.division{font-size:1.4rem}}</style></head><body><main><header><h1>Density conversion</h1><p>Convert a supplied mass-per-volume value without assuming a material.</p></header>
<section class="density-strip" aria-live="polite"><span id="source">0.8 g/mL</span><span class="unit-arrow">→</span><div><div class="big" id="result">800 kg/m³</div><span id="normal">Normalized: 800 kg/m³</span></div></section>
<section class="panel below"><div class="triple"><label for="value">Density value<input id="value" value="0.8" inputmode="decimal" ></label><label for="from">From<select id="from"><option>g/mL</option><option>kg/m³</option><option>g/cm³</option><option>kg/L</option><option>g/L</option></select></label><label for="to">To<select id="to"><option>kg/m³</option><option>g/cm³</option><option>g/mL</option><option>kg/L</option><option>g/L</option></select></label></div><div class="actions"><button type="button" id="convert">Convert</button><button type="button" id="swap" class="secondary">Swap using exact result</button><button type="button" id="reset" class="secondary">Clear / reset</button></div><p id="status" class="status" role="status"></p><p id="error" class="error" role="status"></p><p id="swapReason" class="muted"></p></section>
<section class="below panel"><h2>Mass changes, volume changes three times</h2><div class="dimensional"><div><b>1 g = 0.001 kg</b><span>Mass numerator</span></div><div class="division">÷</div><div><b>1 cm³ = (0.01 m)³</b><span>= 0.000001 m³ · Volume denominator</span></div></div><p class="formula">1 g/cm³ = 0.001 / 0.000001 = 1000 kg/m³</p><p id="derive" class="formula"></p><p id="exactRecord" class="formula"></p></section>
<details class="below"><summary>Units, precision, and scope</summary><table><tr><th>Density unit</th><th>Multiplier to kg/m³</th></tr><tr><td>kg/m³, g/L</td><td>1</td></tr><tr><td>g/cm³, g/mL, kg/L</td><td>1000</td></tr></table><p>1 mL = 1 cm³; 1 L = 0.001 m³. This converts density units; it does not convert 25 mL to grams without an independently supplied density.</p><p>Positive values ≤1 billion; a digit before the decimal, up to six fractional places. No zero, signs, exponents, commas, blank, or unsupported units. Input changes clear the result until Convert. Display rounds to six places; tiny positives remain visibly positive. Swap uses the exact result only when it fits the same input scope. No material lookup, temperature assumption, measurements, or saved entries.</p></details></main><script>const $=id=>document.getElementById(id),put=(id,s)=>{$(id).textContent=s};
function esc(s){return String(s).replace(/[&<>"']/g,c=>({'&':'&amp;','<':'&lt;','>':'&gt;','"':'&quot;',"'":'&#39;'}[c]));}
function gcd(a,b){a=a<0n?-a:a;b=b<0n?-b:b;while(b){[a,b]=[b,a%b]}return a||1n;}
function R(n,d=1n){n=BigInt(n);d=BigInt(d);if(d===0n)throw Error('Undefined denominator.');if(d<0n){n=-n;d=-d}const g=gcd(n,d);return {n:n/g,d:d/g};}
function mul(a,b){return R(a.n*b.n,a.d*b.d)}function div(a,b){return R(a.n*b.d,a.d*b.n)}function add(a,b){return R(a.n*b.d+b.n*a.d,a.d*b.d)}function sub(a,b){return R(a.n*b.d-b.n*a.d,a.d*b.d)}function cmp(a,b){const x=a.n*b.d-b.n*a.d;return x<0n?-1:x>0n?1:0}
function parse(s,{max=1000000,positive=false,places=6}={}){const t=String(s).trim();if(!t)throw Error('Enter a value; blank is not zero.');const re=new RegExp('^[0-9]+(?:\.[0-9]{1,'+places+'})?$');if(!re.test(t))throw Error('Use digits and a US decimal point, up to '+places+' places; no signs, commas, or exponents.');const v=Number(t);if(!Number.isFinite(v)||v>max||(positive&&v===0))throw Error('Value must be '+(positive?'greater than zero':'nonnegative')+' and at most '+max+'.');const [a,b='']=t.split('.');return R(BigInt(a+b),10n**BigInt(b.length));}
function format(a,places=6){const neg=a.n<0n,n=neg?-a.n:a.n,scale=10n**BigInt(places),v=n*scale,q=v/a.d,rem=v%a.d,k=q+(rem*2n>=a.d?1n:0n);const f=(k%scale).toString().padStart(places,'0').replace(/0+$/,'');return {text:(neg&&k!==0n?'-':'')+(k/scale)+(f?'.'+f:''),approx:rem!==0n};}
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;}
function display(a,places=6){if(a.n>0n&&cmp(a,R(1n,10n**BigInt(places)))<0)return '< '+format(R(1n,10n**BigInt(places)),places).text;const f=format(a,places);return (f.approx?'≈ ':'')+f.text;}
function listen(ids,fn){ids.forEach(id=>{ $(id).addEventListener('input',fn);$(id).addEventListener('change',fn); });}

const factors={'kg/m³':R(1n),'g/cm³':R(1000n),'g/mL':R(1000n),'kg/L':R(1000n),'g/L':R(1n)};let current=null;
function convertDensity(s,from,to){if(!factors[from]||!factors[to])throw Error('Choose a supported density unit.');const value=parse(s,{max:1000000000,positive:true}),normalized=mul(value,factors[from]),out=div(normalized,factors[to]);return {value,normalized,out,from,to};}
function swapEntry(out){const t=exact(out);try{parse(t,{max:1000000000,positive:true});return t}catch(e){return null}}
function clear(){current=null;put('result','—');['source','normal','derive','exactRecord','error'].forEach(id=>put(id,''));put('status','Inputs changed. Select Convert for a current result.');$('swap').disabled=true;put('swapReason','Swap needs a valid exact result.');}
function calculate(){try{current=convertDensity($('value').value,$('from').value,$('to').value);put('source',$('value').value.trim()+' '+current.from);put('result',display(current.out)+' '+current.to);put('normal','Normalized: '+exact(current.normalized)+' kg/m³');put('derive',$('value').value.trim()+' × '+exact(factors[current.from])+' ÷ '+exact(factors[current.to])+' = '+exact(current.out)+' '+current.to);put('exactRecord','Unrounded value: '+exact(current.out)+' '+current.to);put('status','Current conversion. Display digits do not establish measurement precision.');put('error','');const entry=swapEntry(current.out);$('swap').disabled=entry===null;put('swapReason',entry===null?'Swap unavailable: the exact result exceeds the range or six-place input scope.':'Swap will use '+entry+', not rounded display text.');}catch(e){clear();put('status','No current conversion.');put('error',e.message);}}
listen(['value','from','to'],clear);$('convert').addEventListener('click',calculate);$('swap').addEventListener('click',()=>{if(!current)return;const entry=swapEntry(current.out);if(entry===null)return;const old=current.from;$('value').value=entry;$('from').value=current.to;$('to').value=old;calculate()});$('reset').addEventListener('click',()=>{$('value').value='';$('from').value='g/mL';$('to').value='kg/m³';clear();put('status','Enter a supplied density to begin.');put('swapReason','');$('value').focus()});globalThis.Tool={convertDensity,swapEntry,calculate,clear,exact};calculate();</script></body></html>