Percent slope → degrees

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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>Percent slope → degrees</title><style>*{box-sizing:border-box}html{color-scheme:light}body{margin:0;background:var(--bg,#eef1f4);color:var(--ink,#233449);font:16px/1.5 system-ui,-apple-system,Segoe UI,sans-serif}main{max-width:1040px;margin:auto;padding:26px 28px 44px}header{margin-bottom:20px}h1{font-size:clamp(26px,4vw,36px);letter-spacing:-.035em;line-height:1.15;margin:5px 0 10px}h2{font-size:21px;line-height:1.3;margin:0 0 15px}h3{font-size:17px;margin:0 0 9px}p{margin:8px 0 16px}.kicker{font-size:12px;text-transform:uppercase;letter-spacing:.12em;font-weight:750;color:var(--accent,#315b87)}.muted,small{color:#556473}.panel{margin:20px 0;padding:24px;border:1px solid var(--line,#ccd5df);border-radius:10px;background:#fff}.hero{padding:24px;background:var(--hero,#183b5c);color:#fff;border-radius:12px;margin:18px 0}.hero .kicker,.hero 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#4f7b87}.slope-result figure{margin:0}.slope-result svg{width:100%;height:auto;max-height:250px}.slope-result figcaption{font-size:13px;color:#546673}.slope-result .big{font-family:Georgia,serif;font-size:clamp(32px,5vw,48px)}</style></head><body style="--bg:#eff3f5;--accent:#386a7b"><main><header><div class="kicker">Classroom ratio inspector</div><h1>Percent slope → degrees</h1><p class="muted">Use the horizontal run as the denominator, then take the inverse tangent.</p></header><section id="result" class="surface slope-result" aria-live="polite"><div class="grid"><div><div class="kicker" id="basis"></div><div class="big" id="angle"></div><p id="ratio"></p><p id="inverse"></p></div><figure><svg viewBox="0 0 340 240" role="img" aria-label="Schematic right triangle; horizontal run, vertical rise and slanted segment separately labeled"><path id="triangle" fill="#e4f0f2" stroke="#386a7b" stroke-width="3"/><text x="155" y="228" text-anchor="middle" font-size="14">Horizontal run: 100 units</text><text id="riseLabel" x="315" y="30" text-anchor="end" font-size="13"></text><text x="30" y="20" font-size="13">Slanted segment ≠ run</text></svg><figcaption id="diagramNote"></figcaption></figure></div></section><p id="error" class="error" role="alert"></p><form id="form" class="panel" novalidate><div class="row"><label for="mode">Conversion direction<select id="mode"><option value="forward">Percent slope → degrees</option><option value="inverse">Degrees → percent slope</option></select></label><label for="value"><span id="valueLabel">Percent slope (P ≥ 0)</span><input id="value" value="12" inputmode="decimal" autocomplete="off"></label></div><div class="actions"><button>Calculate slope</button><button type="button" id="equal" class="secondary">Try 100%</button><button type="button" id="steep" class="secondary">Try 200%</button><button type="button" id="reset" class="secondary">Reset</button></div></form><section class="panel"><h2>Calculation record</h2><pre id="trace"></pre></section><details><summary>Scope and precision</summary><p>The schematic fixes horizontal run at 100 units; rise uses the same unit. Both legs are scaled together to fit. A very steep or shallow triangle can make one leg smaller than a screen pixel; the actual numbers remain authoritative.</p><p>Unsigned finite percent values, including those above 100%, are accepted. Inverse angles must be at least 0 and below 90°. Plain dot decimals or scientific notation are accepted; signs for negative inputs, blanks, nonfinite values, overflow, and ratios that collapse to exactly 90° at numeric precision are rejected. Results use JavaScript numeric precision; display is rounded to nine places, and inverse checks use the unrounded angle.</p><p>Original classroom schematic, not measured terrain or a construction, access, legal-grade, ramp, or hiking recommendation.</p></details><footer>Local session only · No network or saved progress. Keep maintained source records authoritative.</footer></main><script>const $=id=>document.getElementById(id);const esc=s=>String(s).replace(/[&<>"']/g,c=>({'&':'&amp;','<':'&lt;','>':'&gt;','"':'&quot;',"'":'&#39;'}[c]));

function parse(s){const t=s.trim();if(!t||! /^(?:[0-9]+(?:[.][0-9]*)?|[.][0-9]+)(?:[eE][+-]?[0-9]+)?$/.test(t))throw Error('Enter a nonnegative finite number; blank is missing.');const n=Number(t);if(n===0&&/[1-9]/.test(t.split(/[eE]/)[0]))throw Error('Input is too small to represent at numeric precision.');if(!Number.isFinite(n))throw Error('Value must be finite.');return n}function calculate(mode,raw){const n=parse(raw);let p,theta;if(mode==='forward'){p=n;theta=Math.atan(p/100)*180/Math.PI;if(theta>=90)throw Error('This ratio is too large to resolve below 90° at numeric precision.')}else if(mode==='inverse'){theta=n;if(theta>=90)throw Error('Inverse angle must be below 90°; 90° has no finite slope percent.');p=Math.tan(theta*Math.PI/180)*100;if(theta>0&&p===0)throw Error('Angle is too small to represent a nonzero slope at numeric precision.');}else throw Error('Choose a conversion direction.');if(p>0&&p/100===0)throw Error('Slope ratio is too small to represent at numeric precision.');const rise=p,ratio=p/100,check=Math.tan(theta*Math.PI/180)*100;if(!Number.isFinite(rise)||!Number.isFinite(check))throw Error('Result exceeds finite numeric range.');return {p,theta,ratio,rise,check}}
function degreeDisplay(theta){const rounded=theta.toFixed(9);if(theta>0&&Number(rounded)===0)return '<0.000000001°';if(theta<90&&Number(rounded)===90)return '<90° · within 0.000000001°';return rounded+'°'}
function clear(){$('result').hidden=true;$('trace').textContent='';$('error').textContent=''}function run(){try{const r=calculate($('mode').value,$('value').value);$('basis').textContent=String(r.p)+'% slope · horizontal run 100';$('angle').textContent=degreeDisplay(r.theta);$('ratio').textContent='Rise / horizontal run = '+r.ratio.toPrecision(10);$('inverse').textContent='Inverse check from unrounded angle: '+r.check.toPrecision(12)+'%';const scale=190/Math.max(100,r.rise),w=100*scale,h=r.rise*scale;$('triangle').setAttribute('d','M35 205 L'+(35+w)+' 205 L'+(35+w)+' '+(205-h)+' Z');$('riseLabel').textContent='Rise: '+r.rise.toPrecision(8)+' units';$('diagramNote').textContent='Original schematic · legs share scale '+scale.toPrecision(4)+' drawing units per length unit.';$('trace').textContent='Input: '+$('value').value+' ('+$('mode').value+')\nHorizontal run: 100 length units, positive\nImplied rise: '+r.rise+' same length units\nRatio P/100: '+r.ratio+'\nUnrounded degree angle: '+r.theta+'\natan(P/100) × 180/π\nInverse: tan(unrounded angle × π/180) × 100 = '+r.check+'%';$('result').hidden=false;$('error').textContent=''}catch(e){clear();$('error').textContent=e.message}}function sample(n){$('valueLabel').textContent='Percent slope (P ≥ 0)';$('mode').value='forward';$('value').value=String(n);$('value').setAttribute('aria-label','Percent slope P, nonnegative');run()}$('form').addEventListener('submit',e=>{e.preventDefault();run()});$('value').addEventListener('input',clear);$('mode').addEventListener('change',()=>{clear();$('value').value='';$('value').setAttribute('aria-label',$('mode').value==='forward'?'Percent slope P, nonnegative':'Angle in degrees, zero to less than ninety');$('valueLabel').textContent=$('mode').value==='forward'?'Percent slope (P ≥ 0)':'Angle (0° ≤ θ < 90°)'});$('equal').onclick=()=>sample(100);$('steep').onclick=()=>sample(200);$('reset').onclick=()=>{$('mode').value='forward';$('value').value='';$('valueLabel').textContent='Percent slope (P ≥ 0)';$('value').setAttribute('aria-label','Percent slope P, nonnegative');clear()};run();</script>
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