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  <title>Circular Loop Inductance Calculator | RF Toolbox</title>
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<h3>Circular Loop Inductance</h3>
<div class="tool-concept">
  <p>Calculates the self-inductance of a single-turn circular conductor loop using the Rosa/Neumann formula. This is the starting point for MRI surface coil design, tuning capacitor calculation, and any loop antenna.</p>
  <details style="margin-top:8px;">
  <summary style="cursor:pointer;font-size:11px;color:#AA77FF;font-weight:bold;letter-spacing:0.05em;text-transform:uppercase;user-select:none;">Equations &amp; Parameters ▸</summary>

<div style="background:#f0eeff;border-left:3px solid #AA77FF;padding:8px 12px 6px;border-radius:0 4px 4px 0;margin:6px 0 10px;font-size:12.5px;line-height:2.0;overflow-x:auto;">\(L = \mu_0 r \!\left[\ln\!\left(\tfrac{8r}{a}\right) - 2\right]\)</div>
<table style="font-size:12px;border-collapse:collapse;margin-top:6px;"><tr><td style="padding:3px 14px 3px 0;font-weight:bold;color:#5533aa;white-space:nowrap;vertical-align:top;">D</td><td style="padding:3px 0;">Loop diameter (mm) — centre-to-centre of wire.</td></tr><tr><td style="padding:3px 14px 3px 0;font-weight:bold;color:#5533aa;white-space:nowrap;vertical-align:top;">d</td><td style="padding:3px 0;">Wire (or tube) diameter (mm).</td></tr><tr><td style="padding:3px 14px 3px 0;font-weight:bold;color:#5533aa;white-space:nowrap;vertical-align:top;">L</td><td style="padding:3px 0;">Self-inductance. Increases with loop size; decreases with thicker wire.</td></tr></table>

<div style="margin-top:10px;padding-top:8px;border-top:1px solid #e0d8ff;"><div style="font-size:10px;font-weight:bold;color:#AA77FF;letter-spacing:0.07em;text-transform:uppercase;margin-bottom:4px;">Physical constants used</div><table style="font-size:12px;border-collapse:collapse;"><tr><td style="padding:3px 14px 3px 0;font-weight:bold;color:#5533aa;">c</td><td>Speed of light = 2.998×10⁸ m/s</td></tr>
          <tr><td style="padding:3px 14px 3px 0;font-weight:bold;color:#5533aa;">µ₀</td><td>Permeability of free space = 4π×10⁻⁷ H/m ≈ 1.2566×10⁻⁶ H/m</td></tr>
          <tr><td style="padding:3px 14px 3px 0;font-weight:bold;color:#5533aa;">ε₀</td><td>Permittivity of free space = 8.854×10⁻¹² F/m</td></tr></table></div>
<div style="margin-top:8px;padding-top:6px;border-top:1px solid #e0d8ff;font-size:11.5px;color:#666;"><span style="font-weight:bold;color:#AA77FF;">Reference: </span>M. Pozar, <em>Microwave Engineering</em>, 4th ed., §7.6 (Wiley, 2012)</div>
</details>
</div>
<div class="sec-lbl">Inputs</div>
<div class="inp-grid"><div class="inp-row"><label>Loop diameter, <span class="var">D</span></label><div class="inp-inline"><input type="text" id="D" placeholder="Enter mm"  data-tip="Loop diameter, measured centre-to-centre of the conductor. Larger D → more inductance."><span class="inp-units">mm</span></div><span class="inp-hint">Centre-to-centre of conductor</span></div><div class="inp-row"><label>Wire diameter, <span class="var">d</span></label><div class="inp-inline"><input type="text" id="d" placeholder="Enter mm"  data-tip="Conductor (wire or tube) diameter. Thicker wire lowers resistance and raises Q."><span class="inp-units">mm</span></div><span class="inp-hint">Conductor diameter (not radius)</span></div></div>
<div style="display:flex;gap:8px;align-items:center;margin:12px 0 6px;"><button class="calc-btn" id="btn">Calculate</button> <button class="example-btn" onclick="loadExample({&quot;D&quot;: &quot;100&quot;, &quot;d&quot;: &quot;1.5&quot;})" title="100 mm loop, 1.5 mm wire">Load Example</button></div>
<div id="error" class="err-msg" style="color:#c0392b;font-size:12px;margin-bottom:6px;min-height:16px;"></div>
<div class="sec-lbl">Results</div>
<div class="res-grid"><div class="res-card"><h4>Inductance</h4><div class="res-row"><span class="res-lbl">Self-inductance, L</span><span class="res-val " id="L">—</span></div></div></div>

<div class="sec-lbl">Diagram</div>
<div class="schematic-box"><div id="tool-diagram"></div></div>
<script>

function drawDiagram() {
  var Lv = document.getElementById('L') ? document.getElementById('L').textContent : '—';
  var Dv = document.getElementById('D') ? (parseFloat(document.getElementById('D').value)||0) : 0;
  var dv = document.getElementById('d') ? (parseFloat(document.getElementById('d').value)||0) : 0;
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  s+='<circle cx="'+cx+'" cy="'+cy+'" r="'+R+'" fill="none" stroke="#5533aa" stroke-width="'+Math.max(2,wireR)+'" stroke-linecap="round"/>';
  // Feed gap at right
  s+='<circle cx="'+(cx+R)+'" cy="'+cy+'" r="5" fill="white" stroke="#AA77FF" stroke-width="2"/>';
  s+='<circle cx="'+(cx+R)+'" cy="'+cy+'" r="1.5" fill="#AA77FF"/>';
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  s+='<line x1="'+(cx-R)+'" y1="'+cy+'" x2="'+(cx+R-8)+'" y2="'+cy+'" stroke="#888" stroke-width="1" stroke-dasharray="3,3"/>';
  s+='<polygon points="'+(cx-R)+','+cy+' '+(cx-R+7)+','+(cy-3)+' '+(cx-R+7)+','+(cy+3)+'" fill="#888"/>';
  s+='<polygon points="'+(cx+R-2)+','+cy+' '+(cx+R-9)+','+(cy-3)+' '+(cx+R-9)+','+(cy+3)+'" fill="#888"/>';
  s+='<text x="'+cx+'" y="'+(cy-8)+'" text-anchor="middle" font-size="10.5" fill="#888">D'+(Dv?' = '+Dv+' mm':'')+'</text>';
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    var xc2=cx-R*0.7, yc2=cy-R*0.7;
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    s+='<text x="'+(xc2-wireR-4)+'" y="'+(yc2+4)+'" text-anchor="end" font-size="9" fill="#888">d = '+dv+' mm</text>';
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  // Result
  s+='<text x="'+cx+'" y="'+(cy+R+22)+'" text-anchor="middle" font-size="12" fill="#5533aa" font-weight="bold">L = '+Lv+'</text>';
  s+='</svg>';
  document.getElementById('tool-diagram').innerHTML=s;
}

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