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  <title>Dipole Antenna Calculator — Length & Resonant Frequency | RF Toolbox</title>
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<h3>Dipole Antenna Calculator</h3>
<div class="tool-concept">
  <p>A thin half-wave dipole is the fundamental antenna reference. At resonance it has ≈73 Ω feed impedance and 2.15 dBi gain. Practical dipoles are slightly shorter than λ/2 (shortening factor k ≈ 0.95–0.98) to account for end effects.</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;">\(\ell_{arm} = \dfrac{k\lambda}{4} = \dfrac{kc}{4f}\)</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;">f</td><td style="padding:3px 0;">Resonant frequency. Sets λ and therefore physical length.</td></tr><tr><td style="padding:3px 14px 3px 0;font-weight:bold;color:#5533aa;white-space:nowrap;vertical-align:top;">k</td><td style="padding:3px 0;">Shortening factor (0–1). Accounts for finite wire diameter; typically 0.95–0.98.</td></tr><tr><td style="padding:3px 14px 3px 0;font-weight:bold;color:#5533aa;white-space:nowrap;vertical-align:top;">Arm</td><td style="padding:3px 0;">One arm of the dipole (total length = 2 × arm).</td></tr><tr><td style="padding:3px 14px 3px 0;font-weight:bold;color:#5533aa;white-space:nowrap;vertical-align:top;">λ/2</td><td style="padding:3px 0;">Free-space half-wavelength.</td></tr><tr><td style="padding:3px 14px 3px 0;font-weight:bold;color:#5533aa;white-space:nowrap;vertical-align:top;">Monopole</td><td style="padding:3px 0;">Quarter-wave monopole over ground = half-arm length.</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>C. Balanis, <em>Antenna Theory</em>, 3rd ed., §4.4 (Wiley, 2005)</div>
</details>
</div>
<div class="sec-lbl">Inputs</div>
<div class="inp-grid"><div class="inp-row"><label>Frequency, <span class="var">f</span></label><div class="inp-inline"><input type="text" id="dp-f" placeholder="value"  data-tip="Resonant frequency. Sets λ and therefore the physical arm length."><select id="dp-fu"><option value="1e3">kHz</option><option value="1e6" selected>MHz</option><option value="1e9">GHz</option></select></div></div><div class="inp-row"><label>Shortening factor, <span class="var">k</span></label><div class="inp-inline"><input type="text" id="dp-k" value="0.97"  data-tip="Shortening factor accounts for end effects. Thin wire: 0.96–0.98, fat element: down to 0.92."></div><span class="inp-hint">0.95–0.98 for thin wire dipole</span></div></div>
<div style="display:flex;gap:8px;align-items:center;margin:12px 0 6px;"><button class="calc-btn" id="dp-btn">Calculate</button> <button class="example-btn" onclick="loadExample({&quot;dp-f&quot;: &quot;433&quot;, &quot;dp-fu&quot;: &quot;1e6&quot;, &quot;dp-k&quot;: &quot;0.97&quot;})" title="433 MHz ISM band dipole">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>Dimensions</h4><div class="res-row"><span class="res-lbl">Arm length</span><span class="res-val " id="dp-arm">—</span></div><div class="res-row"><span class="res-lbl">Total dipole (λ/2)</span><span class="res-val " id="dp-half">—</span></div><div class="res-row"><span class="res-lbl">Monopole length (λ/4)</span><span class="res-val " id="dp-mono">—</span></div></div><div class="res-card"><h4>Reference</h4><div class="res-row"><span class="res-lbl">Free-space wavelength, λ</span><span class="res-val " id="dp-lam">—</span></div></div></div>

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

function drawDiagram() {
  var armEl = document.getElementById('dp-arm'); var arm = armEl ? armEl.textContent : '—';
  var lamEl = document.getElementById('dp-lam'); var lam = lamEl ? lamEl.textContent : '—';
  var W=560,H=160,cx=W/2,cy=76,armLen=58;
  var s='<svg viewBox="0 0 '+W+' '+H+'" width="'+W+'" height="'+H+'" xmlns="http://www.w3.org/2000/svg" style="font-family:monospace;max-width:100%;">';
  s+='<rect width="'+W+'" height="'+H+'" fill="#faf9ff" rx="4"/>';
  // Radiation pattern (simple ellipses for visual)
  s+='<ellipse cx="'+cx+'" cy="'+cy+'" rx="'+(armLen*0.8)+'" ry="'+(armLen*0.45)+'" fill="none" stroke="#AA77FF" stroke-width="1" opacity="0.4" stroke-dasharray="4,3"/>';
  s+='<ellipse cx="'+cx+'" cy="'+cy+'" rx="'+(armLen*0.5)+'" ry="'+(armLen*0.28)+'" fill="rgba(170,119,255,0.07)" stroke="#AA77FF" stroke-width="1" opacity="0.5" stroke-dasharray="3,3"/>';
  // Dipole arms (vertical)
  s+='<line x1="'+cx+'" y1="'+(cy-armLen)+'" x2="'+cx+'" y2="'+(cy-8)+'" stroke="#5533aa" stroke-width="4" stroke-linecap="round"/>';
  s+='<line x1="'+cx+'" y1="'+(cy+8)+'" x2="'+cx+'" y2="'+(cy+armLen)+'" stroke="#5533aa" stroke-width="4" stroke-linecap="round"/>';
  // Feed gap
  s+='<rect x="'+(cx-6)+'" y="'+(cy-8)+'" width="12" height="16" fill="white" stroke="#AA77FF" stroke-width="2" rx="2"/>';
  s+='<text x="'+(cx+14)+'" y="'+(cy+4)+'" font-size="10" fill="#AA77FF">feed</text>';
  // Arm length annotation
  s+='<line x1="'+(cx+20)+'" y1="'+(cy-armLen)+'" x2="'+(cx+20)+'" y2="'+(cy-8)+'" stroke="#888" stroke-width="1" stroke-dasharray="2,3"/>';
  s+='<line x1="'+(cx+16)+'" y1="'+(cy-armLen)+'" x2="'+(cx+24)+'" y2="'+(cy-armLen)+'" stroke="#888" stroke-width="1.2"/>';
  s+='<line x1="'+(cx+16)+'" y1="'+(cy-8)+'" x2="'+(cx+24)+'" y2="'+(cy-8)+'" stroke="#888" stroke-width="1.2"/>';
  s+='<text x="'+(cx+32)+'" y="'+(cy-armLen/2+4)+'" font-size="10.5" fill="#888">λ/4 = '+arm+'</text>';
  // λ label
  s+='<text x="'+W/2+'" y="150" text-anchor="middle" font-size="11" fill="#888">λ = '+lam+'  |  total dipole = 2 × λ/4</text>';
  s+='</svg>';
  document.getElementById('tool-diagram').innerHTML=s;
}

</script>
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