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  <title>Friis Equation Calculator — RF Link Power Calculator | RF Toolbox</title>
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<h3>Friis Transmission Equation</h3>
<div class="tool-concept">
  <p>The Friis equation gives the power received in a free-space radio link given transmit power, antenna gains, distance, and frequency. It assumes far-field, line-of-sight propagation with no atmospheric loss.</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;">\(P_r = P_t G_t G_r \!\left(\dfrac{\lambda}{4\pi d}\right)^{\!2}\)</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;">Pₜ</td><td style="padding:3px 0;">Transmit power (dBm).</td></tr><tr><td style="padding:3px 14px 3px 0;font-weight:bold;color:#5533aa;white-space:nowrap;vertical-align:top;">Gₜ, Gᵣ</td><td style="padding:3px 0;">Transmit and receive antenna gains (dBi). A half-wave dipole has 2.15 dBi.</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;">Link distance (m).</td></tr><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;">Carrier frequency. Longer wavelengths have less free-space path loss.</td></tr><tr><td style="padding:3px 14px 3px 0;font-weight:bold;color:#5533aa;white-space:nowrap;vertical-align:top;">FSPL</td><td style="padding:3px 0;">Free-space path loss = 20·log₁₀(4πd/λ) dB.</td></tr><tr><td style="padding:3px 14px 3px 0;font-weight:bold;color:#5533aa;white-space:nowrap;vertical-align:top;">Pᵣ</td><td style="padding:3px 0;">Received power = Pₜ + Gₜ + Gᵣ − FSPL (in dB arithmetic).</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>H. Friis, "A note on a simple transmission formula," <em>Proc. IRE</em> 34, 254 (1946)</div>
</details>
</div>
<div class="sec-lbl">Inputs</div>
<div class="inp-grid"><div class="inp-row"><label>Transmit power, <span class="var">Pₜ</span></label><div class="inp-inline"><input type="text" id="fr-pt" value="20"  data-tip="Transmit power in dBm. 0 dBm = 1 mW, 20 dBm = 100 mW, 30 dBm = 1 W."><span class="inp-units">dBm</span></div><span class="inp-hint">Typical WiFi: 20 dBm = 100 mW</span></div><div class="inp-row"><label>TX antenna gain, <span class="var">Gₜ</span></label><div class="inp-inline"><input type="text" id="fr-gt" value="2"  data-tip="TX antenna gain in dBi relative to an isotropic radiator. Half-wave dipole = 2.15 dBi."><span class="inp-units">dBi</span></div><span class="inp-hint">Isotropic = 0, dipole ≈ 2.15</span></div><div class="inp-row"><label>RX antenna gain, <span class="var">Gᵣ</span></label><div class="inp-inline"><input type="text" id="fr-gr" value="2"  data-tip="RX antenna gain in dBi. Same reference as Gₜ."><span class="inp-units">dBi</span></div></div><div class="inp-row"><label>Distance, <span class="var">d</span></label><div class="inp-inline"><input type="text" id="fr-d" placeholder="m"  data-tip="Free-space distance between antennas in metres. FSPL increases 6 dB per doubling."><span class="inp-units">m</span></div><span class="inp-hint">Straight-line distance</span></div><div class="inp-row"><label>Frequency, <span class="var">f</span></label><div class="inp-inline"><input type="text" id="fr-f" placeholder="value"  data-tip="Carrier frequency. Higher frequency → shorter wavelength → higher path loss."><select id="fr-fu"><option value="1e6">MHz</option><option value="1e9" selected>GHz</option></select></div></div></div>
<div style="display:flex;gap:8px;align-items:center;margin:12px 0 6px;"><button class="calc-btn" id="fr-btn">Calculate</button> <button class="example-btn" onclick="loadExample({&quot;fr-pt&quot;: &quot;20&quot;, &quot;fr-gt&quot;: &quot;2&quot;, &quot;fr-gr&quot;: &quot;2&quot;, &quot;fr-d&quot;: &quot;50&quot;, &quot;fr-f&quot;: &quot;2.4&quot;, &quot;fr-fu&quot;: &quot;1e9&quot;})" title="2.4 GHz Wi-Fi at 50 m, 20 dBm TX">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>Path</h4><div class="res-row"><span class="res-lbl">Free-space path loss (FSPL)</span><span class="res-val " id="fr-fspl">—</span></div></div><div class="res-card"><h4>Received Power</h4><div class="res-row"><span class="res-lbl">Pᵣ (dBm)</span><span class="res-val " id="fr-pr-dbm">—</span></div><div class="res-row"><span class="res-lbl">Pᵣ (watts)</span><span class="res-val " id="fr-pr-w">—</span></div></div></div>

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

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  s+='<text x="'+(pathX1+130)+'" y="'+(wy+12)+'" text-anchor="middle" font-size="10" fill="#aa6600">'+fspl+'</text>';
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  s+='<text x="'+(pathX2+45)+'" y="'+(wy-28)+'" text-anchor="middle" font-size="9" fill="#888">Gᵣ = '+gr+' dBi</text>';
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</script>
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