{"id":25017,"date":"2026-10-30T01:59:14","date_gmt":"2026-10-30T01:59:14","guid":{"rendered":"https:\/\/www.mechstream.com\/?p=25017"},"modified":"2026-10-30T01:59:17","modified_gmt":"2026-10-30T01:59:17","slug":"cutting-force-estimator-calculator","status":"publish","type":"post","link":"https:\/\/www.mechstream.com\/es\/cutting-force-estimator-calculator\/","title":{"rendered":"Cutting Force Estimator Calculator"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">The Cutting Force Estimator Calculator helps engineers and machining professionals estimate the cutting force required for metal machining operations. By selecting the workpiece material and entering the specific cutting force, depth of cut, and feed rate, users can quickly calculate the estimated cutting force in Newtons (N) and kilonewtons (kN). This tool supports machine selection, cutting tool evaluation, machining parameter optimization, and improved production efficiency.<\/p>\n\n\n\n<iframe class=\"cfe-frame skip-lazy no-lazyload\" data-no-lazy=\"1\" data-skip-lazy=\"1\" title=\"Cutting Force Estimator\" scrolling=\"no\" style=\"display:block !important;width:100% !important;max-width:1000px !important;height:620px;border:0 !important;margin:0 auto !important;padding:0 !important;overflow:hidden;background:transparent;float:none !important\" srcdoc=\"&lt;!DOCTYPE html&gt;&#10;&lt;html lang=&quot;en&quot;&gt;&#10;&lt;head&gt;&#10;&lt;meta charset=&quot;UTF-8&quot;&gt;&#10;&lt;meta name=&quot;viewport&quot; content=&quot;width=device-width, initial-scale=1&quot;&gt;&#10;&lt;title&gt;Cutting Force Estimator&lt;\/title&gt;&#10;&lt;style&gt;&#10;\/* =====================================================================&#10;   Cutting Force Estimator \u2014 all selectors scoped under .cfe-root&#10;   so the calculator never 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28px;border-radius:0}&#10;  .cfe-root .cfe-card{padding:16px}&#10;  .cfe-root .cfe-row{grid-template-columns:minmax(0,1fr)}&#10;  .cfe-root .cfe-bar-row{grid-template-columns:minmax(0,1fr) 84px;gap:4px 10px}&#10;  .cfe-root .cfe-bar-label{grid-column:1 \/ -1}&#10;}&#10;@media (prefers-reduced-motion:reduce){&#10;  .cfe-root *{transition:none !important}&#10;}&#10;html,body{margin:0;padding:0;background:transparent}&#10;&lt;\/style&gt;&#10;&lt;\/head&gt;&#10;&lt;body&gt;&#10;&#10;&lt;div class=&quot;cfe-root&quot; id=&quot;cfe-app&quot;&gt;&#10;  &lt;div class=&quot;cfe-stack&quot;&gt;&#10;&#10;    &lt;!-- ================= INPUT PANEL ================= --&gt;&#10;    &lt;section class=&quot;cfe-card&quot; aria-labelledby=&quot;cfe-inputs-title&quot;&gt;&#10;      &lt;div class=&quot;cfe-card-title&quot;&gt;&lt;h2 id=&quot;cfe-inputs-title&quot;&gt;Calculation Inputs&lt;\/h2&gt;&lt;\/div&gt;&#10;&#10;      &lt;form id=&quot;cfe-form&quot; novalidate autocomplete=&quot;off&quot;&gt;&#10;        &lt;div class=&quot;cfe-row&quot;&gt;&#10;          &lt;!-- Workpiece material --&gt;&#10;          &lt;div class=&quot;cfe-field&quot;&gt;&#10;            &lt;label for=&quot;cfe-mat&quot;&gt;Workpiece Material&lt;\/label&gt;&#10;            &lt;select id=&quot;cfe-mat&quot; class=&quot;cfe-select&quot; aria-describedby=&quot;cfe-mat-help&quot;&gt;&#10;              &lt;option value=&quot;mild&quot;&gt;Mild Steel&lt;\/option&gt;&#10;              &lt;option value=&quot;carbon&quot;&gt;Carbon Steel&lt;\/option&gt;&#10;              &lt;option value=&quot;alloy&quot;&gt;Alloy Steel&lt;\/option&gt;&#10;              &lt;option value=&quot;stainless&quot;&gt;Stainless Steel&lt;\/option&gt;&#10;              &lt;option value=&quot;aluminum&quot;&gt;Aluminum Alloy&lt;\/option&gt;&#10;              &lt;option value=&quot;copper&quot;&gt;Copper&lt;\/option&gt;&#10;              &lt;option value=&quot;brass&quot;&gt;Brass&lt;\/option&gt;&#10;              &lt;option value=&quot;castiron&quot;&gt;Cast Iron&lt;\/option&gt;&#10;              &lt;option value=&quot;titanium&quot;&gt;Titanium Alloy&lt;\/option&gt;&#10;              &lt;option value=&quot;custom&quot;&gt;Custom Material&lt;\/option&gt;&#10;            &lt;\/select&gt;&#10;            &lt;p class=&quot;cfe-help&quot; id=&quot;cfe-mat-help&quot;&gt;Selecting a material fills in its reference kc value.&lt;\/p&gt;&#10;          &lt;\/div&gt;&#10;&#10;          &lt;!-- Specific cutting force --&gt;&#10;          &lt;div class=&quot;cfe-field&quot;&gt;&#10;            &lt;label for=&quot;cfe-kc&quot;&gt;Specific Cutting Force (kc)&lt;\/label&gt;&#10;            &lt;div class=&quot;cfe-suffix&quot;&gt;&#10;              &lt;input id=&quot;cfe-kc&quot; class=&quot;cfe-input&quot; type=&quot;text&quot; inputmode=&quot;decimal&quot; aria-describedby=&quot;cfe-kc-err cfe-kc-help&quot;&gt;&#10;              &lt;span class=&quot;cfe-suffix-u&quot; aria-hidden=&quot;true&quot;&gt;N\/mm\u00b2&lt;\/span&gt;&#10;            &lt;\/div&gt;&#10;            &lt;p class=&quot;cfe-err&quot; id=&quot;cfe-kc-err&quot; hidden&gt;&lt;\/p&gt;&#10;            &lt;p class=&quot;cfe-help&quot; id=&quot;cfe-kc-help&quot;&gt;Approximate force to remove a unit cross-sectional area of material.&lt;\/p&gt;&#10;          &lt;\/div&gt;&#10;&#10;          &lt;!-- Depth of cut --&gt;&#10;          &lt;div class=&quot;cfe-field&quot;&gt;&#10;            &lt;label for=&quot;cfe-ap&quot;&gt;Depth of Cut (ap)&lt;\/label&gt;&#10;            &lt;div class=&quot;cfe-suffix&quot;&gt;&#10;              &lt;input id=&quot;cfe-ap&quot; class=&quot;cfe-input&quot; type=&quot;text&quot; inputmode=&quot;decimal&quot; aria-describedby=&quot;cfe-ap-err cfe-ap-help&quot;&gt;&#10;              &lt;span class=&quot;cfe-suffix-u&quot; aria-hidden=&quot;true&quot;&gt;mm&lt;\/span&gt;&#10;            &lt;\/div&gt;&#10;            &lt;p class=&quot;cfe-err&quot; id=&quot;cfe-ap-err&quot; hidden&gt;&lt;\/p&gt;&#10;            &lt;p class=&quot;cfe-help&quot; id=&quot;cfe-ap-help&quot;&gt;Depth of material removed in one cutting pass.&lt;\/p&gt;&#10;          &lt;\/div&gt;&#10;&#10;          &lt;!-- Feed rate --&gt;&#10;          &lt;div class=&quot;cfe-field&quot;&gt;&#10;            &lt;label for=&quot;cfe-f&quot;&gt;Feed Rate (f)&lt;\/label&gt;&#10;            &lt;div class=&quot;cfe-suffix&quot;&gt;&#10;              &lt;input id=&quot;cfe-f&quot; class=&quot;cfe-input&quot; type=&quot;text&quot; inputmode=&quot;decimal&quot; aria-describedby=&quot;cfe-f-err cfe-f-help&quot;&gt;&#10;              &lt;span class=&quot;cfe-suffix-u&quot; aria-hidden=&quot;true&quot;&gt;mm\/rev&lt;\/span&gt;&#10;            &lt;\/div&gt;&#10;            &lt;p class=&quot;cfe-err&quot; id=&quot;cfe-f-err&quot; hidden&gt;&lt;\/p&gt;&#10;            &lt;p class=&quot;cfe-help&quot; id=&quot;cfe-f-help&quot;&gt;Tool advance per revolution of the workpiece.&lt;\/p&gt;&#10;          &lt;\/div&gt;&#10;&#10;          &lt;!-- Correction factor --&gt;&#10;          &lt;div class=&quot;cfe-field&quot;&gt;&#10;            &lt;label for=&quot;cfe-k&quot;&gt;Cutting Force Correction Factor (K)&lt;\/label&gt;&#10;            &lt;input id=&quot;cfe-k&quot; class=&quot;cfe-input&quot; type=&quot;text&quot; inputmode=&quot;decimal&quot; aria-describedby=&quot;cfe-k-err cfe-k-help&quot;&gt;&#10;            &lt;p class=&quot;cfe-err&quot; id=&quot;cfe-k-err&quot; hidden&gt;&lt;\/p&gt;&#10;            &lt;p class=&quot;cfe-help&quot; id=&quot;cfe-k-help&quot;&gt;Accounts for tool geometry, wear and machining conditions (0.5\u20132.0).&lt;\/p&gt;&#10;          &lt;\/div&gt;&#10;        &lt;\/div&gt;&#10;&#10;        &lt;div class=&quot;cfe-calc-wrap&quot;&gt;&#10;          &lt;button type=&quot;submit&quot; class=&quot;cfe-btn&quot; id=&quot;cfe-btn-calc&quot;&gt;Calculate&lt;\/button&gt;&#10;        &lt;\/div&gt;&#10;      &lt;\/form&gt;&#10;    &lt;\/section&gt;&#10;&#10;    &lt;!-- ================= RESULTS PANEL ================= --&gt;&#10;    &lt;section class=&quot;cfe-card&quot; aria-labelledby=&quot;cfe-results-title&quot; id=&quot;cfe-results&quot; tabindex=&quot;-1&quot; hidden&gt;&#10;      &lt;div class=&quot;cfe-card-title&quot;&gt;&lt;h2 id=&quot;cfe-results-title&quot;&gt;Results&lt;\/h2&gt;&lt;\/div&gt;&#10;&#10;      &lt;div class=&quot;cfe-alert&quot; id=&quot;cfe-error&quot; role=&quot;alert&quot; hidden&gt;&lt;\/div&gt;&#10;&#10;      &lt;div id=&quot;cfe-result-body&quot; aria-live=&quot;polite&quot;&gt;&#10;        &lt;div class=&quot;cfe-rgrid&quot;&gt;&#10;          &lt;div class=&quot;cfe-rcard cfe-hl&quot;&gt;&#10;            &lt;span class=&quot;cfe-rcard-label&quot;&gt;Estimated Cutting Force (Fc)&lt;\/span&gt;&#10;            &lt;div class=&quot;cfe-rcard-value&quot;&gt;&lt;span id=&quot;cfe-r-fc&quot;&gt;&lt;\/span&gt;&lt;span class=&quot;cfe-rcard-unit&quot;&gt;N&lt;\/span&gt;&lt;\/div&gt;&#10;            &lt;div class=&quot;cfe-rcard-sub&quot; id=&quot;cfe-r-fc-sub&quot;&gt;&lt;\/div&gt;&#10;          &lt;\/div&gt;&#10;          &lt;div class=&quot;cfe-rcard&quot;&gt;&#10;            &lt;span class=&quot;cfe-rcard-label&quot;&gt;Cutting Force&lt;\/span&gt;&#10;            &lt;div class=&quot;cfe-rcard-value&quot;&gt;&lt;span id=&quot;cfe-r-kn&quot;&gt;&lt;\/span&gt;&lt;span class=&quot;cfe-rcard-unit&quot;&gt;kN&lt;\/span&gt;&lt;\/div&gt;&#10;            &lt;div class=&quot;cfe-rcard-sub&quot;&gt;Fc \u00f7 1000&lt;\/div&gt;&#10;          &lt;\/div&gt;&#10;          &lt;div class=&quot;cfe-rcard&quot;&gt;&#10;            &lt;span class=&quot;cfe-rcard-label&quot;&gt;Uncut Chip Area (A)&lt;\/span&gt;&#10;            &lt;div class=&quot;cfe-rcard-value&quot;&gt;&lt;span id=&quot;cfe-r-a&quot;&gt;&lt;\/span&gt;&lt;span class=&quot;cfe-rcard-unit&quot;&gt;mm\u00b2&lt;\/span&gt;&lt;\/div&gt;&#10;            &lt;div class=&quot;cfe-rcard-sub&quot;&gt;A = ap \u00d7 f&lt;\/div&gt;&#10;          &lt;\/div&gt;&#10;          &lt;div class=&quot;cfe-rcard&quot;&gt;&#10;            &lt;span class=&quot;cfe-rcard-label&quot;&gt;Specific Cutting Force (kc)&lt;\/span&gt;&#10;            &lt;div class=&quot;cfe-rcard-value&quot;&gt;&lt;span id=&quot;cfe-r-kc&quot;&gt;&lt;\/span&gt;&lt;span class=&quot;cfe-rcard-unit&quot;&gt;N\/mm\u00b2&lt;\/span&gt;&lt;\/div&gt;&#10;            &lt;div class=&quot;cfe-rcard-sub&quot; id=&quot;cfe-r-kc-sub&quot;&gt;&lt;\/div&gt;&#10;          &lt;\/div&gt;&#10;        &lt;\/div&gt;&#10;&#10;        &lt;!-- Visual comparison: effect of changing ap or f --&gt;&#10;        &lt;div class=&quot;cfe-cmp&quot;&gt;&#10;          &lt;h3&gt;How Depth of Cut and Feed Rate Affect Cutting Force&lt;\/h3&gt;&#10;          &lt;p class=&quot;cfe-cmp-intro&quot;&gt;Estimated force if you change one parameter while keeping all others the same.&lt;\/p&gt;&#10;          &lt;div id=&quot;cfe-bars&quot;&gt;&lt;\/div&gt;&#10;        &lt;\/div&gt;&#10;&#10;        &lt;div class=&quot;cfe-explain&quot;&gt;&#10;          &lt;strong&gt;Interpreting the result.&lt;\/strong&gt; The estimated cutting force increases when:&#10;          &lt;ul&gt;&#10;            &lt;li&gt;the depth of cut (ap) increases;&lt;\/li&gt;&#10;            &lt;li&gt;the feed rate (f) increases;&lt;\/li&gt;&#10;            &lt;li&gt;the workpiece material has a higher specific cutting force (kc);&lt;\/li&gt;&#10;            &lt;li&gt;machining conditions require a higher correction factor (K).&lt;\/li&gt;&#10;          &lt;\/ul&gt;&#10;        &lt;\/div&gt;&#10;&#10;        &lt;p class=&quot;cfe-note&quot;&gt;This is a simplified estimate of the main cutting force in turning. kc values are approximate reference values, not material constants. Actual forces vary with tool geometry, tool wear, cutting speed, coolant and chip thickness. Use these results for preliminary machine and tool selection only.&lt;\/p&gt;&#10;&#10;        &lt;details class=&quot;cfe-details&quot;&gt;&#10;          &lt;summary&gt;Calculation Details&lt;\/summary&gt;&#10;          &lt;div class=&quot;cfe-formula&quot;&gt;&#10;            &lt;div class=&quot;cfe-formula-block&quot;&gt;&#10;              &lt;span class=&quot;cfe-formula-label&quot;&gt;Uncut chip cross-sectional area&lt;\/span&gt;&#10;              &lt;p class=&quot;cfe-formula-main&quot;&gt;A = ap \u00d7 f&lt;\/p&gt;&#10;              &lt;p class=&quot;cfe-formula-sub&quot; id=&quot;cfe-d-a&quot;&gt;&lt;\/p&gt;&#10;            &lt;\/div&gt;&#10;            &lt;div class=&quot;cfe-formula-block&quot;&gt;&#10;              &lt;span class=&quot;cfe-formula-label&quot;&gt;Main cutting force&lt;\/span&gt;&#10;              &lt;p class=&quot;cfe-formula-main&quot;&gt;Fc = kc \u00d7 ap \u00d7 f \u00d7 K = kc \u00d7 A \u00d7 K&lt;\/p&gt;&#10;              &lt;p class=&quot;cfe-formula-sub&quot; id=&quot;cfe-d-fc&quot;&gt;&lt;\/p&gt;&#10;            &lt;\/div&gt;&#10;            &lt;div class=&quot;cfe-formula-block&quot;&gt;&#10;              &lt;span class=&quot;cfe-formula-label&quot;&gt;Conversion to kilonewtons&lt;\/span&gt;&#10;              &lt;p class=&quot;cfe-formula-main&quot;&gt;Fc (kN) = Fc (N) \/ 1000&lt;\/p&gt;&#10;              &lt;p class=&quot;cfe-formula-sub&quot; id=&quot;cfe-d-kn&quot;&gt;&lt;\/p&gt;&#10;            &lt;\/div&gt;&#10;          &lt;\/div&gt;&#10;        &lt;\/details&gt;&#10;      &lt;\/div&gt;&#10;    &lt;\/section&gt;&#10;&#10;  &lt;\/div&gt;&#10;&lt;\/div&gt;&#10;&#10;&lt;script&gt;&#10;\/* =====================================================================&#10;   Cutting Force Estimator \u2014 Vanilla JavaScript (no globals)&#10;   Units: kc in N\/mm\u00b2, ap in mm, f in mm\/rev, A in mm\u00b2, Fc in N.&#10;   ===================================================================== *\/&#10;(function () {&#10;  &#x27;use strict&#x27;;&#10;&#10;  var root = document.getElementById(&#x27;cfe-app&#x27;);&#10;  if (!root || root.getAttribute(&#x27;data-cfe-ready&#x27;) === &#x27;1&#x27;) return;&#10;  root.setAttribute(&#x27;data-cfe-ready&#x27;, &#x27;1&#x27;);&#10;&#10;  function $(id) { return document.getElementById(id); }&#10;&#10;  \/* ---------- 1. Reference data ---------- *\/&#10;  \/\/ Approximate reference specific cutting force kc (N\/mm\u00b2) \u2014 estimation values, not universal constants&#10;  var MATERIALS = {&#10;    mild:      { name: &#x27;Mild Steel&#x27;,      kc: 1800 },&#10;    carbon:    { name: &#x27;Carbon Steel&#x27;,    kc: 2200 },&#10;    alloy:     { name: &#x27;Alloy Steel&#x27;,     kc: 2500 },&#10;    stainless: { name: &#x27;Stainless Steel&#x27;, kc: 2400 },&#10;    aluminum:  { name: &#x27;Aluminum Alloy&#x27;,  kc: 700 },&#10;    copper:    { name: &#x27;Copper&#x27;,          kc: 1000 },&#10;    brass:     { name: &#x27;Brass&#x27;,           kc: 800 },&#10;    castiron:  { name: &#x27;Cast Iron&#x27;,       kc: 1500 },&#10;    titanium:  { name: &#x27;Titanium Alloy&#x27;,  kc: 2500 },&#10;    custom:    { name: &#x27;Custom Material&#x27;, kc: null }&#10;  };&#10;&#10;  var DEFAULTS = { mat: &#x27;mild&#x27;, ap: &#x27;2&#x27;, f: &#x27;0.2&#x27;, k: &#x27;1.0&#x27; };&#10;  var K_MIN = 0.5, K_MAX = 2.0;&#10;&#10;  \/* ---------- 2. Parsing &amp; formatting ---------- *\/&#10;  \/** Accepts &quot;1,5&quot; (decimal comma), &quot;1,000.5&quot;, and scientific notation. *\/&#10;  function parseNum(raw) {&#10;    var s = String(raw == null ? &#x27;&#x27; : raw).trim().replace(\/\\s+\/g, &#x27;&#x27;);&#10;    if (s === &#x27;&#x27;) return { empty: true, ok: false };&#10;    if (\/^[+-]?\\d{1,3}(,\\d{3})+(\\.\\d+)?$\/.test(s)) s = s.replace(\/,\/g, &#x27;&#x27;);&#10;    else if (\/^[+-]?\\d*,\\d+$\/.test(s)) s = s.replace(&#x27;,&#x27;, &#x27;.&#x27;);&#10;    if (!\/^[+-]?(\\d+\\.?\\d*|\\.\\d+)(e[+-]?\\d+)?$\/i.test(s)) return { empty: false, ok: false };&#10;    var n = Number(s);&#10;    if (!isFinite(n)) return { empty: false, ok: false };&#10;    return { empty: false, ok: true, n: n };&#10;  }&#10;&#10;  \/** Two-decimal display; falls back to 3 significant figures when the value would round to 0. *\/&#10;  function fx(n, d) {&#10;    if (d == null) d = 2;&#10;    if (typeof n !== &#x27;number&#x27; || !isFinite(n)) return &#x27;\u2014&#x27;;&#10;    if (n !== 0 &amp;&amp; Math.abs(n) &lt; 0.5 * Math.pow(10, -d)) return Number(n.toPrecision(3)).toString();&#10;    return n.toLocaleString(&#x27;en-US&#x27;, { minimumFractionDigits: d, maximumFractionDigits: d });&#10;  }&#10;  \/** Compact display of an input value (no forced decimals). *\/&#10;  function g(n) {&#10;    if (typeof n !== &#x27;number&#x27; || !isFinite(n)) return &#x27;\u2014&#x27;;&#10;    return Number(n.toPrecision(8)).toLocaleString(&#x27;en-US&#x27;, { maximumFractionDigits: 10 });&#10;  }&#10;  function esc(s) {&#10;    return String(s).replace(\/[&amp;&lt;&gt;&quot;&#x27;]\/g, function (c) {&#10;      return { &#x27;&amp;&#x27;: &#x27;&amp;amp;&#x27;, &#x27;&lt;&#x27;: &#x27;&amp;lt;&#x27;, &#x27;&gt;&#x27;: &#x27;&amp;gt;&#x27;, &#x27;&quot;&#x27;: &#x27;&amp;quot;&#x27;, &quot;&#x27;&quot;: &#x27;&amp;#39;&#x27; }[c];&#10;    });&#10;  }&#10;&#10;  \/* ---------- 3. Validation ---------- *\/&#10;  var KEYS = [&#x27;kc&#x27;, &#x27;ap&#x27;, &#x27;f&#x27;, &#x27;k&#x27;];&#10;  var LABEL = { kc: &#x27;Specific cutting force (kc)&#x27;, ap: &#x27;Depth of cut (ap)&#x27;, f: &#x27;Feed rate (f)&#x27;, k: &#x27;Correction factor (K)&#x27; };&#10;&#10;  function setErr(key, msg) {&#10;    var el = $(&#x27;cfe-&#x27; + key), er = $(&#x27;cfe-&#x27; + key + &#x27;-err&#x27;);&#10;    if (msg) {&#10;      el.classList.add(&#x27;cfe-invalid&#x27;); el.setAttribute(&#x27;aria-invalid&#x27;, &#x27;true&#x27;);&#10;      er.textContent = msg; er.hidden = false;&#10;    } else {&#10;      el.classList.remove(&#x27;cfe-invalid&#x27;); el.removeAttribute(&#x27;aria-invalid&#x27;);&#10;      er.textContent = &#x27;&#x27;; er.hidden = true;&#10;    }&#10;  }&#10;  function clearAllErrors() { KEYS.forEach(function (k) { setErr(k, null); }); }&#10;&#10;  \/** Returns an error message for a field, or null when valid. *\/&#10;  function check(key) {&#10;    var p = parseNum($(&#x27;cfe-&#x27; + key).value);&#10;    if (p.empty) {&#10;      if (key === &#x27;kc&#x27; &amp;&amp; $(&#x27;cfe-mat&#x27;).value === &#x27;custom&#x27;) return &#x27;Enter a specific cutting force (kc) for the custom material.&#x27;;&#10;      return LABEL[key] + &#x27; is required.&#x27;;&#10;    }&#10;    if (!p.ok) return LABEL[key] + &#x27; must be a valid number.&#x27;;&#10;    if (p.n &lt; 0) return LABEL[key] + &#x27; cannot be negative.&#x27;;&#10;    if (p.n === 0) return LABEL[key] + &#x27; must be greater than zero.&#x27;;&#10;    if (key === &#x27;k&#x27; &amp;&amp; (p.n &lt; K_MIN || p.n &gt; K_MAX)) return &#x27;Correction factor (K) must be between 0.5 and 2.0.&#x27;;&#10;    return null;&#10;  }&#10;  function read(key, errs) {&#10;    var msg = check(key);&#10;    setErr(key, msg);&#10;    if (msg) { errs.push(msg); return null; }&#10;    return parseNum($(&#x27;cfe-&#x27; + key).value).n;&#10;  }&#10;&#10;  \/* ---------- 4. Calculation ---------- *\/&#10;  \/**&#10;   * Main cutting force for turning:&#10;   *   A  = ap \u00d7 f              (uncut chip cross-section, mm\u00b2)&#10;   *   Fc = kc \u00d7 A \u00d7 K          (N)  \u2014 equivalently Fc = kc \u00d7 ap \u00d7 f \u00d7 K&#10;   *   Fc(kN) = Fc(N) \/ 1000&#10;   *\/&#10;  function cuttingForce(kc, ap, f, K) { return kc * ap * f * K; }&#10;&#10;  function compute() {&#10;    var errs = [];&#10;    clearAllErrors();&#10;    var kc = read(&#x27;kc&#x27;, errs), ap = read(&#x27;ap&#x27;, errs), f = read(&#x27;f&#x27;, errs), K = read(&#x27;k&#x27;, errs);&#10;    if (errs.length) { showErrors(errs); return false; }&#10;&#10;    var A = ap * f;                       \/\/ chip cross-sectional area, mm\u00b2&#10;    var Fc = cuttingForce(kc, ap, f, K);  \/\/ N&#10;    var FcKN = Fc \/ 1000;                 \/\/ kN&#10;&#10;    if (!isFinite(A) || !isFinite(Fc)) {&#10;      showErrors([&#x27;The result is outside the numeric range that can be represented. Check the magnitude of your inputs.&#x27;]);&#10;      return false;&#10;    }&#10;&#10;    render({ kc: kc, ap: ap, f: f, K: K, A: A, Fc: Fc, FcKN: FcKN, mat: $(&#x27;cfe-mat&#x27;).value });&#10;    return true;&#10;  }&#10;&#10;  \/* ---------- 5. Rendering ---------- *\/&#10;  function showErrors(errs) {&#10;    var box = $(&#x27;cfe-error&#x27;);&#10;    box.innerHTML = &#x27;&lt;strong&gt;Please correct the following input&#x27; + (errs.length &gt; 1 ? &#x27;s&#x27; : &#x27;&#x27;) + &#x27;:&lt;\/strong&gt;&lt;ul&gt;&#x27; +&#10;      errs.map(function (e) { return &#x27;&lt;li&gt;&#x27; + esc(e) + &#x27;&lt;\/li&gt;&#x27;; }).join(&#x27;&#x27;) + &#x27;&lt;\/ul&gt;&#x27;;&#10;    box.hidden = false;&#10;    $(&#x27;cfe-result-body&#x27;).hidden = true;&#10;  }&#10;&#10;  \/** Sensitivity bars: Fc when ap or f is scaled, others held constant (Fc is linear in both). *\/&#10;  function renderBars(R) {&#10;    var rows = [&#10;      { label: &#x27;ap \u00d7 0.5 (&#x27; + g(R.ap * 0.5) + &#x27; mm)&#x27;,     fc: cuttingForce(R.kc, R.ap * 0.5, R.f, R.K) },&#10;      { label: &#x27;f \u00d7 0.5 (&#x27; + g(R.f * 0.5) + &#x27; mm\/rev)&#x27;,   fc: cuttingForce(R.kc, R.ap, R.f * 0.5, R.K) },&#10;      { label: &#x27;Current settings&#x27;,                          fc: R.Fc, cur: true },&#10;      { label: &#x27;ap \u00d7 1.5 (&#x27; + g(R.ap * 1.5) + &#x27; mm)&#x27;,     fc: cuttingForce(R.kc, R.ap * 1.5, R.f, R.K) },&#10;      { label: &#x27;f \u00d7 1.5 (&#x27; + g(R.f * 1.5) + &#x27; mm\/rev)&#x27;,   fc: cuttingForce(R.kc, R.ap, R.f * 1.5, R.K) },&#10;      { label: &#x27;ap \u00d7 2 (&#x27; + g(R.ap * 2) + &#x27; mm)&#x27;,         fc: cuttingForce(R.kc, R.ap * 2, R.f, R.K) },&#10;      { label: &#x27;f \u00d7 2 (&#x27; + g(R.f * 2) + &#x27; mm\/rev)&#x27;,       fc: cuttingForce(R.kc, R.ap, R.f * 2, R.K) },&#10;      { label: &#x27;ap \u00d7 2 and f \u00d7 2&#x27;,                          fc: cuttingForce(R.kc, R.ap * 2, R.f * 2, R.K) }&#10;    ];&#10;    var max = 0;&#10;    rows.forEach(function (r) { if (r.fc &gt; max) max = r.fc; });&#10;    $(&#x27;cfe-bars&#x27;).innerHTML = rows.map(function (r) {&#10;      var w = max &gt; 0 ? Math.max(1, (r.fc \/ max) * 100) : 0;&#10;      return &#x27;&lt;div class=&quot;cfe-bar-row&#x27; + (r.cur ? &#x27; cfe-cur&#x27; : &#x27;&#x27;) + &#x27;&quot;&gt;&#x27; +&#10;        &#x27;&lt;span class=&quot;cfe-bar-label&quot;&gt;&#x27; + esc(r.label) + &#x27;&lt;\/span&gt;&#x27; +&#10;        &#x27;&lt;div class=&quot;cfe-bar-track&quot; aria-hidden=&quot;true&quot;&gt;&lt;div class=&quot;cfe-bar-fill&quot; style=&quot;width:&#x27; + w.toFixed(2) + &#x27;%&quot;&gt;&lt;\/div&gt;&lt;\/div&gt;&#x27; +&#10;        &#x27;&lt;span class=&quot;cfe-bar-val&quot;&gt;&#x27; + fx(r.fc) + &#x27; N&lt;\/span&gt;&lt;\/div&gt;&#x27;;&#10;    }).join(&#x27;&#x27;);&#10;  }&#10;&#10;  function render(R) {&#10;    $(&#x27;cfe-error&#x27;).hidden = true;&#10;    $(&#x27;cfe-result-body&#x27;).hidden = false;&#10;&#10;    $(&#x27;cfe-r-fc&#x27;).textContent = fx(R.Fc);&#10;    $(&#x27;cfe-r-fc-sub&#x27;).textContent = &#x27;Main cutting force for turning with K = &#x27; + g(R.K);&#10;    $(&#x27;cfe-r-kn&#x27;).textContent = fx(R.FcKN);&#10;    $(&#x27;cfe-r-a&#x27;).textContent = fx(R.A);&#10;    $(&#x27;cfe-r-kc&#x27;).textContent = fx(R.kc);&#10;&#10;    var m = MATERIALS[R.mat];&#10;    var sub;&#10;    if (R.mat === &#x27;custom&#x27;) sub = &#x27;User-defined value&#x27;;&#10;    else if (m.kc === R.kc) sub = &#x27;Reference value for &#x27; + m.name;&#10;    else sub = &#x27;Manually adjusted (reference for &#x27; + m.name + &#x27;: &#x27; + g(m.kc) + &#x27;)&#x27;;&#10;    $(&#x27;cfe-r-kc-sub&#x27;).textContent = sub;&#10;&#10;    renderBars(R);&#10;&#10;    \/\/ Calculation details (substituted values)&#10;    $(&#x27;cfe-d-a&#x27;).textContent = &#x27;A = &#x27; + g(R.ap) + &#x27; mm \u00d7 &#x27; + g(R.f) + &#x27; mm\/rev = &#x27; + fx(R.A) + &#x27; mm\u00b2&#x27;;&#10;    $(&#x27;cfe-d-fc&#x27;).textContent = &#x27;Fc = &#x27; + g(R.kc) + &#x27; N\/mm\u00b2 \u00d7 &#x27; + g(R.ap) + &#x27; mm \u00d7 &#x27; + g(R.f) + &#x27; mm\/rev \u00d7 &#x27; + g(R.K) + &#x27; = &#x27; + fx(R.Fc) + &#x27; N&#x27;;&#10;    $(&#x27;cfe-d-kn&#x27;).textContent = &#x27;Fc = &#x27; + fx(R.Fc) + &#x27; N \/ 1000 = &#x27; + fx(R.FcKN) + &#x27; kN&#x27;;&#10;  }&#10;&#10;  \/* ---------- 6. Material handling ---------- *\/&#10;  function applyMaterial() {&#10;    var key = $(&#x27;cfe-mat&#x27;).value, m = MATERIALS[key];&#10;    setErr(&#x27;kc&#x27;, null);&#10;    if (key === &#x27;custom&#x27;) {&#10;      $(&#x27;cfe-kc&#x27;).value = &#x27;&#x27;;&#10;      $(&#x27;cfe-kc&#x27;).placeholder = &#x27;Enter kc&#x27;;&#10;      $(&#x27;cfe-kc-help&#x27;).textContent = &#x27;Enter the specific cutting force for your material.&#x27;;&#10;      $(&#x27;cfe-kc&#x27;).focus();&#10;    } else {&#10;      $(&#x27;cfe-kc&#x27;).value = String(m.kc);&#10;      $(&#x27;cfe-kc&#x27;).placeholder = &#x27;&#x27;;&#10;      $(&#x27;cfe-kc-help&#x27;).textContent = &#x27;Reference value for &#x27; + m.name + &#x27;. You can adjust it manually.&#x27;;&#10;    }&#10;  }&#10;&#10;  \/* ---------- 7. Events ---------- *\/&#10;  $(&#x27;cfe-mat&#x27;).addEventListener(&#x27;change&#x27;, function () {&#10;    applyMaterial();&#10;    \/\/ Re-calculate when material changes after results are already shown&#10;    if (!$(&#x27;cfe-results&#x27;).hidden &amp;&amp; $(&#x27;cfe-mat&#x27;).value !== &#x27;custom&#x27;) compute();&#10;  });&#10;&#10;  root.addEventListener(&#x27;input&#x27;, function (e) {&#10;    var t = e.target;&#10;    if (!t.classList || !t.classList.contains(&#x27;cfe-input&#x27;)) return;&#10;    var key = t.id.replace(&#x27;cfe-&#x27;, &#x27;&#x27;);&#10;    \/\/ Clear the inline error as soon as the field becomes valid&#10;    if (t.classList.contains(&#x27;cfe-invalid&#x27;) &amp;&amp; !check(key)) setErr(key, null);&#10;  });&#10;&#10;  $(&#x27;cfe-form&#x27;).addEventListener(&#x27;submit&#x27;, function (e) {&#10;    e.preventDefault();                \/\/ never reload the page&#10;    var res = $(&#x27;cfe-results&#x27;), first = res.hidden;&#10;    res.hidden = false;&#10;    var ok = compute();&#10;    if (!ok) {&#10;      var bad = root.querySelector(&#x27;.cfe-invalid&#x27;);&#10;      if (bad) bad.focus();&#10;    } else if (first &amp;&amp; res.scrollIntoView) {&#10;      res.scrollIntoView({ behavior: &#x27;smooth&#x27;, block: &#x27;nearest&#x27; });&#10;    }&#10;  });&#10;&#10;  \/* ---------- 8. Init ---------- *\/&#10;  $(&#x27;cfe-mat&#x27;).value = DEFAULTS.mat;&#10;  $(&#x27;cfe-kc&#x27;).value = String(MATERIALS[DEFAULTS.mat].kc);&#10;  $(&#x27;cfe-kc-help&#x27;).textContent = &#x27;Reference value for &#x27; + MATERIALS[DEFAULTS.mat].name + &#x27;. 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