{"id":64485,"date":"2025-05-12T09:47:47","date_gmt":"2025-05-12T06:47:47","guid":{"rendered":"https:\/\/wpcalc.com\/en\/?p=64485"},"modified":"2026-09-30T18:35:01","modified_gmt":"2026-09-30T15:35:01","slug":"solenoid-electromagnetic-force","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/engineering\/solenoid-electromagnetic-force\/","title":{"rendered":"Solenoid Coil Electromagnetic Force Calculator"},"content":{"rendered":"<section class=\"not-prose calculator-box\" aria-labelledby=\"calculator-title\"><div class=\"flex items-baseline sm:items-center justify-between gap-2 sm:gap-3\"><div class=\"flex flex-col sm:flex-row sm:items-center gap-2\"><span class=\"icon icon-calculator text-primary-700! text-base! dark:text-primary-300!\" aria-hidden=\"true\"><\/span><h2 id=\"calculator-title\" class=\"text-lg font-display font-bold\">Solenoid Magnetic Force Estimator<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"64485\" data-favorite-title=\"Solenoid Coil Electromagnetic Force\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/engineering\/solenoid-electromagnetic-force\/\" data-favorite-excerpt=\"Estimate the pulling force of a solenoid coil from the number of turns, current, core cross-sectional area, and air gap length. Enter your coil parameters to get the electromagnetic force in newtons.\" aria-label=\"Add to Favorites\" data-favorite-icon=\"icon icon-magnet\">\n    <span class=\"icon icon-shape-star-empty\" aria-hidden=\"true\"><\/span>\n  <\/button>\n  <div class=\"calcdash-favorite__tip\" aria-hidden=\"true\">\n   <span class=\"favorite-tooltip\" id=\"favorite-tooltip\"><\/span>\n  <\/div>\n  <span class=\"sr-only\" role=\"status\" id=\"favorite-status\"><\/span>\n<\/div><\/div><form action=\"https:\/\/wpcalc.com\/en\/engineering\/solenoid-electromagnetic-force\/\" method=\"POST\" class=\"calculator\" id=\"calculator-64485\" data-post=\"64485\"><fieldset class=\"fieldset-input\"><legend class=\"sr-only\">Input Fields<\/legend><div class=\"field has-term\" id=\"input-1\"><label for=\"field-1\">Number of turns<\/label><div class=\"term\">N<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"number_of_turns\" id=\"field-1\" aria-describedby=\"calc-info-1\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"1\" value=\"100\"\/><small id=\"calc-info-1\">Total number of turns in the coil<\/small><\/div><div class=\"field has-term\" id=\"input-2\"><label for=\"field-2\">Current<\/label><div class=\"term\">I<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"current\" id=\"field-2\" aria-describedby=\"calc-unit-2 calc-info-2\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0.01\" value=\"2\"\/><div class=\"unit\" id=\"calc-unit-2\">A<\/div><small id=\"calc-info-2\">Current through the coil<\/small><\/div><div class=\"field has-term\" id=\"input-3\"><label for=\"field-3\">Core area<\/label><div class=\"term\">A<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"core_area\" id=\"field-3\" aria-describedby=\"calc-unit-3 calc-info-3\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0.01\" value=\"2\"\/><div class=\"unit\" id=\"calc-unit-3\">cm\u00b2<\/div><small id=\"calc-info-3\">Cross-sectional area of core (cm\u00b2)<\/small><\/div><div class=\"field has-term\" id=\"input-4\"><label for=\"field-4\">Air gap<\/label><div class=\"term\">g<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"air_gap\" id=\"field-4\" aria-describedby=\"calc-unit-4 calc-info-4\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0.01\" value=\"1\"\/><div class=\"unit\" id=\"calc-unit-4\">mm<\/div><small id=\"calc-info-4\">Gap between core and armature (mm)<\/small><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Re-Calculate\" id=\"calculate-button\" data-post=\"64485\">Calculate<\/button><button type=\"reset\">Reset<\/button><\/div><div class=\"field is-checkbox hidden!\" id=\"field-auto-calc\"><input type=\"checkbox\" id=\"auto-calc\"><label for=\"auto-calc\">Calculate automatically<\/label><small>If enabled, the result will update automatically when you change any value.<\/small><\/div><div class=\"fieldset-result is-hidden\" aria-labelledby=\"result-title\" aria-live=\"polite\" role=\"region\"> <h3 class=\"result-title bg-gradient-to-r from-primary-50 to-gray-50 dark:from-primary-900 dark:to-gray-800\" id=\"result-title\"><span class=\"icon icon-s-pulse\" aria-hidden=\"true\"><\/span> Your Results<\/h3><div class=\"result-box\"><div class=\"field-result\" id=\"output-1\"><span class=\"field-title\"><span>Electromagnetic Force<\/span><\/span><span class=\"field-value\" id=\"result-1\" data-unit=\"N\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copy Result\" aria-label=\"Copy Result\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><\/div><div class=\"result-actions\"><button type=\"button\" class=\"copy-link\"><svg viewBox=\"0 0 20 20\" fill=\"currentColor\" aria-hidden=\"true\"><path d=\"M12.232 4.232a2.5 2.5 0 0 1 3.536 3.536l-1.225 1.224a.75.75 0 0 0 1.061 1.06l1.224-1.224a4 4 0 0 0-5.656-5.656l-3 3a4 4 0 0 0 .225 5.865.75.75 0 0 0 .977-1.138 2.5 2.5 0 0 1-.142-3.667l3-3Z\"\/><path d=\"M11.603 7.963a.75.75 0 0 0-.977 1.138 2.5 2.5 0 0 1 .142 3.667l-3 3a2.5 2.5 0 0 1-3.536-3.536l1.225-1.224a.75.75 0 0 0-1.061-1.06l-1.224 1.224a4 4 0 1 0 5.656 5.656l3-3a4 4 0 0 0-.225-5.865Z\"\/><\/svg><span class=\"copy-link__text\">Copy link to this calculation<\/span><\/button><span class=\"sr-only\" role=\"status\" id=\"copy-link-status\"><\/span><\/div><\/div><a href=\"#respond\" class=\"hidden transition-opacity duration-300 opacity-0 w-50 text-sm justify-center items-center gap-2 px-4 py-2 rounded bg-gray-200 text-gray-700 hover:bg-gray-300\" id=\"leave-comment\"><span class=\"icon icon-comments\" aria-hidden=\"true\"><\/span>Leave a Comment<\/a><\/form><\/section><section id=\"calc-reactions\" class=\"not-prose hidden my-12 bg-gradient-to-r from-primary-50 to-gray-50 border border-indigo-100 rounded-xl px-6 py-4 shadow-sm\" data-post=\"64485\" aria-live=\"polite\" aria-labelledby=\"calc-reactions-title\"><p id=\"calc-reactions-title\" class=\"text-sm text-gray-500 text-center mb-2\">How did this result make you feel?<\/p><div role=\"group\" aria-labelledby=\"calc-reactions-title\" class=\"grid grid-cols-3 sm:flex sm:flex-row sm:justify-around gap-4 sm:items-center sm:flex-wrap\"><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"like\"><span class=\"reaction-count\" data-reaction-count=\"like\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude00 <\/span><span class=\"reaction-description font-medium\">Like <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"helpful\"><span class=\"reaction-count\" data-reaction-count=\"helpful\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\udca1 <\/span><span class=\"reaction-description font-medium\">Helpful <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"confused\"><span class=\"reaction-count\" data-reaction-count=\"confused\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude15 <\/span><span class=\"reaction-description font-medium\">Confused <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"disappointed\"><span class=\"reaction-count\" data-reaction-count=\"disappointed\">2<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude1e <\/span><span class=\"reaction-description font-medium\">Disappointed <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"inaccurate\"><span class=\"reaction-count\" data-reaction-count=\"inaccurate\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\u274c <\/span><span class=\"reaction-description font-medium\">Inaccurate <\/span><\/button><\/div><div id=\"reaction-message\" class=\"hidden mt-8 rounded-md border border-primary-100 bg-white\/50 backdrop-blur-sm px-4 py-2 text-sm text-center shadow-sm\"><\/div><\/section><div class=\"calcdash-ad not-prose calcdash-ad--calc_result calcdash-ad--in-article\"><ins class=\"adsbygoogle\" style=\"display:block\" data-ad-client=\"ca-pub-1721569815777345\" data-ad-slot=\"6317458308\" data-ad-layout=\"in-article\" data-ad-format=\"fluid\"><\/ins><script>(adsbygoogle = window.adsbygoogle || []).push({});<\/script><\/div>\n<style id=\"wpcoderpro-inline-1\">.formula-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section class=\"formula-box\" aria-labelledby=\"formula-title\">\r\n\t<div id=\"formula-title\" class=\"not-prose font-display mb-4\"><span class=\"icon icon-formula\" aria-hidden=\"true\"><\/span><h2>Solenoid Electromagnetic Force Formula<\/h2><\/div>\r\n\t<figure class=\"not-prose formula\">\r\n\t\t<figcaption class=\"formula-title\">Formula<\/figcaption>\r\n\t\t<div class=\"text-base text-gray-800\" id=\"formula\">\n\\[ F = \\frac{B^2 A}{2\\mu_0} \\]\n\\[ B \\approx \\mu_0 \\frac{N I}{g} \\]\n\\[ F = \\frac{\\mu_0 (N I)^2 A}{2 g^2} \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Where:<\/strong><\/p>\n<ul>\n<li>\\(F\\) \u2014 electromagnetic force (N)<\/li>\n<li>\\(N\\) \u2014 number of turns in the coil<\/li>\n<li>\\(I\\) \u2014 current through the coil (A)<\/li>\n<li>\\(A\\) \u2014 cross-sectional area of the core (m\u00b2)<\/li>\n<li>\\(g\\) \u2014 length of the air gap between core and armature (m)<\/li>\n<li>\\(B\\) \u2014 magnetic flux density in the gap (T)<\/li>\n<li>\\(\\mu_0\\) \u2014 permeability of free space, \\(4\\pi \\times 10^{-7}\\) H\/m<\/li>\n<\/ul>\n<p>The first equation is the standard force law for a magnetic field acting across an air gap. Because the air gap dominates the magnetic reluctance of the circuit, the flux density can be approximated as \\(B \\approx \\mu_0 N I \/ g\\), which combines into the working formula used by the calculator.<\/p>\n<p>\r\n<\/section>\n<style id=\"wpcoderpro-inline-459\">.calculation-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section id=\"calculation\" class=\"calculation-box\" aria-labelledby=\"calculation-title\">\r\n\t<div id=\"calculation-title\" class=\"not-prose font-display\"><span class=\"icon icon-unordered-list\" aria-hidden=\"true\"><\/span><h2>Solenoid Coil Electromagnetic Force \u2013 Calculation Example<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Example:<\/strong> a solenoid actuator has 100 turns, carries a current of 2 A, the core cross-section is 2 cm\u00b2, and the armature sits 1 mm away from the core.<\/p>\n<p>Convert the units: \\(A = 2~\\text{cm}^2 = 2 \\times 10^{-4}~\\text{m}^2\\), \\(g = 1~\\text{mm} = 0.001~\\text{m}\\).<\/p>\n<p>\\[ F = \\frac{4\\pi \\times 10^{-7} \\times (100 \\times 2)^2 \\times 2 \\times 10^{-4}}{2 \\times (0.001)^2} \\]<\/p>\n<p>\\[ F = \\frac{4\\pi \\times 10^{-7} \\times 40000 \\times 2 \\times 10^{-4}}{2 \\times 10^{-6}} \\approx 5.03~\\text{N} \\]<\/p>\n<p><strong>Result:<\/strong> the solenoid produces an electromagnetic force of approximately 5.03 N, or about 0.51 kgf of pull.<\/p>\n<p>\n\r\n<\/section>\n<h2>How to use the calculator<\/h2>\n<ol>\n<li>Enter the <strong>Number of turns<\/strong> in the coil (default: 100).<\/li>\n<li>Enter the <strong>Current<\/strong> flowing through the coil in amperes.<\/li>\n<li>Enter the <strong>Core area<\/strong> \u2014 the cross-sectional area of the magnetic core \u2014 in cm\u00b2.<\/li>\n<li>Enter the <strong>Air gap<\/strong>, the distance between the core and the armature (the moving part), in mm.<\/li>\n<li>Read the <strong>Electromagnetic Force<\/strong> in newtons below the inputs.<\/li>\n<\/ol>\n<h2>What is solenoid electromagnetic force?<\/h2>\n<p>A solenoid is a coil of wire that generates a magnetic field when current flows through it. When the coil is wrapped around a ferromagnetic core and placed near a movable armature, the magnetic field pulls the armature toward the core, converting electrical energy into mechanical motion. This pulling force is what the calculator estimates.<\/p>\n<p>The force arises from the energy stored in the air gap. As the gap closes, the magnetic circuit's reluctance drops and the field does mechanical work on the armature. The classic result, valid for a uniform field across a small gap, is \\(F = B^2 A \/ (2\\mu_0)\\) \u2014 the force grows with the square of the flux density and with the pole face area.<\/p>\n<p>Two practical consequences follow from the formula. First, the force scales with \\((NI)^2\\), so doubling either the current or the number of turns quadruples the force. Second, the force scales with \\(1\/g^2\\), meaning the pull rises very steeply as the armature approaches the core. A solenoid that can only manage a few newtons at a 5 mm gap may deliver hundreds of newtons once seated.<\/p>\n<p>Solenoids are found in relays, valves, door locks, starters, printers, and robotic grippers. This calculator is most useful during the early design stage, when you need to check whether a given coil geometry and drive current can produce enough force to move a load at the required stroke.<\/p>\n<h2>Assumptions and limitations<\/h2>\n<ul>\n<li><strong>Linear, unsaturated core.<\/strong> The formula assumes the iron's permeability is so high that the air gap dominates the total reluctance. If the core saturates, the actual force will be lower than predicted.<\/li>\n<li><strong>Fringing is neglected.<\/strong> Real flux bulges out at the edges of the gap, effectively increasing the area. The effect is usually small for gap lengths much shorter than the pole dimensions.<\/li>\n<li><strong>Uniform field.<\/strong> The gap should be small and the pole faces parallel for the \\(1\/g^2\\) relationship to hold.<\/li>\n<li><strong>DC operation.<\/strong> For AC solenoids, use the RMS current; inductance and eddy-current effects are not modeled.<\/li>\n<li><strong>Copper losses and heating are not included.<\/strong> Check the coil's resistance and duty cycle separately; a coil that produces enough force but overheats is still a failed design. For winding-related parameters, see the <a href=\"https:\/\/wpcalc.com\/en\/engineering\/coil-physical-properties\/\">Physical Properties of Coil<\/a> and <a href=\"https:\/\/wpcalc.com\/en\/engineering\/wire-gauge\/\">Wire Gauge<\/a> calculators.<\/li>\n<\/ul>\n<h2>Practical tips<\/h2>\n<p>To increase force without raising current, add turns or reduce the gap \u2014 both are more effective than increasing the core area, because force depends on \\((NI)^2\\) and \\(1\/g^2\\) but only linearly on \\(A\\). Keep in mind that more turns mean higher resistance and a longer, weaker magnetic path if the coil grows.<\/p>\n<p>If you are designing the driver circuit or analyzing the coil as a circuit element, the <a href=\"https:\/\/wpcalc.com\/en\/engineering\/straight-wire-inductor\/\">Straight Wire Inductance<\/a> and <a href=\"https:\/\/wpcalc.com\/en\/engineering\/series-inductance\/\">Series Inductance<\/a> calculators can help you estimate the inductive load the solenoid presents.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Estimate the pulling force of a solenoid coil from the number of turns, current, core cross-sectional area, and air gap length. Enter your coil parameters to get the electromagnetic force in newtons.<\/p>\n","protected":false},"author":70,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[4],"tags":[93],"class_list":["post-64485","post","type-post","status-publish","format-standard","hentry","category-engineering","tag-coils-transformers"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/64485","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/users\/70"}],"replies":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/comments?post=64485"}],"version-history":[{"count":3,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/64485\/revisions"}],"predecessor-version":[{"id":66013,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/64485\/revisions\/66013"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=64485"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=64485"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=64485"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}