{"id":65882,"date":"2026-09-30T13:56:42","date_gmt":"2026-09-30T10:56:42","guid":{"rendered":"https:\/\/wpcalc.com\/en\/?p=65882"},"modified":"2026-09-30T13:56:42","modified_gmt":"2026-09-30T10:56:42","slug":"coulombs-law-calculator","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/physics\/coulombs-law-calculator\/","title":{"rendered":"Coulomb's Law 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\">Find the Electric Force Between Two Charges<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"65882\" data-favorite-title=\"Coulomb&#039;s Law\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/physics\/coulombs-law-calculator\/\" data-favorite-excerpt=\"Calculate the electrostatic force between two point charges using Coulomb&#039;s law. Enter the two charges (nC, \u03bcC, mC, C or e), the distance between them, and get the force in newtons plus its direction.\" aria-label=\"Add to Favorites\" data-favorite-icon=\"icon icon-physic\">\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\/physics\/coulombs-law-calculator\/\" method=\"POST\" class=\"calculator\" id=\"calculator-65882\" data-post=\"65882\"><fieldset class=\"fieldset-input is-1\"><legend class=\"sr-only\">Input Fields<\/legend><div class=\"field is-single has-term\" id=\"input-1\"><label for=\"field-1\">Charge 1 (q\u2081)<\/label><div class=\"term\">q\u2081<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"number\" name=\"charge_1_q\" id=\"field-1\" aria-describedby=\"calc-info-1\" placeholder=\"e.g. 5\" step=\"any\" value=\"5\"\/><div class=\"grid grid-cols-1\"><select id=\"field-2\" name=\"unit\" aria-label=\"Unit\"><option value=\"nC\">nC<\/option><option value=\"uCl\" selected>\u03bcC<\/option><option value=\"mC\">mC<\/option><option value=\"C\">C<\/option><option value=\"e\">e (elementary)<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><small id=\"calc-info-1\">Electric charge of the first particle. Enter a negative value for a negative charge.<\/small><\/div><div class=\"field is-single has-term\" id=\"input-2\"><label for=\"field-3\">Charge 2 (q\u2082)<\/label><div class=\"term\">q\u2082<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"number\" name=\"charge_2_q\" id=\"field-3\" aria-describedby=\"calc-info-3\" placeholder=\"e.g. -3\" step=\"any\" value=\"-3\"\/><div class=\"grid grid-cols-1\"><select id=\"field-4\" name=\"unit\" aria-label=\"Unit\"><option value=\"nC\">nC<\/option><option value=\"uCl\" selected>\u03bcC<\/option><option value=\"mC\">mC<\/option><option value=\"C\">C<\/option><option value=\"e\">e (elementary)<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><small id=\"calc-info-3\">Electric charge of the second particle. Opposite signs attract, like signs repel.<\/small><\/div><div class=\"field is-single has-term\" id=\"input-3\"><label for=\"field-5\">Separation distance (r)<\/label><div class=\"term\">r<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"text\" name=\"separation_distance_r\" id=\"field-5\" aria-describedby=\"calc-info-5\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 10\" min=\"0\" value=\"10\"\/><div class=\"grid grid-cols-1\"><select id=\"field-6\" name=\"unit\" aria-label=\"Unit\"><option value=\"nm\">nm<\/option><option value=\"um\">\u03bcm<\/option><option value=\"mm\">mm<\/option><option value=\"cm\" selected>cm<\/option><option value=\"m\">m<\/option><option value=\"in\">in<\/option><option value=\"ft\">ft<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><small id=\"calc-info-5\">Straight-line distance between the centres of the two charges. Must be greater than zero.<\/small><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Re-Calculate\" id=\"calculate-button\" data-post=\"65882\">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> Coulomb&#039;s Law Results<\/h3><div class=\"result-box\"><div class=\"field-result is-column\" id=\"output-1\"><span class=\"field-title\"><span>Electrostatic force between the charges<\/span><\/span><span class=\"field-value\" id=\"result-1\"><\/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 class=\"field-result is-column\" id=\"output-2\"><span class=\"field-title\"><span>Formula, worked values and notes<\/span><\/span><span class=\"field-value\" id=\"result-2\"><\/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=\"65882\" 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\">0<\/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>Coulomb's Law 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 = k \\, \\frac{|q_1 \\, q_2|}{r^2}, \\qquad k = \\frac{1}{4\\pi\\varepsilon_0} \\approx 8.9875 \\times 10^9 \\ \\text{N\u00b7m}^2\/\\text{C}^2 \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Where:<\/strong><\/p>\n<ul>\n<li>\\(F\\) \u2014 magnitude of the electrostatic force (N)<\/li>\n<li>\\(q_1, q_2\\) \u2014 the two electric charges (C)<\/li>\n<li>\\(r\\) \u2014 distance between the centres of the charges (m)<\/li>\n<li>\\(k\\) \u2014 Coulomb's constant, defined via the vacuum permittivity \\(\\varepsilon_0 = 8.854 \\times 10^{-12}\\) F\/m<\/li>\n<\/ul>\n<p>The formula gives the force magnitude; the sign of the product \\(q_1 q_2\\) tells you the direction: like charges repel, opposite charges attract.<\/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>Coulomb's Law \u2013 Calculation Example<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Example:<\/strong> a charge of \\(q_1 = 5\\ \\mu\\text{C}\\) is placed 10 cm from a charge of \\(q_2 = -3\\ \\mu\\text{C}\\). Find the force between them.<\/p>\n<p>\\[ F = 8.9875 \\times 10^9 \\times \\frac{|5\\times 10^{-6} \\times (-3\\times 10^{-6})|}{(0.10)^2} \\]<br \/>\n\\[ F = 8.9875 \\times 10^9 \\times \\frac{1.5\\times 10^{-11}}{0.01} \\approx 13.48\\ \\text{N} \\]<\/p>\n<p><strong>Result:<\/strong> the force magnitude is about <strong>13.48 N<\/strong>. Because the charges have opposite signs, the force is <strong>attractive<\/strong> \u2014 each charge is pulled toward the other.<\/p>\n<p>\n\r\n<\/section>\n<h2>How to Use the Calculator<\/h2>\n<ol>\n<li>Enter the value of <strong>Charge 1 (q\u2081)<\/strong> and choose its unit (nC, \u03bcC, mC, C or elementary charges). Use a minus sign for a negative charge.<\/li>\n<li>Enter <strong>Charge 2 (q\u2082)<\/strong> with its unit in the same way.<\/li>\n<li>Enter the <strong>Separation distance (r)<\/strong> between the centres of the two charges and pick a length unit (nm, \u03bcm, mm, cm, m, in or ft). The value must be greater than zero.<\/li>\n<li>Read the result: the force magnitude in newtons (with conversions to mN, \u03bcN, kN, lbf and dynes), whether the interaction is attractive or repulsive, and a table showing every intermediate value.<\/li>\n<\/ol>\n<h2>What Is Coulomb's Law?<\/h2>\n<p>Coulomb's law, published by French physicist Charles-Augustin de Coulomb in 1785, describes the electrostatic force between two charged objects. It states that the force is directly proportional to the product of the two charges and inversely proportional to the square of the distance between them. In many ways it mirrors Newton's law of universal gravitation \u2014 but while gravity only attracts, electric forces can attract <em>or<\/em> repel depending on the signs of the charges.<\/p>\n<p>The sign of the result carries meaning. If \\(q_1\\) and \\(q_2\\) have the same sign, their product is positive and the force is repulsive: the charges push each other apart. If the signs are opposite, the product is negative and the force is attractive. The calculator reports the magnitude of the force together with this direction, so you always know both the strength and the nature of the interaction.<\/p>\n<p>The inverse-square dependence on distance is the law's most important practical feature. Halving the distance makes the force four times stronger; doubling the distance makes it four times weaker. This is why electrostatic forces dominate at short range \u2014 two elementary charges 1 nm apart exert forces on the scale of chemical bonds, while the same charges a metre apart would be utterly undetectable.<\/p>\n<p>Coulomb's law is the foundation of electrostatics. It underlies the structure of atoms and molecules, the behaviour of capacitors, electric fields, and technologies from laser printers to electrostatic precipitators. Once you know the force, you can combine it with Newton's second law to predict the motion of charged particles.<\/p>\n<h2>Assumptions, Limitations and Tips<\/h2>\n<ul>\n<li><strong>Point charges:<\/strong> the formula assumes each charge is concentrated at a single point, or is a uniformly charged sphere where r is measured between centres. For irregular charged objects at close range, the true force differs.<\/li>\n<li><strong>Vacuum:<\/strong> the calculation uses the vacuum permittivity \\(\\varepsilon_0\\). In a medium with relative permittivity \\(\\varepsilon_r\\), the force is smaller by a factor of \\(\\varepsilon_r\\) \u2014 about 80\u00d7 weaker in water.<\/li>\n<li><strong>Distance must be positive:<\/strong> two charges at exactly the same point would give an infinite force, so the calculator requires r &gt; 0.<\/li>\n<li><strong>Static charges:<\/strong> Coulomb's law applies to charges at rest. Moving charges additionally create magnetic effects described by electromagnetism.<\/li>\n<li><strong>Realistic values:<\/strong> everyday static electricity involves nanocoulombs to microcoulombs. If the result comes out in kilonewtons or more, double-check your units \u2014 a millicoulomb is already a very large amount of charge.<\/li>\n<li><strong>Force pairs:<\/strong> by Newton's third law, both charges experience the same force magnitude in opposite directions along the line joining them.<\/li>\n<\/ul>\n<p>Once you have found the electric force, you can put it to work in other mechanics problems \u2014 for example, combine it with the <a href=\"https:\/\/wpcalc.com\/en\/physics\/centripetal-force-calculator\/\">Centripetal Force Calculator<\/a> to analyse an electron orbiting a nucleus, check the balance with other forces using the <a href=\"https:\/\/wpcalc.com\/en\/physics\/friction-force-calculator\/\">Friction Force Calculator<\/a> or <a href=\"https:\/\/wpcalc.com\/en\/physics\/tension-in-ropes-calculator\/\">Tension in Ropes Calculator<\/a>, or explore the energy side of the interaction with the <a href=\"https:\/\/wpcalc.com\/en\/physics\/potential-energy\/\">Potential Energy Calculator<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Calculate the electrostatic force between two point charges using Coulomb's law. Enter the two charges (nC, \u03bcC, mC, C or e), the distance between them, and get the force in newtons plus its direction.<\/p>\n","protected":false},"author":3168,"featured_media":0,"comment_status":"open","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[62],"tags":[73],"class_list":["post-65882","post","type-post","status-publish","format-standard","hentry","category-physics","tag-mechanics"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/65882","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\/3168"}],"replies":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/comments?post=65882"}],"version-history":[{"count":1,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/65882\/revisions"}],"predecessor-version":[{"id":65917,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/65882\/revisions\/65917"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=65882"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=65882"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=65882"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}