{"id":66929,"date":"2026-10-13T10:31:56","date_gmt":"2026-10-13T07:31:56","guid":{"rendered":"https:\/\/wpcalc.com\/en\/?p=66929"},"modified":"2026-10-13T10:31:56","modified_gmt":"2026-10-13T07:31:56","slug":"electric-field-of-a-point-charge-calculator","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/physics\/electric-field-of-a-point-charge-calculator\/","title":{"rendered":"Electric Field of a Point Charge 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\">Electric Field from a Point Charge<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"66929\" data-favorite-title=\"Point Charge Electric Field\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/physics\/electric-field-of-a-point-charge-calculator\/\" data-favorite-excerpt=\"Calculate the electric field magnitude created by a point charge at any distance. Enter the charge Q, the distance r, and the medium&#039;s relative permittivity to get the result in N\/C and V\/m.\" 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\/electric-field-of-a-point-charge-calculator\/\" method=\"POST\" class=\"calculator\" id=\"calculator-66929\" data-post=\"66929\"><fieldset class=\"fieldset-input is-2\"><legend class=\"sr-only\">Input Fields<\/legend><div class=\"field has-term\" id=\"input-1\"><label for=\"field-1\">Source Charge (Q)<\/label><div class=\"term\">Q<\/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=\"source_charge_q\" id=\"field-1\" aria-describedby=\"calc-info-1\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 1\" min=\"0\" value=\"1\"\/><div class=\"grid grid-cols-1\"><select id=\"field-2\" name=\"charge_unit\" aria-label=\"Charge unit\"><option value=\"nc\">nC<\/option><option value=\"uc\" selected>\u00b5C<\/option><option value=\"mc\">mC<\/option><option value=\"c\">C<\/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\">Magnitude of the charge creating the field; sign only affects field direction<\/small><\/div><div class=\"field has-term\" id=\"input-2\"><label for=\"field-3\">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=\"distance_r\" id=\"field-3\" aria-describedby=\"calc-info-3\" 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-4\" name=\"distance_unit\" aria-label=\"Distance unit\"><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-3\">Distance from the charge to the point where the field is measured<\/small><\/div><div class=\"field has-term\" id=\"input-3\"><label for=\"field-5\">Relative Permittivity (\u03b5r)<\/label><div class=\"term\">\u03b5r<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"relative_permittivity_r\" id=\"field-5\" aria-describedby=\"calc-info-5\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 1\" min=\"1\" value=\"1\"\/><small id=\"calc-info-5\">Optional: 1 for vacuum\/air, \u22482.2 for oil, \u22484.7 for glass, \u224880 for water<\/small><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Re-Calculate\" id=\"calculate-button\" data-post=\"66929\">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> Electric Field Results<\/h3><div class=\"result-box\"><div class=\"field-result\" id=\"output-1\"><span class=\"field-title\"><span>Electric Field Magnitude<\/span><span class=\"result-term\">E<\/span><\/span><span class=\"field-value\" id=\"result-1\" data-unit=\"N\/C\"><\/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\" id=\"output-2\"><span class=\"field-title\"><span>In Volts per Meter<\/span><span class=\"result-term\">E<\/span><\/span><span class=\"field-value\" id=\"result-2\" data-unit=\"V\/m\"><\/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-3\"><span class=\"field-title\"><span>Calculation Details<\/span><\/span><span class=\"field-value\" id=\"result-3\"><\/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=\"66929\" 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>Point Charge Electric Field 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\\[ E = \\frac{k \\, |Q|}{\\varepsilon_r \\, r^2} \\quad \\text{where} \\quad k = \\frac{1}{4\\pi\\varepsilon_0} \\approx 8.988 \\times 10^9 \\ \\tfrac{\\text{N}\\cdot\\text{m}^2}{\\text{C}^2} \\\\\n\\varepsilon_0 \\approx 8.854 \\times 10^{-12} \\ \\tfrac{\\text{F}}{\\text{m}} \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Where:<\/strong><\/p>\n<ul>\n<li>\\(E\\) \u2014 electric field magnitude (N\/C, or equivalently V\/m)<\/li>\n<li>\\(k\\) \u2014 Coulomb's constant<\/li>\n<li>\\(|Q|\\) \u2014 magnitude of the source charge (C)<\/li>\n<li>\\(\\varepsilon_r\\) \u2014 relative permittivity of the medium (1 for vacuum, \u22481.0006 for air)<\/li>\n<li>\\(r\\) \u2014 distance from the charge to the field point (m)<\/li>\n<\/ul>\n<p>This formula, derived from Coulomb's law, gives the strength of the electric field that a point charge creates in the surrounding space. The field points away from a positive charge and toward a negative charge; the formula returns only the magnitude.<\/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>Point Charge Electric Field \u2013 Calculation Example<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Example:<\/strong> a charge of 1 \u00b5C sits in air. What is the electric field 10 cm away from it?<\/p>\n<p>\\[ E = \\frac{k\\,|Q|}{\\varepsilon_r\\, r^2} = \\frac{8.988\\times 10^9 \\times 1\\times 10^{-6}}{1 \\times (0.10)^2} \\]<\/p>\n<p>\\[ E = \\frac{8.988\\times 10^{3}}{0.01} \\approx 8.988\\times 10^7 \\ \\text{N\/C} \\]<\/p>\n<p><strong>Result:<\/strong> the electric field magnitude is approximately \\(8.99 \\times 10^7\\) N\/C, or \\(8.99 \\times 10^7\\) V\/m \u2014 the two units are identical. Because the charge is positive, the field points radially away from it.<\/p>\n<p>\n\r\n<\/section>\n<h2>How to Use the Calculator<\/h2>\n<ol>\n<li>Enter the <strong>Source Charge (Q)<\/strong> \u2014 the magnitude of the charge creating the field. Use only the absolute value; the sign affects the field's direction, not its strength.<\/li>\n<li>Choose the charge unit from the dropdown: nC, \u00b5C, mC, or C.<\/li>\n<li>Enter the <strong>Distance (r)<\/strong> from the charge to the point where you want to know the field, and pick the unit: mm, cm, m, in, or ft.<\/li>\n<li>Optionally set the <strong>Relative Permittivity (\u03b5r)<\/strong> of the medium. Leave it at 1 for vacuum or air; use \u22482.2 for oil, \u22484.7 for glass, or \u224880 for water.<\/li>\n<li>Read the <strong>Electric Field Magnitude<\/strong> in N\/C and the equivalent value in V\/m, along with a step-by-step breakdown in the Calculation Details block.<\/li>\n<\/ol>\n<h2>What Is the Electric Field of a Point Charge?<\/h2>\n<p>An electric field is the region of space around a charged object where another charge would feel a force. You don't need a second charge to define the field \u2014 it exists whether or not anything is there to detect it. For a point charge, the field spreads out uniformly in all directions, so its strength depends only on how much charge is present and how far away you measure it.<\/p>\n<p>The formula \\( E = k|Q|\/(\\varepsilon_r r^2) \\) shows two key features. First, the field grows in direct proportion to the charge: double the charge and the field doubles. Second, it obeys an inverse-square law: double the distance and the field falls to a quarter of its value. This is the same mathematical behavior as gravity \u2014 you can explore that analogy with our <a href=\"https:\/\/wpcalc.com\/en\/physics\/gravitational-force-calculator\/\">Gravitational Force Calculator<\/a>, which uses an analogous law with mass instead of charge.<\/p>\n<p>The medium matters too. Inside a dielectric such as water or glass, the charges in the material partially cancel the field of the source charge, weakening it by a factor of \\(\\varepsilon_r\\). That is why the same charge produces a field about 80 times weaker in water than in air. If you want the full force between two charges rather than the field of one, see the <a href=\"https:\/\/wpcalc.com\/en\/physics\/coulombs-law-calculator\/\">Coulomb's Law Calculator<\/a> \u2014 the field is simply that force divided by the test charge.<\/p>\n<p>The results are given in both N\/C and V\/m. These are the same unit written two ways: 1 N\/C = 1 V\/m, since a volt is a joule per coulomb and a newton is a joule per meter. For reference, the Earth's fair-weather field at the surface is roughly 100 V\/m, so the example above \u2014 nearly \\(10^8\\) V\/m \u2014 is an enormous field, comparable to what causes air itself to break down and spark.<\/p>\n<h2>Assumptions and Limitations<\/h2>\n<ul>\n<li><strong>Point charge approximation:<\/strong> the source charge is treated as concentrated at a single point. A uniformly charged sphere behaves exactly like a point charge at its center, but only at distances outside the sphere. Inside a charged sphere, this formula does not apply.<\/li>\n<li><strong>Uniform, linear medium:<\/strong> the relative permittivity must be the same everywhere between the charge and the field point. The calculator cannot handle boundaries between different materials (for example, half air, half glass).<\/li>\n<li><strong>No other charges:<\/strong> the result is the field of the source charge alone. With multiple charges present, calculate each field separately and add them as vectors.<\/li>\n<li><strong>Distance must be positive:<\/strong> the field is undefined at the exact location of the charge, where the formula predicts an infinite value.<\/li>\n<li><strong>Static charges:<\/strong> the formula assumes the charge is not moving. Rapidly changing charges radiate electromagnetic waves and require a more complete treatment.<\/li>\n<\/ul>\n<p>When interpreting results, keep everyday magnitudes in mind: fields below about \\(10^6\\) V\/m are common in electronics and lab equipment, while air breaks down at roughly \\(3\\times 10^6\\) V\/m. If your result approaches that range, expect sparking, corona discharge, or other nonlinear effects that this simple formula does not capture.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Calculate the electric field magnitude created by a point charge at any distance. Enter the charge Q, the distance r, and the medium's relative permittivity to get the result in N\/C and V\/m.<\/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-66929","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\/66929","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=66929"}],"version-history":[{"count":1,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66929\/revisions"}],"predecessor-version":[{"id":66931,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66929\/revisions\/66931"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=66929"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=66929"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=66929"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}