{"id":66939,"date":"2026-10-13T10:35:19","date_gmt":"2026-10-13T07:35:19","guid":{"rendered":"https:\/\/wpcalc.com\/en\/?p=66939"},"modified":"2026-10-13T10:35:19","modified_gmt":"2026-10-13T07:35:19","slug":"electric-potential-of-a-point-charge-calculator","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/physics\/electric-potential-of-a-point-charge-calculator\/","title":{"rendered":"Electric Potential 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 Potential from a Point Charge<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"66939\" data-favorite-title=\"Point Charge Electric Potential\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/physics\/electric-potential-of-a-point-charge-calculator\/\" data-favorite-excerpt=\"Calculate the electric potential V at any distance from a point charge. Enter the source charge Q, the distance r, and the medium&#039;s relative permittivity to get the result in volts and kilovolts.\" 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-potential-of-a-point-charge-calculator\/\" method=\"POST\" class=\"calculator\" id=\"calculator-66939\" data-post=\"66939\"><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; the sign only affects the sign of the potential<\/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 potential 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=\"66939\">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 Potential Results<\/h3><div class=\"result-box\"><div class=\"field-result\" id=\"output-1\"><span class=\"field-title\"><span>Electric Potential<\/span><span class=\"result-term\">V<\/span><\/span><span class=\"field-value\" id=\"result-1\" data-unit=\"V\"><\/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 Kilovolts<\/span><span class=\"result-term\">V<\/span><\/span><span class=\"field-value\" id=\"result-2\" data-unit=\"kV\"><\/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=\"66939\" 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 Potential<\/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\\[ V = \\frac{k \\, Q}{\\varepsilon_r \\, r} = \\frac{1}{4 \\pi \\varepsilon_0 \\varepsilon_r} \\cdot \\frac{Q}{r} \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Where:<\/strong><\/p>\n<ul>\n<li>\\(V\\) \u2014 electric potential at the point, in volts (V)<\/li>\n<li>\\(k = 8.988 \\times 10^9\\ \\text{N\u00b7m}^2\/\\text{C}^2\\) \u2014 the Coulomb constant<\/li>\n<li>\\(Q\\) \u2014 source charge, in coulombs (C)<\/li>\n<li>\\(\\varepsilon_r\\) \u2014 relative permittivity of the medium (1 for vacuum or air)<\/li>\n<li>\\(r\\) \u2014 distance from the charge to the measurement point, in meters (m)<\/li>\n<\/ul>\n<p>The formula gives the potential relative to infinity (\\(V(\\infty) = 0\\)): the work per unit charge needed to bring a small positive test charge from infinitely far away to the distance \\(r\\).<\/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 Potential \u2013 Calculation Example<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Example:<\/strong> a charge of \\(Q = 1\\ \\mu\\text{C}\\) sits in air, and you want the potential at a distance of \\(r = 10\\ \\text{cm}\\).<\/p>\n<p>\\[ V = \\frac{8.988 \\times 10^9 \\times 1 \\times 10^{-6}}{1 \\times 0.1} = \\frac{8.988 \\times 10^3}{0.1} \\]<\/p>\n<p><strong>Result:<\/strong> \\(V \\approx 89\\,876\\ \\text{V} \\approx 89.9\\ \\text{kV}\\).<\/p>\n<p>\n\r\n<\/section>\n<h2>How to Use the Calculator<\/h2>\n<ol>\n<li>Enter the magnitude of the <strong>Source Charge (Q)<\/strong> and pick its unit (nC, \u00b5C, mC or C). The sign of the potential follows the sign of the charge.<\/li>\n<li>Enter the <strong>Distance (r)<\/strong> from the charge to the measurement point and select the unit (mm, cm, m, in or ft).<\/li>\n<li>Optionally set the <strong>Relative Permittivity (\u03b5r)<\/strong> of the surrounding medium \u2014 leave it at 1 for vacuum or air, or use \u22482.2 for oil, \u22484.7 for glass, \u224880 for water.<\/li>\n<li>Click <strong>Calculate<\/strong>. The result appears as the potential in volts (V) and kilovolts (kV), along with a step-by-step calculation breakdown.<\/li>\n<\/ol>\n<h2>What Is the Electric Potential of a Point Charge?<\/h2>\n<p>The electric potential \\(V\\) at a point in space describes how much electric potential energy a charged object would have there, per unit of charge. It is a scalar quantity: unlike the <a href=\"https:\/\/wpcalc.com\/en\/physics\/electric-field-of-a-point-charge-calculator\/\">electric field<\/a>, which points in a specific direction, the potential is just a single number \u2014 positive near positive charges, negative near negative charges. Potential is always measured relative to a chosen reference level, and for an isolated point charge the conventional choice is \\(V = 0\\) at infinity.<\/p>\n<p>For a point charge, the potential falls off as \\(1\/r\\): doubling the distance halves the potential. This is a slower falloff than the electric field, which drops as \\(1\/r^2\\). Because potential is a scalar, the total potential from several charges at a point is simply the algebraic sum of the individual potentials \u2014 a property that makes it much easier to work with than vector fields.<\/p>\n<p>A useful way to interpret the result: \\(V\\) equals the work per coulomb required to move a small positive test charge from infinitely far away to that point. If the calculator returns \\(V = 90\\ \\text{kV}\\), a charge of \\(+1\\ \\mu\\text{C}\\) brought to that location would have \\(90 \\times 10^3 \\times 10^{-6} = 0.09\\ \\text{J}\\) of electric potential energy. The potential also determines the electric field through \\(E = -dV\/dr\\), so a steep potential gradient means a strong field.<\/p>\n<h2>Assumptions, Limitations and Practical Tips<\/h2>\n<ul>\n<li><strong>Point charge assumption:<\/strong> the formula is exact for a point charge, and equally valid outside a uniformly charged sphere (a charged conducting sphere behaves as if all its charge were concentrated at its center).<\/li>\n<li><strong>Zero reference at infinity:<\/strong> results assume \\(V(\\infty) = 0\\). In circuits or near large grounded objects, measured potentials may differ because a different reference (e.g., earth ground) is used.<\/li>\n<li><strong>Uniform medium:<\/strong> the calculation assumes a single, uniform, linear dielectric filling all the space around the charge. If the charge sits at a boundary between two media, the simple formula no longer applies.<\/li>\n<li><strong>Distance must be positive:<\/strong> the potential is undefined exactly at the location of a point charge (it diverges as \\(r \\to 0\\)), so the distance must be greater than zero.<\/li>\n<li><strong>Sign matters:<\/strong> enter a negative charge to get a negative (attractive) potential; the magnitude of the result is unchanged.<\/li>\n<li>Dielectric media reduce the potential by the factor \\(\\varepsilon_r\\) \u2014 water, for instance, cuts the potential by roughly a factor of 80 compared with air.<\/li>\n<\/ul>\n<p>To explore the vector counterpart of this quantity, try the <a href=\"https:\/\/wpcalc.com\/en\/physics\/electric-field-of-a-point-charge-calculator\/\">Point Charge Electric Field Calculator<\/a>. If you are interested in other inverse-square and energy-related physics, the <a href=\"https:\/\/wpcalc.com\/en\/physics\/gravitational-force-calculator\/\">Gravitational Force Calculator<\/a> and the <a href=\"https:\/\/wpcalc.com\/en\/physics\/rotational-kinetic-energy-calculator\/\">Rotational Kinetic Energy Calculator<\/a> cover related concepts.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Calculate the electric potential V at any distance from a point charge. Enter the source charge Q, the distance r, and the medium's relative permittivity to get the result in volts and kilovolts.<\/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":[91],"class_list":["post-66939","post","type-post","status-publish","format-standard","hentry","category-physics","tag-energy-work"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66939","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=66939"}],"version-history":[{"count":1,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66939\/revisions"}],"predecessor-version":[{"id":66940,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66939\/revisions\/66940"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=66939"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=66939"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=66939"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}