{"id":66979,"date":"2026-10-13T10:45:11","date_gmt":"2026-10-13T07:45:11","guid":{"rendered":"https:\/\/wpcalc.com\/en\/?p=66979"},"modified":"2026-10-13T10:45:11","modified_gmt":"2026-10-13T07:45:11","slug":"schwarzschild-radius-calculator","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/physics\/schwarzschild-radius-calculator\/","title":{"rendered":"Schwarzschild Radius 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 Event-Horizon Radius of Any Mass<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"66979\" data-favorite-title=\"Schwarzschild Radius\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/physics\/schwarzschild-radius-calculator\/\" data-favorite-excerpt=\"Enter any mass in kg, tonnes, Earth masses or Solar masses to find its Schwarzschild radius \u2014 the event-horizon size the object would have as a black hole, with interpretation of the result.\" aria-label=\"Add to Favorites\" data-favorite-icon=\"icon icon-astronomy\">\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\/schwarzschild-radius-calculator\/\" method=\"POST\" class=\"calculator\" id=\"calculator-66979\" data-post=\"66979\"><fieldset class=\"fieldset-input is-1\"><legend class=\"sr-only\">Input Fields<\/legend><div class=\"field has-term\" id=\"input-1\"><label for=\"field-1\">Mass of the object (M)<\/label><div class=\"term\">M<\/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=\"mass_of_the_object_m\" 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=\"unit\" aria-label=\"Unit\"><option value=\"kg\">kg<\/option><option value=\"g\">g<\/option><option value=\"t\">tonnes<\/option><option value=\"lb\">lb<\/option><option value=\"earth\">Earth masses<\/option><option value=\"sun\" selected>Solar masses<\/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\">Any mass squeezed inside its Schwarzschild radius becomes a black hole. One solar mass \u2248 1.989 \u00d7 10\u00b3\u2070 kg; Earth \u2248 5.972 \u00d7 10\u00b2\u2074 kg.<\/small><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Re-Calculate\" id=\"calculate-button\" data-post=\"66979\">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> Schwarzschild Radius Results<\/h3><div class=\"result-box\"><div class=\"field-result is-column\" id=\"output-1\"><span class=\"field-title\"><span>Schwarzschild radius (rs)<\/span><span class=\"result-term\">rs<\/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>Details and interpretation<\/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=\"66979\" 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>Schwarzschild Radius 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\">\nr_s = \\frac{2GM}{c^2}\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Where:<\/strong><\/p>\n<ul>\n<li>\\(r_s\\) \u2014 Schwarzschild radius, the radius of the event horizon (m)<\/li>\n<li>\\(G\\) \u2014 gravitational constant, \\(6.674 \\times 10^{-11}\\ \\mathrm{m^3\\,kg^{-1}\\,s^{-2}}\\)<\/li>\n<li>\\(M\\) \u2014 mass of the object (kg)<\/li>\n<li>\\(c\\) \u2014 speed of light in vacuum, \\(299{,}792{,}458\\ \\mathrm{m\/s}\\)<\/li>\n<\/ul>\n<p>The formula gives the critical radius at which the escape velocity of a mass equals the speed of light. Squeeze the whole mass inside this radius and nothing \u2014 not even light \u2014 can escape: the object becomes a black hole.<\/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>Schwarzschild Radius \u2013 Calculation Example<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Example:<\/strong> a star with a mass equal to the Sun collapses after exhausting its nuclear fuel. What is the event-horizon radius of the resulting black hole? Take \\(M = 1\\) Solar mass \\(= 1.98847 \\times 10^{30}\\) kg.<\/p>\n<p>\\[ r_s = \\frac{2 \\times 6.674 \\times 10^{-11} \\times 1.98847 \\times 10^{30}}{(2.998 \\times 10^{8})^2} = \\frac{2.654 \\times 10^{20}}{8.988 \\times 10^{16}} \\approx 2953\\ \\mathrm{m} \\]<\/p>\n<p><strong>Result:<\/strong> the Schwarzschild radius is about <strong>2,953 m, or roughly 2.95 km<\/strong>. All of the Sun's mass compressed within a sphere just under 3 km across would form a black hole with this horizon.<\/p>\n<p>\n\r\n<\/section>\n<h2>How to Use the Calculator<\/h2>\n<ol>\n<li>Enter the <strong>Mass of the object (M)<\/strong> in the number field \u2014 for example, 1 for a Sun-mass object.<\/li>\n<li>Choose the matching <strong>Unit<\/strong> from the dropdown: kg, g, tonnes, lb, Earth masses or Solar masses.<\/li>\n<li>Read the <strong>Schwarzschild radius (rs)<\/strong> result, shown in metres and kilometres and converted into cm, mm, miles, feet and astronomical units.<\/li>\n<li>Check the <strong>Details and interpretation<\/strong> block for the escape velocity at the horizon, the average density inside it, and a plain-language explanation of what the number means.<\/li>\n<\/ol>\n<h2>What Is the Schwarzschild Radius?<\/h2>\n<p>The Schwarzschild radius is the distance from the centre of a mass at which its escape velocity equals the speed of light. It is named after Karl Schwarzschild, who found this solution to Einstein's general relativity equations in 1916, just months after the theory was published. The sphere of radius \\(r_s\\) around a collapsed object is its <strong>event horizon<\/strong>: the boundary beyond which no signal, matter or light can ever return to the outside universe.<\/p>\n<p>Every object has a Schwarzschild radius \u2014 it is simply proportional to its mass. The catch is that for ordinary objects the radius is absurdly small. A 70 kg human has \\(r_s \\approx 10^{-25}\\) m, many orders of magnitude smaller than a proton, which is why people do not spontaneously become black holes. Only when matter is compressed within its own \\(r_s\\) does gravitational collapse become unstoppable.<\/p>\n<p>Because \\(r_s\\) scales linearly with mass while volume grows with the cube of the radius, larger black holes are actually <em>less<\/em> dense on average. A supermassive black hole of a billion Solar masses has an average density comparable to air, while a stellar-mass black hole packs densities far above nuclear matter. The calculator's density output lets you see this counter-intuitive trend directly.<\/p>\n<p>The result is also a handy yardstick in astronomy: a black hole of one Solar mass has \\(r_s \\approx 2.95\\) km, Earth's would be about 8.87 mm, and Sagittarius A*, the Milky Way's central black hole of roughly 4 million Solar masses, has a horizon about 12,000 km across \u2014 a sphere a bit larger than Earth.<\/p>\n<h2>Assumptions, Limitations and Tips<\/h2>\n<ul>\n<li><strong>Non-rotating, uncharged object.<\/strong> The formula describes an idealized Schwarzschild black hole. Real black holes spin (Kerr black holes) and their horizons are somewhat smaller \u2014 up to a factor of 2 for a maximally rotating one. For everyday estimates the difference is usually acceptable.<\/li>\n<li><strong>Classical treatment.<\/strong> Quantum-gravity effects are ignored. For extremely tiny masses the classical horizon size can be smaller than the Planck length \\(\\approx 1.6 \\times 10^{-35}\\) m, where the formula loses physical meaning.<\/li>\n<li><strong>All mass counted at the centre.<\/strong> The formula assumes the entire mass lies within \\(r_s\\). A star or planet of the same mass that is <em>larger<\/em> than its Schwarzschild radius is simply an ordinary object \u2014 it only becomes a black hole if compressed inside that radius.<\/li>\n<li><strong>Use big units for big objects.<\/strong> Entering a huge mass in kilograms may overflow the calculation. Switch the unit dropdown to Solar masses or Earth masses to keep the numbers manageable.<\/li>\n<li>Working with radiation from hot accretion disks? The disk glows like a blackbody, so the <a href=\"https:\/\/wpcalc.com\/en\/physics\/stefan-boltzmann-law-calculator\/\">Stefan\u2013Boltzmann law calculator<\/a> and <a href=\"https:\/\/wpcalc.com\/en\/physics\/wiens-displacement-law-calculator\/\">Wien's displacement law calculator<\/a> can help you estimate its power output and peak wavelength.<\/li>\n<\/ul>\n<h2>Reference Values<\/h2>\n<table>\n<thead>\n<tr>\n<th>Object<\/th>\n<th>Approximate mass<\/th>\n<th>Schwarzschild radius<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>Human (70 kg)<\/td>\n<td>70 kg<\/td>\n<td>\\(\\sim 10^{-25}\\) m<\/td>\n<\/tr>\n<tr>\n<td>Earth<\/td>\n<td>\\(5.97 \\times 10^{24}\\) kg<\/td>\n<td>8.87 mm<\/td>\n<\/tr>\n<tr>\n<td>Sun<\/td>\n<td>\\(1.99 \\times 10^{30}\\) kg<\/td>\n<td>2.95 km<\/td>\n<\/tr>\n<tr>\n<td>Sagittarius A* (Milky Way centre)<\/td>\n<td>\\(\\sim 4 \\times 10^6\\) Solar masses<\/td>\n<td>\\(\\sim 1.2 \\times 10^7\\) km<\/td>\n<\/tr>\n<tr>\n<td>M87* (first imaged black hole)<\/td>\n<td>\\(\\sim 6.5 \\times 10^9\\) Solar masses<\/td>\n<td>\\(\\sim 1.9 \\times 10^{10}\\) km<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>You can verify each row by entering the mass in the calculator with the appropriate unit selected \u2014 the results above use the same formula and constants.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Enter any mass in kg, tonnes, Earth masses or Solar masses to find its Schwarzschild radius \u2014 the event-horizon size the object would have as a black hole, with interpretation of the result.<\/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":[89],"class_list":["post-66979","post","type-post","status-publish","format-standard","hentry","category-physics","tag-gravity-space"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66979","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=66979"}],"version-history":[{"count":1,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66979\/revisions"}],"predecessor-version":[{"id":66980,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66979\/revisions\/66980"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=66979"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=66979"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=66979"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}