{"id":66949,"date":"2026-10-13T10:38:30","date_gmt":"2026-10-13T07:38:30","guid":{"rendered":"https:\/\/wpcalc.com\/en\/?p=66949"},"modified":"2026-10-13T10:38:30","modified_gmt":"2026-10-13T07:38:30","slug":"newtons-law-of-cooling-calculator","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/physics\/newtons-law-of-cooling-calculator\/","title":{"rendered":"Newton's Law of Cooling 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\">Predict Cooling or Warming of an Object over Time<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"66949\" data-favorite-title=\"Newton&#039;s Law of Cooling\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/physics\/newtons-law-of-cooling-calculator\/\" data-favorite-excerpt=\"Estimate how quickly an object cools down or warms up to the ambient temperature. Enter the initial and ambient temperatures, the cooling constant k, and the elapsed time to get the object&#039;s temperature, plus the time needed to reach any target temperature.\" 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\/newtons-law-of-cooling-calculator\/\" method=\"POST\" class=\"calculator\" id=\"calculator-66949\" data-post=\"66949\"><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\">Initial temperature (T\u2080)<\/label><div class=\"term\">T\u2080<\/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=\"initial_temperature_t\" id=\"field-1\" aria-describedby=\"calc-info-1\" placeholder=\"e.g. 90\" step=\"any\" value=\"90\"\/><div class=\"grid grid-cols-1\"><select id=\"field-2\" name=\"unit\" aria-label=\"Unit\"><option value=\"c\" selected>\u00b0C<\/option><option value=\"f\">\u00b0F<\/option><option value=\"k\">K<\/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\">Temperature of the object at the start (t = 0).<\/small><\/div><div class=\"field has-term\" id=\"input-2\"><label for=\"field-3\">Ambient temperature (T\u2090)<\/label><div class=\"term\">T\u2090<\/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=\"ambient_temperature_t\" id=\"field-3\" aria-describedby=\"calc-info-3\" placeholder=\"e.g. 20\" step=\"any\" value=\"20\"\/><div class=\"grid grid-cols-1\"><select id=\"field-4\" name=\"unit\" aria-label=\"Unit\"><option value=\"c\" selected>\u00b0C<\/option><option value=\"f\">\u00b0F<\/option><option value=\"k\">K<\/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\">Constant temperature of the surrounding medium (room air, water bath, etc.).<\/small><\/div><div class=\"field has-term\" id=\"input-3\"><label for=\"field-5\">Cooling constant (k)<\/label><div class=\"term\">k<\/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=\"cooling_constant_k\" id=\"field-5\" aria-describedby=\"calc-info-5\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 0.05\" min=\"0\" value=\"0.05\"\/><div class=\"grid grid-cols-1\"><select id=\"field-6\" name=\"unit\" aria-label=\"Unit\"><option value=\"s\">1\/s<\/option><option value=\"min\" selected>1\/min<\/option><option value=\"h\">1\/h<\/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\">Positive rate constant of the object. A cup of coffee in air \u2248 0.02\u20130.08 per minute; a small metal part in water can be much higher.<\/small><\/div><div class=\"field has-term\" id=\"input-4\"><label for=\"field-7\">Elapsed time (t)<\/label><div class=\"term\">t<\/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=\"elapsed_time_t\" id=\"field-7\" aria-describedby=\"calc-info-7\" 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-8\" name=\"unit\" aria-label=\"Unit\"><option value=\"s\">s<\/option><option value=\"min\" selected>min<\/option><option value=\"h\">h<\/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-7\">Time since the start of cooling (or warming) for which you want the object temperature.<\/small><\/div><div class=\"field has-term\" id=\"input-5\"><label for=\"field-9\">Target temperature (optional)<\/label><div class=\"term\">Tt<\/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=\"target_temperature_optional\" id=\"field-9\" aria-describedby=\"calc-info-9\" placeholder=\"e.g. 40 (leave blank to skip)\" step=\"any\" value=\"40\"\/><div class=\"grid grid-cols-1\"><select id=\"field-10\" name=\"unit\" aria-label=\"Unit\"><option value=\"c\" selected>\u00b0C<\/option><option value=\"f\">\u00b0F<\/option><option value=\"k\">K<\/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-9\">Optional. If entered, the calculator also finds how long it takes for the object to reach this temperature.<\/small><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Re-Calculate\" id=\"calculate-button\" data-post=\"66949\">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> Cooling Results<\/h3><div class=\"result-box\"><div class=\"field-result is-column\" id=\"output-1\"><span class=\"field-title\"><span>Object temperature after the elapsed time<\/span><span class=\"result-term\">T(t)<\/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>Time to reach the target temperature<\/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=\"66949\" 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>Newton's Law of Cooling 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\\[ T(t) = T_a + (T_0 - T_a)\\, e^{-kt} \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Where:<\/strong><\/p>\n<ul>\n<li>\\(T(t)\\) \u2014 temperature of the object after time \\(t\\) (\u00b0C, \u00b0F or K)<\/li>\n<li>\\(T_0\\) \u2014 initial temperature of the object at \\(t = 0\\)<\/li>\n<li>\\(T_a\\) \u2014 ambient temperature of the surroundings (assumed constant)<\/li>\n<li>\\(k\\) \u2014 cooling constant, a positive number describing how fast heat is exchanged (per second, minute or hour)<\/li>\n<li>\\(t\\) \u2014 elapsed time, in units consistent with \\(k\\)<\/li>\n<\/ul>\n<p>The formula says that the object's temperature approaches the ambient temperature exponentially: the <em>difference<\/em> \\(T - T_a\\) shrinks by the same factor \\(e^{-k}\\) every unit of time, regardless of how hot or cold the object is.<\/p>\n<p>If you instead want the time needed to reach a given target temperature \\(T_t\\), invert the formula:<\/p>\n<p>\\[ t = -\\frac{\\ln\\left(\\dfrac{T_t - T_a}{T_0 - T_a}\\right)}{k} \\]<br \/>\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>Newton's Law of Cooling \u2013 Calculation Example<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Example:<\/strong> a cup of coffee at 90 \u00b0C is left in a room at 20 \u00b0C. The cooling constant is about \\(k = 0.05\\) per minute. What is its temperature after 10 minutes, and how long until it cools to 40 \u00b0C?<\/p>\n<p>\\[ T(10) = 20 + (90 - 20)\\,e^{-0.05 \\times 10} = 20 + 70\\,e^{-0.5} \\approx 20 + 70 \\times 0.6065 \\approx 62.46\\ \\text{\u00b0C} \\]<\/p>\n<p>\\[ t = -\\frac{\\ln\\left(\\dfrac{40 - 20}{90 - 20}\\right)}{0.05} = -\\frac{\\ln(0.2857)}{0.05} \\approx \\frac{1.2528}{0.05} \\approx 25.06\\ \\text{min} \\]<\/p>\n<p><strong>Result:<\/strong> after 10 minutes the coffee is at about <strong>62.46 \u00b0C<\/strong>, and it reaches 40 \u00b0C after roughly <strong>25 minutes<\/strong> (about 25.06 min).<\/p>\n<p>\n\r\n<\/section>\n<h2>How to use the calculator<\/h2>\n<ol>\n<li>Enter the <strong>Initial temperature (T\u2080)<\/strong> of the object and pick its unit (\u00b0C, \u00b0F or K).<\/li>\n<li>Enter the <strong>Ambient temperature (T\u2090)<\/strong> \u2014 the constant temperature of the surroundings \u2014 and its unit.<\/li>\n<li>Enter the <strong>Cooling constant (k)<\/strong> and choose whether it is given per second, per minute or per hour. It must be greater than zero.<\/li>\n<li>Enter the <strong>Elapsed time (t)<\/strong> since the start, with its unit.<\/li>\n<li>Optionally, enter a <strong>Target temperature<\/strong>. If you do, the calculator also reports how long it takes for the object to reach that temperature. Leave this field blank to skip it.<\/li>\n<li>Read the results: the object's temperature after the elapsed time (shown in \u00b0C, \u00b0F and K) and, if a target was set, the time needed to reach it.<\/li>\n<\/ol>\n<h2>What is Newton's law of cooling?<\/h2>\n<p>Newton's law of cooling states that the rate at which an object loses (or gains) heat is proportional to the temperature difference between the object and its surroundings. In other words, the hotter the object is relative to the room, the faster it cools; as it gets closer to the ambient temperature, the cooling slows down. Solving the resulting differential equation gives the exponential formula used above: the temperature difference decays steadily, shrinking by the same percentage each time interval.<\/p>\n<p>A key consequence is that an object never <em>exactly<\/em> reaches the ambient temperature \u2014 it only approaches it asymptotically. In practice, the difference quickly becomes so small that it is undetectable. That is why the calculator warns you if you set the target temperature equal to the ambient temperature: mathematically, it takes infinite time. It is better to aim for a value slightly above or below the ambient one, such as \"within 1 \u00b0C of room temperature\".<\/p>\n<p>The same law works for warming. If the initial temperature is below the ambient temperature (a cold drink in a warm room, for instance), the formula still applies \u2014 the temperature difference is simply negative, and the object warms up exponentially toward the surroundings. The calculator handles both directions automatically.<\/p>\n<p>The law is used in engineering (heat exchangers, quenching of metal parts), forensic science (estimating time of death from body cooling), food safety (cooling of cooked food) and everyday situations like tea or coffee going cold. It is the same exponential-decay mathematics that appears in radioactive decay and capacitor discharge.<\/p>\n<h2>Choosing the cooling constant k<\/h2>\n<p>The cooling constant \\(k\\) depends on the object's size, shape, material and the surrounding medium \u2014 not just on the object itself. The same object cools much faster in stirred water than in still air. Some typical orders of magnitude:<\/p>\n<ul>\n<li>A cup of coffee or tea in still air: \\(k \\approx 0.02\\)\u2013\\(0.08\\) per minute<\/li>\n<li>A small metal part in a water bath: \\(k\\) can reach several per minute<\/li>\n<li>A large roast taken out of the oven: \\(k \\approx 0.01\\)\u2013\\(0.03\\) per minute<\/li>\n<\/ul>\n<p>If you don't know \\(k\\), you can measure it: note the temperature at two known times, plug the values into the formula, and solve for \\(k\\). Alternatively, run this calculator with a guessed \\(k\\), compare the predicted temperature at your measurement time, and adjust until it matches.<\/p>\n<h2>Assumptions and limitations<\/h2>\n<ul>\n<li><strong>Constant ambient temperature.<\/strong> The surroundings must stay at \\(T_a\\) throughout \u2014 a large room or a well-stirred bath. A small closed space heats up along with the object.<\/li>\n<li><strong>Uniform object temperature.<\/strong> The object is assumed to have the same temperature throughout (lumped-system assumption). This is a good approximation for small objects made of good thermal conductors; it fails for large or poorly conducting bodies, which cool from the outside in.<\/li>\n<li><strong>Linear heat transfer.<\/strong> The law models convective heat transfer with a constant heat-transfer coefficient. It ignores radiation (significant for very hot objects) and phase changes such as boiling or freezing.<\/li>\n<li><strong>Exponential behavior.<\/strong> Because cooling is exponential, the last few degrees near the ambient temperature take disproportionately long \u2014 doubling the temperature difference always takes the same time, no matter how small the difference already is.<\/li>\n<\/ul>\n<p>For related physics calculations, see our <a href=\"https:\/\/wpcalc.com\/en\/physics\/free-fall-calculator\/\">Free Fall Calculator<\/a>, the <a href=\"https:\/\/wpcalc.com\/en\/physics\/drag-force-calculator\/\">Drag Force Calculator<\/a> (another situation where a velocity-like quantity decays exponentially in time), or the <a href=\"https:\/\/wpcalc.com\/en\/physics\/speed-of-sound-in-air-calculator\/\">Speed of Sound in Air Calculator<\/a> for other temperature-dependent properties of air.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Estimate how quickly an object cools down or warms up to the ambient temperature. Enter the initial and ambient temperatures, the cooling constant k, and the elapsed time to get the object's temperature, plus the time needed to reach any target temperature.<\/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-66949","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\/66949","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=66949"}],"version-history":[{"count":1,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66949\/revisions"}],"predecessor-version":[{"id":66950,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66949\/revisions\/66950"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=66949"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=66949"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=66949"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}