{"id":1571,"date":"2012-07-05T10:49:32","date_gmt":"2012-07-05T10:49:32","guid":{"rendered":"https:\/\/www.ophiropt.com\/blog\/laser-measurement\/?p=1571"},"modified":"2026-03-01T16:11:41","modified_gmt":"2026-03-01T16:11:41","slug":"a-shortcut-for-calculating-power-density-of-a-laser-beam","status":"publish","type":"post","link":"https:\/\/www.ophiropt.com\/blog\/a-shortcut-for-calculating-power-density-of-a-laser-beam\/","title":{"rendered":"A Shortcut for Calculating Laser Power Density"},"content":{"rendered":"<p>Here&#8217;s a\u00a0<a href=\"https:\/\/www.ophiropt.com\/en\/power-density-calculator\">laser power density calculator<\/a>, if that&#8217;s what you wanted.<\/p>\n<p>Read on if you&#8217;re interested in an easy way to calculate power density &#8211; even in your head.<\/p>\n<p>Laser engineers and technicians are often required to calculate a laser\u2019s power density to determine whether a beam would damage an optic or <a href=\"https:\/\/www.ophiropt.com\/en\/c\/laser-power-sensors\">sensor<\/a> or for other various applications. By definition, power density is power per unit area which is usually expressed in terms of <em>W<\/em>\/<em>cm<sup>2<\/sup><\/em>.\u00a0<!--more--><\/p>\n<p>The Calculation of power density is straightforward. By simply calculating the area of a beam using the radius in cm and dividing the beam\u2019s power by that area the power density in units of <em>W<\/em>\/<em>cm<sup>2<\/sup><\/em> is easily obtained. However, since <a href=\"https:\/\/www.ophiropt.com\/en\/c\/laser-position-sensors\">beam size<\/a> is usually given with the <a href=\"https:\/\/www.ophiropt.com\/en\/c\/nanoscan-profilers\">beam diameter<\/a> in terms of millimeters to calculate power density in <em>W<\/em>\/<em>cm<sup>2<\/sup><\/em> a user has to convert the diameter to cm, divide the diameter by two to find the radius, use <em>\u03c0r<sup>2<\/sup><\/em> to find the area in <em>cm<sup>2<\/sup><\/em>, and finally divide the laser power by the area to obtain power density. This calculation can be a bit tedious and time consuming especially for technicians and field engineers who want to make as quick and easy a calculation as possible.<\/p>\n<p><iframe data-src=\"https:\/\/www.youtube.com\/embed\/U2oliO-Cz8M?rel=0&amp;amp\" width=\"560\" height=\"315\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\" src=\"data:image\/svg+xml;base64,PHN2ZyB3aWR0aD0iMSIgaGVpZ2h0PSIxIiB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciPjwvc3ZnPg==\" class=\"lazyload\" data-load-mode=\"1\"><\/iframe><\/p>\n<p>With the following formula you can directly find power density of a laser beam using the diameter of the beam in millimeters:<\/p>\n<p align=\"center\"><em>\u00a0<a href=\"\/blog\/wp-content\/uploads\/2012\/07\/beam_in_millimeters.png\"><img decoding=\"async\" class=\"aligncenter size-full wp-image-3252 lazyload\" title=\"beam_in_millimeters\" data-src=\"\/blog\/wp-content\/uploads\/2012\/07\/beam_in_millimeters.png\" alt=\"\" width=\"327\" height=\"59\" src=\"data:image\/svg+xml;base64,PHN2ZyB3aWR0aD0iMSIgaGVpZ2h0PSIxIiB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciPjwvc3ZnPg==\" style=\"--smush-placeholder-width: 327px; --smush-placeholder-aspect-ratio: 327\/59;\" \/><\/a><\/em><\/p>\n<p>Here is how this equation is derived: We can write an expression for the power density of a1 mmdiameter beam, which is simply:<\/p>\n<p align=\"center\"><a href=\"\/blog\/wp-content\/uploads\/2012\/07\/Power_Density.png\"><img decoding=\"async\" class=\"aligncenter size-full wp-image-3253 lazyload\" title=\"Power_Density\" data-src=\"\/blog\/wp-content\/uploads\/2012\/07\/Power_Density.png\" alt=\"\" width=\"486\" height=\"53\" src=\"data:image\/svg+xml;base64,PHN2ZyB3aWR0aD0iMSIgaGVpZ2h0PSIxIiB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciPjwvc3ZnPg==\" style=\"--smush-placeholder-width: 486px; --smush-placeholder-aspect-ratio: 486\/53;\" \/><\/a><\/p>\n<p>Dividing the expression of power density of a 1 mm beam &#8212; <em>Power <\/em>\/<em> \u03c0<\/em>(0.5<em>mm<\/em>)<em><sup>2 <\/sup><\/em>&#8212; by an expression of power density as a function of diameter &#8212; <em>Power <\/em>\/<em> \u03c0<\/em>(0.5<em>d<\/em>)<em><sup>2 <\/sup><\/em>&#8212; we find that the ratio is<em> d<sup>2<\/sup><\/em>. Thus, power density as a function of diameter can be expressed as the power density of a 1 mm beam divided by <em>d<sup>2<\/sup><\/em>:<\/p>\n<p align=\"center\"><a href=\"\/blog\/wp-content\/uploads\/2012\/07\/111.png\"><img decoding=\"async\" class=\"aligncenter size-full wp-image-3254 lazyload\" title=\"power density \" data-src=\"\/blog\/wp-content\/uploads\/2012\/07\/111.png\" alt=\"\" width=\"302\" height=\"51\" src=\"data:image\/svg+xml;base64,PHN2ZyB3aWR0aD0iMSIgaGVpZ2h0PSIxIiB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciPjwvc3ZnPg==\" style=\"--smush-placeholder-width: 302px; --smush-placeholder-aspect-ratio: 302\/51;\" \/><\/a><\/p>\n<p>This formula assumes the beam is a flat top beam where the beam power density is uniform. For a Gaussian beam with a given beam waist in mm, \u00a0multiply this formula by two to obtain the formula given above (The multiplication factor is due to the fact that for a Gaussian beam, the peak power in the center is twice the average power density of the beam. The value is actually closer to 255, not 250, but this difference is trivial, introducing only ~2% error.\u00a0 We use 250 simply because it\u2019s easier to remember and perform mental calculations than 255! )<\/p>\n<p>Information source: <a href=\"https:\/\/www.newport.com\/medias\/sys_master\/images\/images\/h96\/hb2\/8797062889502\/Calculating-Power-Density-Tech-Note-2.pdf\">technical note from Newport corporations Website<\/a><\/p>\n<p><em>You might also like to read:<a title=\"How to measure the peak power of a pulsed laser?\" href=\"\/?p=642\">\u00a0How to measure the peak power of a pulsed laser?\u00a0<\/a><\/em><\/p>\n<p>Share this:<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Here&#8217;s a\u00a0laser power density calculator, if that&#8217;s what you wanted. Read on if you&#8217;re interested in an easy way to [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":8703,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[5,6,374],"tags":[17,62],"ophirposttype":[349],"class_list":["post-1571","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-laser-power-energy-measurement","category-laser-power-energy-sensors-en","category-power-density-calculator","tag-beamtrack-powerpositionsize-sensors","tag-power-measurement","ophirposttype-blogpost-en"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.2 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>A Shortcut for Calculating Laser Power Density - Ophir Photonics<\/title>\n<meta name=\"description\" content=\"Here&#039;s a\u00a0laser power density calculator, if that&#039;s what you wanted. 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