{"id":66921,"date":"2026-10-13T10:15:14","date_gmt":"2026-10-13T07:15:14","guid":{"rendered":"https:\/\/wpcalc.com\/en\/?p=66921"},"modified":"2026-10-13T10:15:14","modified_gmt":"2026-10-13T07:15:14","slug":"capillary-rise-calculator","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/chemistry\/capillary-rise-calculator\/","title":{"rendered":"Capillary Rise 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 Capillary Rise from Surface Tension, Density and Tube Radius<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"66921\" data-favorite-title=\"Capillary Rise\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/chemistry\/capillary-rise-calculator\/\" data-favorite-excerpt=\"Calculate how far a liquid rises (or is depressed) in a capillary tube using Jurin&#039;s law. Enter surface tension, liquid density, tube radius, contact angle and gravity to get the capillary rise in mm, cm, m or inches.\" aria-label=\"Add to Favorites\" data-favorite-icon=\"icon icon-molecule\">\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\/chemistry\/capillary-rise-calculator\/\" method=\"POST\" class=\"calculator\" id=\"calculator-66921\" data-post=\"66921\"><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\">Surface Tension (\u03b3)<\/label><div class=\"term\">\u03b3<\/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=\"surface_tension_\" id=\"field-1\" aria-describedby=\"calc-info-1\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 72.8\" min=\"0\" value=\"72.8\"\/><div class=\"grid grid-cols-1\"><select id=\"field-2\" name=\"unit\" aria-label=\"Unit\"><option value=\"mN_m\" selected>mN\/m<\/option><option value=\"N_m\">N\/m<\/option><option value=\"dyn_cm\">dyn\/cm<\/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\">Surface tension of the liquid against air. Water \u2248 72.8 mN\/m, ethanol \u2248 22.3 mN\/m, mercury \u2248 486 mN\/m (all at 20 \u00b0C).<\/small><\/div><div class=\"field has-term\" id=\"input-2\"><label for=\"field-3\">Liquid Density (\u03c1)<\/label><div class=\"term\">\u03c1<\/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=\"liquid_density_\" id=\"field-3\" aria-describedby=\"calc-info-3\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 998\" min=\"0\" value=\"998\"\/><div class=\"grid grid-cols-1\"><select id=\"field-4\" name=\"unit\" aria-label=\"Unit\"><option value=\"kg_m3\" selected>kg\/m\u00b3<\/option><option value=\"g_cm3\">g\/cm\u00b3<\/option><option value=\"lb_ft3\">lb\/ft\u00b3<\/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\">Density of the liquid, not of the surrounding air. Water \u2248 998 kg\/m\u00b3 at 20 \u00b0C, mercury \u2248 13546 kg\/m\u00b3.<\/small><\/div><div class=\"field has-term\" id=\"input-3\"><label for=\"field-5\">Tube Radius (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=\"tube_radius_r\" id=\"field-5\" aria-describedby=\"calc-info-5\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 0.5\" min=\"0\" value=\"0.5\"\/><div class=\"grid grid-cols-1\"><select id=\"field-6\" name=\"unit\" aria-label=\"Unit\"><option value=\"mm\" selected>mm<\/option><option value=\"um\">\u00b5m<\/option><option value=\"cm\">cm<\/option><option value=\"m\">m<\/option><option value=\"in\">in<\/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\">Inner radius of the capillary tube. A 1 mm inner diameter tube has a radius of 0.5 mm.<\/small><\/div><div class=\"field has-term\" id=\"input-4\"><label for=\"field-7\">Contact Angle (\u03b8)<\/label><div class=\"term\">\u03b8<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"contact_angle_\" id=\"field-7\" aria-describedby=\"calc-unit-7 calc-info-7\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 0\" min=\"0\" max=\"180\" value=\"0\"\/><div class=\"unit\" id=\"calc-unit-7\">\u00b0<\/div><small id=\"calc-info-7\">Angle between the liquid surface and the tube wall. Water in clean glass \u2248 0\u00b0 (wetting), mercury in glass \u2248 140\u00b0 (non-wetting, gives a depression).<\/small><\/div><div class=\"field has-term\" id=\"input-5\"><label for=\"field-8\">Gravitational Acceleration (g)<\/label><div class=\"term\">g<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"gravitational_acceleration_g\" id=\"field-8\" aria-describedby=\"calc-unit-8 calc-info-8\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 9.81\" min=\"0\" value=\"9.81\"\/><div class=\"unit\" id=\"calc-unit-8\">m\/s\u00b2<\/div><small id=\"calc-info-8\">Earth \u2248 9.81 m\/s\u00b2, the Moon \u2248 1.62 m\/s\u00b2. A larger g reduces the rise.<\/small><\/div><div class=\"field is-single\" id=\"input-6\"><label for=\"field-9\">Show Capillary Rise in<\/label><div class=\"grid grid-cols-1\"><select id=\"field-9\" name=\"show_capillary_rise_in\"><option value=\"mm\" selected>millimeters (mm)<\/option><option value=\"cm\">centimeters (cm)<\/option><option value=\"m\">meters (m)<\/option><option value=\"in\">inches (in)<\/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><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Re-Calculate\" id=\"calculate-button\" data-post=\"66921\">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> Capillary Rise Results<\/h3><div class=\"result-box\"><div class=\"field-result\" id=\"output-1\"><span class=\"field-title\"><span>Capillary Rise \/ Depression (h)<\/span><span class=\"result-term\">h<\/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>Rise or Depression and Other Units<\/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 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 class=\"field-result is-column\" id=\"output-4\"><span class=\"field-title\"><span>About Capillary Action<\/span><\/span><span class=\"field-value\" id=\"result-4\"><\/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=\"66921\" 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>Capillary Rise<\/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\\[ h = \\frac{2\\,\\gamma\\,\\cos\\theta}{\\rho\\, g\\, r} \\\\\\]\n\\[ \\Delta p = \\frac{2\\,\\gamma\\,\\cos\\theta}{r} \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Where:<\/strong><\/p>\n<ul>\n<li>\\(h\\) \u2014 capillary rise or depression of the liquid column (m)<\/li>\n<li>\\(\\gamma\\) \u2014 surface tension of the liquid against air (N\/m)<\/li>\n<li>\\(\\theta\\) \u2014 contact angle between the liquid and the tube wall (\u00b0)<\/li>\n<li>\\(\\rho\\) \u2014 density of the liquid (kg\/m\u00b3)<\/li>\n<li>\\(g\\) \u2014 gravitational acceleration (m\/s\u00b2)<\/li>\n<li>\\(r\\) \u2014 inner radius of the capillary tube (m)<\/li>\n<\/ul>\n<p>The first equation is <strong>Jurin's law<\/strong>: it follows from balancing the upward capillary force \\(2\\pi r\\,\\gamma\\cos\\theta\\) with the weight \\(\\rho g \\pi r^2 h\\) of the liquid column. The second gives the capillary (Laplace) pressure jump across the curved meniscus that drives the motion.<\/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>Capillary Rise \u2013 Calculation Example<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Example:<\/strong> water at 20 \u00b0C (surface tension 72.8 mN\/m, density 998 kg\/m\u00b3) rises in a clean glass capillary of inner radius 0.5 mm. Water perfectly wets clean glass, so the contact angle is 0\u00b0, and gravity is 9.81 m\/s\u00b2.<\/p>\n<p>\\[ \\gamma = 72.8\\ \\text{mN\/m} = 0.0728\\ \\text{N\/m}, \\quad r = 0.5\\ \\text{mm} = 5\\times10^{-4}\\ \\text{m} \\]<br \/>\n\\[ h = \\frac{2 \\times 0.0728 \\times \\cos 0\u00b0}{998 \\times 9.81 \\times 5\\times10^{-4}} = \\frac{0.1456}{4.895} \\approx 0.02974\\ \\text{m} \\]<br \/>\n\\[ h \\approx 29.74\\ \\text{mm} \\approx 2.97\\ \\text{cm} \\approx 1.17\\ \\text{in} \\]\n<\/p>\n<p><strong>Result:<\/strong> the water rises about <strong>29.74 mm<\/strong> (\u2248 2.97 cm) above the surrounding water level \u2014 exactly what the calculator shows with its default values.<\/p>\n<p>\n\r\n<\/section>\n<h2>How to Use the Capillary Rise Calculator<\/h2>\n<ol>\n<li>Enter the <strong>Surface Tension (\u03b3)<\/strong> of the liquid and pick its unit (mN\/m, N\/m or dyn\/cm). Water at 20 \u00b0C is about 72.8 mN\/m.<\/li>\n<li>Enter the <strong>Liquid Density (\u03c1)<\/strong> and its unit (kg\/m\u00b3, g\/cm\u00b3 or lb\/ft\u00b3). Use the density of the liquid, not of the surrounding air.<\/li>\n<li>Enter the inner <strong>Tube Radius (r)<\/strong> \u2014 remember this is the radius, so a 1 mm inner diameter tube takes 0.5 mm. Choose mm, \u00b5m, cm, m or in.<\/li>\n<li>Set the <strong>Contact Angle (\u03b8)<\/strong> in degrees: 0\u00b0 for water in clean glass, around 140\u00b0 for mercury in glass (which produces a depression instead of a rise).<\/li>\n<li>Adjust the <strong>Gravitational Acceleration (g)<\/strong> if needed; 9.81 m\/s\u00b2 is the Earth default, and 1.62 m\/s\u00b2 approximates the Moon.<\/li>\n<li>Choose the output unit under <strong>Show Capillary Rise in<\/strong> (mm, cm, m or in) \u2014 the rise grows quickly as tubes get narrower, so switch units if the number is unwieldy.<\/li>\n<\/ol>\n<p>The result is signed: a positive value is a rise above the surrounding liquid level, and a negative value is a depression below it.<\/p>\n<h2>What Is Capillary Rise and Why Does It Happen?<\/h2>\n<p>Capillary rise is the phenomenon in which a liquid climbs up a narrow tube (a <em>capillary<\/em>) dipped into it, apparently defying gravity. It is driven by <strong>surface tension<\/strong>: the molecules at the liquid surface pull the meniscus outward along the tube wall, and if the liquid wets the wall (contact angle below 90\u00b0), the meniscus is concave and its curvature generates a pressure deficit that sucks liquid upward. The column stops rising when its weight exactly balances the capillary force \u2014 that balance is Jurin's law.<\/p>\n<p>The most striking feature of the formula is the inverse proportionality to the tube radius: <em>halving the radius doubles the rise<\/em>. Water in a 0.5 mm tube rises only about 3 cm, but in a 10 \u00b5m pore it climbs roughly 1.5 m. This scaling explains why paper towels soak up spills, why wicks and sponges work, and how trees lift water tens of meters through microscopic xylem channels \u2014 capillarity, together with osmosis and transpiration, is one of the key transport mechanisms in plants.<\/p>\n<p>The contact angle determines the direction of the effect. Wetting liquids (\\(\\theta &lt; 90\u00b0\\), water in glass) rise; \\(\\theta = 90\u00b0\\) leaves the surface flat; and non-wetting liquids (\\(\\theta &gt; 90\u00b0\\), mercury in glass) are <strong>depressed<\/strong> below the surrounding level, because \\(\\cos\\theta\\) is negative. The calculator reports the sign automatically and tells you whether you have a rise or a depression. It also shows the radius of curvature of the meniscus (\\(R = r\/\\cos\\theta\\)) and the capillary pressure \\(\\Delta p\\), which is what a porous material or a wick actually \"feels\".<\/p>\n<h2>Assumptions, Limitations and Practical Tips<\/h2>\n<ul>\n<li><strong>Tube geometry:<\/strong> the formula assumes a vertical circular cylinder of uniform radius. Square channels, tapered bores or porous networks only follow it approximately.<\/li>\n<li><strong>Small radius:<\/strong> the meniscus is treated as a perfect spherical cap, which is accurate when the radius is well below the <em>capillary length<\/em> of the liquid (about 2.7 mm for water). Around 1 mm, neglecting the meniscus volume introduces an error of a few percent; below 0.5 mm it is negligible.<\/li>\n<li><strong>Constant contact angle:<\/strong> real surfaces are rarely perfectly clean or uniform, so the effective angle can differ from textbook values. Contamination, grease or surfactants can change \\(\\gamma\\) and \\(\\theta\\) substantially \u2014 adding detergent to water lowers both surface tension and rise.<\/li>\n<li><strong>Static liquid:<\/strong> the result is the equilibrium height; it says nothing about how fast the liquid climbs (which depends on viscosity, via the Washburn equation).<\/li>\n<li><strong>Temperature:<\/strong> both surface tension and density vary with temperature, so use values at the temperature of interest for accurate results.<\/li>\n<\/ul>\n<p>If you are working with other liquid or gas properties, you may also find our <a href=\"https:\/\/wpcalc.com\/en\/chemistry\/gas-density-calculator\/\">Gas Density Calculator<\/a>, the <a href=\"https:\/\/wpcalc.com\/en\/chemistry\/antoine-equation-calculator\/\">Antoine Equation Calculator<\/a> for vapor pressures, or the <a href=\"https:\/\/wpcalc.com\/en\/chemistry\/mean-free-path-of-gas-molecules-calculator\/\">Mean Free Path Calculator<\/a> useful for related transport problems.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Calculate how far a liquid rises (or is depressed) in a capillary tube using Jurin's law. Enter surface tension, liquid density, tube radius, contact angle and gravity to get the capillary rise in mm, cm, m or inches.<\/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":[54],"tags":[61],"class_list":["post-66921","post","type-post","status-publish","format-standard","hentry","category-chemistry","tag-bonding"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66921","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=66921"}],"version-history":[{"count":1,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66921\/revisions"}],"predecessor-version":[{"id":66922,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66921\/revisions\/66922"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=66921"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=66921"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=66921"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}