{"id":66826,"date":"2026-10-15T09:20:31","date_gmt":"2026-10-15T06:20:31","guid":{"rendered":"https:\/\/wpcalc.com\/en\/?p=66826"},"modified":"2026-10-15T09:20:31","modified_gmt":"2026-10-15T06:20:31","slug":"midpoint-calculator","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/mathematics\/midpoint-calculator\/","title":{"rendered":"Midpoint 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 Midpoint of a Segment<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"66826\" data-favorite-title=\"Midpoint\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/mathematics\/midpoint-calculator\/\" data-favorite-excerpt=\"Find the midpoint of a line segment in 2D or 3D. Enter the coordinates of the two endpoints and get the midpoint plus the segment length instantly.\" aria-label=\"Add to Favorites\" data-favorite-icon=\"icon icon-geometry\">\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\/mathematics\/midpoint-calculator\/\" method=\"POST\" class=\"calculator\" id=\"calculator-66826\" data-post=\"66826\"><fieldset class=\"fieldset-input is-2\"><legend class=\"sr-only\">Input Fields<\/legend><div class=\"is-single field\" id=\"input-1\"><span class=\"font-semibold\">Point 1 (x\u2081, y\u2081)<\/span><\/div><div class=\"field has-term\" id=\"input-2\"><label for=\"field-2\">X coordinate<\/label><div class=\"term\">x\u2081<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"number\" name=\"x_coordinate\" id=\"field-2\" aria-describedby=\"calc-info-2\" step=\"any\" value=\"2\"\/><small id=\"calc-info-2\">Horizontal coordinate of the first point.<\/small><\/div><div class=\"field has-term\" id=\"input-3\"><label for=\"field-3\">Y coordinate<\/label><div class=\"term\">y\u2081<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"number\" name=\"y_coordinate\" id=\"field-3\" aria-describedby=\"calc-info-3\" step=\"any\" value=\"3\"\/><small id=\"calc-info-3\">Vertical coordinate of the first point.<\/small><\/div><div class=\"field has-term\" id=\"input-4\" hidden><label for=\"field-4\">Z coordinate<\/label><div class=\"term\">z\u2081<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"number\" name=\"z_coordinate\" id=\"field-4\" aria-describedby=\"calc-info-4\" step=\"any\" value=\"1\"\/><small id=\"calc-info-4\">Depth coordinate of the first point (3D mode).<\/small><\/div><div class=\"is-single field\" id=\"input-5\"><span class=\"font-semibold\">Point 2 (x\u2082, y\u2082)<\/span><\/div><div class=\"field has-term\" id=\"input-6\"><label for=\"field-6\">X coordinate<\/label><div class=\"term\">x\u2082<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"number\" name=\"x_coordinate\" id=\"field-6\" aria-describedby=\"calc-info-6\" step=\"any\" value=\"8\"\/><small id=\"calc-info-6\">Horizontal coordinate of the second point.<\/small><\/div><div class=\"field has-term\" id=\"input-7\"><label for=\"field-7\">Y coordinate<\/label><div class=\"term\">y\u2082<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"number\" name=\"y_coordinate\" id=\"field-7\" aria-describedby=\"calc-info-7\" step=\"any\" value=\"7\"\/><small id=\"calc-info-7\">Vertical coordinate of the second point.<\/small><\/div><div class=\"field has-term\" id=\"input-8\" hidden><label for=\"field-8\">Z coordinate<\/label><div class=\"term\">z\u2082<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"number\" name=\"z_coordinate\" id=\"field-8\" aria-describedby=\"calc-info-8\" step=\"any\" value=\"5\"\/><small id=\"calc-info-8\">Depth coordinate of the second point (3D mode).<\/small><\/div><div class=\"field is-checkbox is-single\" id=\"input-9\"><input type=\"checkbox\" id=\"field-9\" value=\"1\"\/><label for=\"field-9\">Work in 3D (use Z coordinates)<\/label><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Re-Calculate\" id=\"calculate-button\" data-post=\"66826\">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> Your Midpoint<\/h3><div class=\"result-box\"><div class=\"field-result is-column\" id=\"output-1\"><span class=\"field-title\"><span>Midpoint Coordinates<\/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\" id=\"output-2\"><span class=\"field-title\"><span>Midpoint X<\/span><span class=\"result-term\">M\u2093<\/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\" id=\"output-3\"><span class=\"field-title\"><span>Midpoint Y<\/span><span class=\"result-term\">M\u1d67<\/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\" id=\"output-4\"><span class=\"field-title\"><span>Midpoint Z<\/span><span class=\"result-term\">M_z<\/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 class=\"field-result\" id=\"output-5\"><span class=\"field-title\"><span>Segment Length<\/span><\/span><span class=\"field-value\" id=\"result-5\"><\/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=\"66826\" 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>Midpoint 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\\[ M = \\left( \\frac{x_1 + x_2}{2},\\ \\frac{y_1 + y_2}{2} \\right) \\]\n\\[ M = \\left( \\frac{x_1 + x_2}{2},\\ \\frac{y_1 + y_2}{2},\\ \\frac{z_1 + z_2}{2} \\right) \\]<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Where:<\/strong><\/p>\n<ul>\n<li>\\(x_1, y_1, z_1\\) \u2014 coordinates of the first endpoint<\/li>\n<li>\\(x_2, y_2, z_2\\) \u2014 coordinates of the second endpoint<\/li>\n<li>\\(M\\) \u2014 the midpoint of the segment<\/li>\n<\/ul>\n<p>The midpoint is simply the average of each coordinate: add the two values and divide by 2. The first formula works for points in the plane (2D), the second for points in space (3D). The calculator also shows the segment length using the Euclidean distance formula:<\/p>\n<p>\\[ d = \\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \\]\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>Midpoint \u2013 Calculation Example<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Example:<\/strong> find the midpoint of the segment connecting \\(A(2, 3, 1)\\) and \\(B(8, 7, 5)\\) in three-dimensional space.<\/p>\n<p>\\[ M_x = \\frac{2 + 8}{2} = \\frac{10}{2} = 5 \\]<\/p>\n<p>\\[ M_y = \\frac{3 + 7}{2} = \\frac{10}{2} = 5 \\]<\/p>\n<p>\\[ M_z = \\frac{1 + 5}{2} = \\frac{6}{2} = 3 \\]<\/p>\n<p>\\[ d = \\sqrt{(8-2)^2 + (7-3)^2 + (5-1)^2} = \\sqrt{36 + 16 + 16} = \\sqrt{68} \\approx 8.246 \\]<\/p>\n<p><strong>Result:<\/strong> the midpoint is \\(M = (5, 5, 3)\\) and the segment length is approximately 8.246 units.<\/p>\n<p>\n\r\n<\/section>\n<h2>How to use the calculator<\/h2>\n<ol>\n<li>Enter the <strong>X coordinate<\/strong> and <strong>Y coordinate<\/strong> of the first point under \u201cPoint 1 (x\u2081, y\u2081)\u201d.<\/li>\n<li>Enter the <strong>X coordinate<\/strong> and <strong>Y coordinate<\/strong> of the second point under \u201cPoint 2 (x\u2082, y\u2082)\u201d.<\/li>\n<li>If your points are in three-dimensional space, tick <strong>Work in 3D (use Z coordinates)<\/strong> and fill in the <strong>Z coordinate<\/strong> fields for both points. If you leave the box unticked, the Z fields are hidden and only the 2D midpoint is computed.<\/li>\n<li>Read the results: <strong>Midpoint X<\/strong>, <strong>Midpoint Y<\/strong> and, in 3D mode, <strong>Midpoint Z<\/strong> give the coordinates of the midpoint, and <strong>Segment Length<\/strong> gives the straight-line distance between the two points.<\/li>\n<\/ol>\n<h2>What is a midpoint?<\/h2>\n<p>The midpoint of a segment is the point that lies exactly halfway between the two endpoints \u2014 it cuts the segment into two pieces of equal length. In coordinate geometry, you find it by averaging the coordinates: each coordinate of the midpoint is the mean of the corresponding coordinates of the endpoints. Since averaging is just adding and <a href=\"https:\/\/wpcalc.com\/en\/mathematics\/division-calculator\/\">dividing by two<\/a>, the same idea works in two dimensions, three dimensions, or any number of dimensions.<\/p>\n<p>The midpoint has a useful geometric property: it is equidistant from both endpoints, each half of the segment being exactly half the total length. It is also the center of the smallest circle (or sphere, in 3D) that has the segment as a diameter. This makes midpoints a building block for many constructions \u2014 perpendicular bisectors, medians of triangles, centers of rectangles, and finding the middle of a route or an object in space.<\/p>\n<p>Interpreting the result is straightforward: if point \\(A\\) is \\(A(2, 3)\\) and point \\(B\\) is \\(B(8, 7)\\), the midpoint \\(M(5, 5)\\) sits at the same \u201cmiddle\u201d position along both the horizontal and the vertical direction. The segment length shown alongside tells you how far apart the endpoints are, which is often useful when you need both the center and the size of the segment.<\/p>\n<h2>Assumptions, limitations and tips<\/h2>\n<ul>\n<li>The calculator uses the straight-line (Euclidean) distance for the segment length. On a map with real roads, the driving distance between the endpoints will be longer than the straight-line value.<\/li>\n<li>Coordinates can be negative, whole numbers or decimals \u2014 for example, the midpoint of \\((-4, 1)\\) and \\((3, 6)\\) is \\((-0.5, 3.5)\\).<\/li>\n<li>If both endpoints coincide, the midpoint equals that point and the segment length is 0.<\/li>\n<li>The midpoint is a special case of a weighted position: if you need a point that divides a segment in a different ratio (for example 1:2 instead of 1:1), you would weight the coordinates accordingly. The <a href=\"https:\/\/wpcalc.com\/en\/mathematics\/weighted-mean-calculator\/\">weighted mean<\/a> is the general tool for that kind of problem, and a simple <a href=\"https:\/\/wpcalc.com\/en\/mathematics\/average-calculator\/\">average calculator<\/a> handles the underlying arithmetic.<\/li>\n<li>For a quick mental check: the midpoint must always lie between the two endpoints in every coordinate, so its X value must fall between \\(x_1\\) and \\(x_2\\), and similarly for Y (and Z in 3D).<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Find the midpoint of a line segment in 2D or 3D. Enter the coordinates of the two endpoints and get the midpoint plus the segment length instantly.<\/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":[7],"tags":[23],"class_list":["post-66826","post","type-post","status-publish","format-standard","hentry","category-mathematics","tag-geometry"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66826","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=66826"}],"version-history":[{"count":1,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66826\/revisions"}],"predecessor-version":[{"id":67135,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66826\/revisions\/67135"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=66826"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=66826"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=66826"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}