{"id":2908,"date":"2026-10-20T12:32:12","date_gmt":"2026-10-20T11:32:12","guid":{"rendered":"https:\/\/wpcalc.com\/pl\/matematyka\/kalkulator-objetosci-walca\/"},"modified":"2026-10-20T12:32:12","modified_gmt":"2026-10-20T11:32:12","slug":"kalkulator-objetosci-walca","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/pl\/matematyka\/kalkulator-objetosci-walca\/","title":{"rendered":"Kalkulator obj\u0119to\u015bci walca"},"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\">Obliczanie obj\u0119to\u015bci, wymiar\u00f3w i pola powierzchni walca<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"2908\" data-favorite-title=\"Obj\u0119to\u015b\u0107 walca\" data-favorite-url=\"https:\/\/wpcalc.com\/pl\/matematyka\/kalkulator-objetosci-walca\/\" data-favorite-excerpt=\"Oblicz obj\u0119to\u015b\u0107, wysoko\u015b\u0107 albo promie\u0144 walca pe\u0142nego lub pustego. Wpisz jego wymiary lub znan\u0105 obj\u0119to\u015b\u0107, wybierz jednostk\u0119 d\u0142ugo\u015bci i zobacz pola powierzchni oraz przeliczenia obj\u0119to\u015bci.\" aria-label=\"Dodaj do ulubionych\" 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\/pl\/matematyka\/kalkulator-objetosci-walca\/\" method=\"POST\" class=\"calculator\" id=\"calculator-2908\" data-post=\"2908\"><fieldset class=\"fieldset-input is-2\"><legend class=\"sr-only\">Pola danych<\/legend><div class=\"field\" id=\"input-1\"><label for=\"field-1\">Oblicz<\/label><div class=\"grid grid-cols-1\"><select id=\"field-1\" name=\"oblicz\"><option value=\"volume\" selected>Obj\u0119to\u015b\u0107<\/option><option value=\"height\">Wysoko\u015b\u0107 z obj\u0119to\u015bci<\/option><option value=\"radius\">Promie\u0144 z obj\u0119to\u015bci i wysoko\u015bci<\/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><div class=\"field\" id=\"input-2\"><label for=\"field-2\">Rodzaj walca<\/label><div class=\"grid grid-cols-1\"><select id=\"field-2\" name=\"rodzaj_walca\"><option value=\"solid\" selected>Walec pe\u0142ny<\/option><option value=\"hollow\">Walec dr\u0105\u017cony (rura)<\/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><div class=\"field\" id=\"input-3\"><label for=\"field-3\">Wymiar walca pe\u0142nego<\/label><div class=\"grid grid-cols-1\"><select id=\"field-3\" name=\"wymiar_walca_penego\"><option value=\"radius\" selected>Promie\u0144<\/option><option value=\"diameter\">\u015arednica<\/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><div class=\"field has-term\" id=\"input-4\"><label for=\"field-4\">Promie\u0144 (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><input type=\"text\" name=\"promie_r\" id=\"field-4\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0\" value=\"5\"\/><\/div><div class=\"field has-term\" id=\"input-5\" hidden><label for=\"field-5\">\u015arednica (d)<\/label><div class=\"term\">d<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"rednica_d\" id=\"field-5\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0\" value=\"10\"\/><\/div><div class=\"field has-term\" id=\"input-6\" hidden><label for=\"field-6\">\u015arednica zewn\u0119trzna (D)<\/label><div class=\"term\">D<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"rednica_zewntrzna_d\" id=\"field-6\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0\" value=\"10\"\/><\/div><div class=\"field has-term\" id=\"input-7\" hidden><label for=\"field-7\">\u015arednica wewn\u0119trzna (d)<\/label><div class=\"term\">d<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"rednica_wewntrzna_d\" id=\"field-7\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0\" value=\"6\"\/><\/div><div class=\"field has-term\" id=\"input-8\"><label for=\"field-8\">Wysoko\u015b\u0107 (h)<\/label><div class=\"term\">h<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"wysoko_h\" id=\"field-8\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0\" value=\"12\"\/><\/div><div class=\"field has-term\" id=\"input-9\" hidden><label for=\"field-9\">Znana obj\u0119to\u015b\u0107 (V)<\/label><div class=\"term\">V<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"znana_objto_v\" id=\"field-9\" aria-describedby=\"calc-info-9\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0\" value=\"1000\"\/><small id=\"calc-info-9\">Wpisz obj\u0119to\u015b\u0107 w jednostce sze\u015bciennej wybranej poni\u017cej.<\/small><\/div><div class=\"field\" id=\"input-10\"><label for=\"field-10\">Jednostka d\u0142ugo\u015bci<\/label><div class=\"grid grid-cols-1\"><select id=\"field-10\" name=\"jednostka_dugoci\"><option value=\"mm\">Milimetry (mm)<\/option><option value=\"cm\" selected>Centymetry (cm)<\/option><option value=\"m\">Metry (m)<\/option><option value=\"in\">Cale (in)<\/option><option value=\"ft\">Stopy (ft)<\/option><option value=\"yd\">Jardy (yd)<\/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=\"Przelicz ponownie\" id=\"calculate-button\" data-post=\"2908\">Oblicz<\/button><button type=\"reset\">Wyczy\u015b\u0107<\/button><\/div><div class=\"field is-checkbox hidden!\" id=\"field-auto-calc\"><input type=\"checkbox\" id=\"auto-calc\"><label for=\"auto-calc\">Obliczaj automatycznie<\/label><small>Po w\u0142\u0105czeniu wynik aktualizuje si\u0119 automatycznie po zmianie dowolnej warto\u015bci.<\/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> Wyniki dla walca<\/h3><div class=\"result-box\"><div class=\"field-result\" id=\"output-1\"><span class=\"field-title\"><span>Obj\u0119to\u015b\u0107<\/span><span class=\"result-term\">V<\/span><\/span><span class=\"field-value\" id=\"result-1\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Kopiuj wynik\" aria-label=\"Kopiuj wynik\"><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>Obj\u0119to\u015b\u0107 w litrach<\/span><\/span><span class=\"field-value\" id=\"result-2\" data-unit=\"L\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Kopiuj wynik\" aria-label=\"Kopiuj wynik\"><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>Obj\u0119to\u015b\u0107 w galonach ameryka\u0144skich<\/span><\/span><span class=\"field-value\" id=\"result-3\" data-unit=\"US gal\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Kopiuj wynik\" aria-label=\"Kopiuj wynik\"><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>Obj\u0119to\u015b\u0107 w stopach sze\u015bciennych<\/span><\/span><span class=\"field-value\" id=\"result-4\" data-unit=\"ft\u00b3\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Kopiuj wynik\" aria-label=\"Kopiuj wynik\"><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>Obj\u0119to\u015b\u0107 w metrach sze\u015bciennych<\/span><\/span><span class=\"field-value\" id=\"result-5\" data-unit=\"m\u00b3\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Kopiuj wynik\" aria-label=\"Kopiuj wynik\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-6\"><span class=\"field-title\"><span>Pole powierzchni bocznej<\/span><span class=\"result-term\">A\u2097<\/span><\/span><span class=\"field-value\" id=\"result-6\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Kopiuj wynik\" aria-label=\"Kopiuj wynik\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-7\"><span class=\"field-title\"><span>Pole powierzchni ca\u0142kowitej<\/span><span class=\"result-term\">A\u209c<\/span><\/span><span class=\"field-value\" id=\"result-7\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Kopiuj wynik\" aria-label=\"Kopiuj wynik\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-8\"><span class=\"field-title\"><span>Promie\u0144 (promie\u0144 zewn\u0119trzny dla rury)<\/span><span class=\"result-term\">R<\/span><\/span><span class=\"field-value\" id=\"result-8\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Kopiuj wynik\" aria-label=\"Kopiuj wynik\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-9\"><span class=\"field-title\"><span>\u015arednica (\u015brednica zewn\u0119trzna dla rury)<\/span><span class=\"result-term\">D<\/span><\/span><span class=\"field-value\" id=\"result-9\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Kopiuj wynik\" aria-label=\"Kopiuj wynik\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-10\"><span class=\"field-title\"><span>Wysoko\u015b\u0107<\/span><span class=\"result-term\">h<\/span><\/span><span class=\"field-value\" id=\"result-10\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Kopiuj wynik\" aria-label=\"Kopiuj wynik\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result is-column\" id=\"output-11\"><span class=\"field-title\"><span>Wz\u00f3r z Twoimi wymiarami<\/span><\/span><span class=\"field-value\" id=\"result-11\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Kopiuj wynik\" aria-label=\"Kopiuj wynik\"><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\">Kopiuj link do tego obliczenia<\/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>Zostaw komentarz<\/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=\"2908\" aria-live=\"polite\" aria-labelledby=\"calc-reactions-title\"><p id=\"calc-reactions-title\" class=\"text-sm text-gray-500 text-center mb-2\">Jak oceniasz ten wynik?<\/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\">Lubi\u0119 to <\/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\">Pomocne <\/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\">Niejasne <\/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\">Rozczarowanie <\/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\">Niedok\u0142adne <\/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>Wz\u00f3r na obj\u0119to\u015b\u0107 walca<\/h2><\/div>\r\n\t<figure class=\"not-prose formula\">\r\n\t\t<figcaption class=\"formula-title\">Wz\u00f3r<\/figcaption>\r\n\t\t<div class=\"text-base text-gray-800\" id=\"formula\">\n\\[\\begin{aligned}V_{\\text{pe\u0142ny}}&amp;=\\pi r^{2}h &amp; V_{\\text{pusty}}&amp;=\\pi(R^{2}-r^{2})h\\\\h&amp;=\\frac{V}{\\pi r^{2}}\\ \\text{(pe\u0142ny)} &amp; h&amp;=\\frac{V}{\\pi(R^{2}-r^{2})}\\ \\text{(pusty)}\\\\r&amp;=\\sqrt{\\frac{V}{\\pi h}}\\ \\text{(pe\u0142ny)} &amp; R&amp;=\\sqrt{\\frac{V}{\\pi h}+r^{2}}\\ \\text{(pusty)}\\\\A_{\\mathrm{l,solid}}&amp;=2\\pi rh &amp; A_{\\mathrm{l,hollow}}&amp;=2\\pi h(R+r)\\\\A_{\\mathrm{t,solid}}&amp;=A_{\\mathrm{l,solid}}+2\\pi r^{2} &amp; A_{\\mathrm{t,hollow}}&amp;=A_{\\mathrm{l,hollow}}+2\\pi(R^{2}-r^{2})\\end{aligned}\\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Gdzie:<\/strong><\/p>\n<ul>\n<li>\\(V\\) \u2014 obj\u0119to\u015b\u0107 walca, w jednostkach sze\u015bciennych<\/li>\n<li>\\(r\\) \u2014 promie\u0144 walca pe\u0142nego albo promie\u0144 wewn\u0119trzny walca pustego<\/li>\n<li>\\(R\\) \u2014 promie\u0144 zewn\u0119trzny walca pustego<\/li>\n<li>\\(h\\) \u2014 wysoko\u015b\u0107 walca<\/li>\n<li>\\(A_{\\mathrm{l}}\\) \u2014 pole powierzchni bocznej, w jednostkach kwadratowych<\/li>\n<li>\\(A_{\\mathrm{t}}\\) \u2014 pole powierzchni ca\u0142kowitej, w jednostkach kwadratowych<\/li>\n<\/ul>\n<p>Obj\u0119to\u015b\u0107 to pole przekroju \u2014 ko\u0142a albo pier\u015bcienia \u2014 pomno\u017cone przez wysoko\u015b\u0107. Dla walca pustego wynik odpowiada obj\u0119to\u015bci materia\u0142u mi\u0119dzy jego powierzchni\u0105 wewn\u0119trzn\u0105 a zewn\u0119trzn\u0105, a nie obj\u0119to\u015bci pustej przestrzeni w \u015brodku.<\/p>\n<p>\r\n<\/section>\n<style id=\"wpcoderpro-inline-2\">.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>Obj\u0119to\u015b\u0107 walca \u2013 przyk\u0142ad obliczenia<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Przyk\u0142ad:<\/strong> przy ustawieniach domy\u015blnych oblicz obj\u0119to\u015b\u0107 walca pe\u0142nego o promieniu 5 cm i wysoko\u015bci 12 cm.<\/p>\n<p>\\[V=\\pi r^{2}h=\\pi(5\\ \\mathrm{cm})^{2}(12\\ \\mathrm{cm})=300\\pi\\ \\mathrm{cm}^{3}\\approx942.477796\\ \\mathrm{cm}^{3}\\]<\/p>\n<p>Pole powierzchni bocznej wynosi \\(2\\pi(5)(12)=120\\pi\\approx376.991118\\ \\mathrm{cm}^{2}\\). Po doliczeniu obu ko\u0142owych podstaw pole powierzchni ca\u0142kowitej wynosi \\(170\\pi\\approx534.070751\\ \\mathrm{cm}^{2}\\).<\/p>\n<p><strong>Wynik:<\/strong> obj\u0119to\u015b\u0107 wynosi oko\u0142o 942,478 cm\u00b3, czyli 0,942478 l.<\/p>\n<p>\n\r\n<\/section>\n<h2>Jak korzysta\u0107 z kalkulatora<\/h2>\n<ol>\n<li>W sekcji <strong>Oblicz<\/strong> wybierz <strong>Obj\u0119to\u015b\u0107<\/strong>, <strong>Wysoko\u015b\u0107 z obj\u0119to\u015bci<\/strong> albo <strong>Promie\u0144 z obj\u0119to\u015bci i wysoko\u015bci<\/strong>. Kalkulator poka\u017ce pola potrzebne do wybranego trybu.<\/li>\n<li>Wybierz <strong>Typ walca<\/strong>: <strong>Walec pe\u0142ny<\/strong> przy pe\u0142nym przekroju ko\u0142owym albo <strong>Walec pusty (rura)<\/strong> przy przekroju pier\u015bcieniowym.<\/li>\n<li>Gdy dla walca pe\u0142nego obliczasz obj\u0119to\u015b\u0107 lub wysoko\u015b\u0107, wybierz w polu <strong>Pomiar walca pe\u0142nego<\/strong> opcj\u0119 <strong>Promie\u0144<\/strong> lub <strong>\u015arednica<\/strong>, a nast\u0119pnie wpisz <strong>Promie\u0144 (r)<\/strong> albo <strong>\u015arednic\u0119 (d)<\/strong>. Dla walca pustego wpisz <strong>\u015arednic\u0119 zewn\u0119trzn\u0105 (D)<\/strong> i <strong>\u015arednic\u0119 wewn\u0119trzn\u0105 (d)<\/strong>, gdy te pola si\u0119 pojawi\u0105. \u015arednica zewn\u0119trzna musi by\u0107 wi\u0119ksza od wewn\u0119trznej.<\/li>\n<li>Wpisz <strong>Wysoko\u015b\u0107 (h)<\/strong> przy obliczaniu obj\u0119to\u015bci lub promienia. Wpisz <strong>Znan\u0105 obj\u0119to\u015b\u0107 (V)<\/strong> przy obliczaniu wysoko\u015bci lub promienia. Aby wyznaczy\u0107 promie\u0144 zewn\u0119trzny rury, podaj tak\u017ce jej <strong>\u015arednic\u0119 wewn\u0119trzn\u0105 (d)<\/strong>.<\/li>\n<li>Wybierz <strong>Jednostk\u0119 d\u0142ugo\u015bci<\/strong>. Wszystkie wpisane d\u0142ugo\u015bci b\u0119d\u0105 wyra\u017cone w tej jednostce, a <strong>Znana obj\u0119to\u015b\u0107 (V)<\/strong> \u2014 w odpowiadaj\u0105cej jej jednostce sze\u015bciennej, na przyk\u0142ad cm i cm\u00b3. Obliczony wymiar, obj\u0119to\u015b\u0107, pola powierzchni i przeliczenia znajdziesz w sekcji <strong>Wyniki dla walca<\/strong>.<\/li>\n<\/ol>\n<h2>Co m\u00f3wi obj\u0119to\u015b\u0107 walca<\/h2>\n<p>Obj\u0119to\u015b\u0107 walca to miara przestrzeni tr\u00f3jwymiarowej. Dla walca pe\u0142nego wyobra\u017a sobie identyczne przekroje ko\u0142owe u\u0142o\u017cone jeden na drugim wzd\u0142u\u017c wysoko\u015bci: ka\u017cdy ma pole \\(\\pi r^{2}\\), wi\u0119c po pomno\u017ceniu przez wysoko\u015b\u0107 otrzymujemy \\(\\pi r^{2}h\\). \u015arednica rozci\u0105ga si\u0119 na ca\u0142\u0105 szeroko\u015b\u0107 ko\u0142a i jest dwa razy wi\u0119ksza od promienia. Gdy podasz \u015brednic\u0119, kalkulator podzieli j\u0105 przez dwa, zanim u\u017cyje promienia we wzorze.<\/p>\n<p>Walec pusty ma materia\u0142 wok\u00f3\u0142 pustego \u015brodka. Jego przekr\u00f3j jest pier\u015bcieniem, wi\u0119c przed pomno\u017ceniem przez wysoko\u015b\u0107 trzeba od pola ko\u0142a zewn\u0119trznego odj\u0105\u0107 pole ko\u0142a wewn\u0119trznego. To rozr\u00f3\u017cnienie ma znaczenie, gdy szacujesz ilo\u015b\u0107 materia\u0142u w rurze. Je\u017celi natomiast potrzebujesz przestrzeni <em>wewn\u0105trz<\/em> rury, oblicz \\(\\pi r^{2}h\\&gt; h\\) z jej promieniem wewn\u0119trznym i odpowiedni\u0105 d\u0142ugo\u015bci\u0105 wewn\u0119trzn\u0105; wy\u015bwietlana obj\u0119to\u015b\u0107 walca pustego nie odpowiada tej pojemno\u015bci.<\/p>\n<p>Mo\u017cna te\u017c liczy\u0107 w drug\u0105 stron\u0119 \u2014 od znanej obj\u0119to\u015bci. Wybierz <strong>Wysoko\u015b\u0107 z obj\u0119to\u015bci<\/strong>, aby znale\u017a\u0107 wysoko\u015b\u0107 potrzebn\u0105 przy zadanym przekroju, albo <strong>Promie\u0144 z obj\u0119to\u015bci i wysoko\u015bci<\/strong>, aby wyznaczy\u0107 promie\u0144 walca pe\u0142nego lub <em>promie\u0144 zewn\u0119trzny<\/em> rury. Wynik obejmuje tak\u017ce obj\u0119to\u015b\u0107 w litrach, galonach ameryka\u0144skich, stopach sze\u015bciennych i metrach sze\u015bciennych, niezale\u017cnie od wybranej jednostki d\u0142ugo\u015bci. Podstawowy wynik pozostaje w jednostce sze\u015bciennej odpowiadaj\u0105cej twojemu wyborowi.<\/p>\n<h2>Pole powierzchni i wskaz\u00f3wki pomiarowe<\/h2>\n<p><strong>Pole powierzchni bocznej<\/strong> to obszar zakrzywionej strony bocznej. Dla walca pe\u0142nego obejmuje tylko zakrzywion\u0105 powierzchni\u0119 zewn\u0119trzn\u0105, a dla walca pustego \u2014 zar\u00f3wno powierzchni\u0119 zewn\u0119trzn\u0105, jak i wewn\u0119trzn\u0105. <strong>Pole powierzchni ca\u0142kowitej<\/strong> dolicza dwie ko\u0142owe podstawy walca pe\u0142nego albo dwa pier\u015bcieniowe ko\u0144ce rury. To wielko\u015bci geometryczne; to, czy w rzeczywistym obiekcie dane powierzchnie s\u0105 ods\u0142oni\u0119te, zakryte czy po\u0142\u0105czone, mo\u017ce zmieni\u0107 pole, kt\u00f3rego faktycznie potrzebujesz. Je\u015bli zale\u017cy Ci g\u0142\u00f3wnie na powierzchni, si\u0119gnij po <a href=\"https:\/\/wpcalc.com\/pl\/matematyka\/pole-powierzchni-walca\/\">Kalkulator pola powierzchni walca<\/a>.<\/p>\n<p>Podawaj dodatnie wymiary i u\u017cywaj jednej jednostki dla wszystkich d\u0142ugo\u015bci \u2014 na przyk\u0142ad przelicz milimetry na centymetry przed wpisaniem wymiar\u00f3w, je\u015bli wysoko\u015b\u0107 masz podan\u0105 w centymetrach. Wymiary powinny opisywa\u0107 prosty walec o sta\u0142ych przekrojach ko\u0142owych; zw\u0119\u017caj\u0105cy si\u0119 pojemnik lepiej opisa\u0107 za pomoc\u0105 <a href=\"https:\/\/wpcalc.com\/pl\/matematyka\/objetosc-i-pole-stozka\/\">Kalkulatora obj\u0119to\u015bci i pola powierzchni sto\u017cka<\/a>. Dla bry\u0142y kulastej u\u017cyj zamiast tego <a href=\"https:\/\/wpcalc.com\/en\/mathematics\/sphere-volume-and-surface-area-calculator\/\">Kalkulatora obj\u0119to\u015bci i pola powierzchni kuli<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Oblicz obj\u0119to\u015b\u0107, wysoko\u015b\u0107 albo promie\u0144 walca pe\u0142nego lub pustego. Wpisz jego wymiary lub znan\u0105 obj\u0119to\u015b\u0107, wybierz jednostk\u0119 d\u0142ugo\u015bci i zobacz pola powierzchni oraz przeliczenia obj\u0119to\u015bci.<\/p>\n","protected":false},"author":3168,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[6],"tags":[41],"class_list":["post-2908","post","type-post","status-publish","format-standard","hentry","category-matematyka","tag-geometria"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/posts\/2908","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/users\/3168"}],"replies":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/comments?post=2908"}],"version-history":[{"count":0,"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/posts\/2908\/revisions"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/media?parent=2908"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/categories?post=2908"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/tags?post=2908"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}