{"id":2552,"date":"2026-10-14T17:44:09","date_gmt":"2026-10-14T16:44:09","guid":{"rendered":"https:\/\/wpcalc.com\/pl\/matematyka\/kalkulator-kola\/"},"modified":"2026-10-14T17:44:09","modified_gmt":"2026-10-14T16:44:09","slug":"kalkulator-kola","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/pl\/matematyka\/kalkulator-kola\/","title":{"rendered":"Kalkulator ko\u0142a"},"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\">Oblicz wymiary ko\u0142a na podstawie jednej znanej warto\u015bci<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"2552\" data-favorite-title=\"Ko\u0142o\" data-favorite-url=\"https:\/\/wpcalc.com\/pl\/matematyka\/kalkulator-kola\/\" data-favorite-excerpt=\"Wpisz jedn\u0105 znan\u0105 warto\u015b\u0107 \u2013 promie\u0144, \u015brednic\u0119, obw\u00f3d lub pole \u2013 i natychmiast otrzymaj wszystkie pozosta\u0142e wymiary ko\u0142a. Wybierz odpowiedni\u0105 jednostk\u0119, a reszt\u0105 zajmie si\u0119 kalkulator.\" 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-kola\/\" method=\"POST\" class=\"calculator\" id=\"calculator-2552\" data-post=\"2552\"><fieldset class=\"fieldset-input is-1\"><legend class=\"sr-only\">Pola danych<\/legend><div class=\"field\" id=\"input-1\"><label for=\"field-1\">Znam<\/label><div class=\"grid grid-cols-1\"><select id=\"field-1\" name=\"znam\"><option value=\"r\" selected>Promie\u0144<\/option><option value=\"d\">\u015arednica<\/option><option value=\"c\">Obw\u00f3d<\/option><option value=\"a\">Pole<\/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-2\"><label for=\"field-2\">Promie\u0144<\/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=\"promie\" id=\"field-2\" aria-describedby=\"calc-info-2\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 5\" min=\"0\" value=\"5\"\/><div class=\"grid grid-cols-1\"><select id=\"field-3\" name=\"jednostka\" aria-label=\"Jednostka\"><option value=\"m\" selected>m<\/option><option value=\"cm\">cm<\/option><option value=\"mm\">mm<\/option><option value=\"ft\">ft<\/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-2\">Odleg\u0142o\u015b\u0107 od \u015brodka do brzegu ko\u0142a.<\/small><\/div><div class=\"field has-term\" id=\"input-3\" hidden><label for=\"field-4\">\u015arednica<\/label><div class=\"term\">d<\/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=\"rednica\" id=\"field-4\" aria-describedby=\"calc-info-4\" 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-5\" name=\"jednostka\" aria-label=\"Jednostka\"><option value=\"m\" selected>m<\/option><option value=\"cm\">cm<\/option><option value=\"mm\">mm<\/option><option value=\"ft\">ft<\/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-4\">Odleg\u0142o\u015b\u0107 mi\u0119dzy brzegami ko\u0142a mierzona przez jego \u015brodek.<\/small><\/div><div class=\"field has-term\" id=\"input-4\" hidden><label for=\"field-6\">Obw\u00f3d<\/label><div class=\"term\">C<\/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=\"obwd\" id=\"field-6\" aria-describedby=\"calc-info-6\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 31.4159\" min=\"0\" value=\"31.4159\"\/><div class=\"grid grid-cols-1\"><select id=\"field-7\" name=\"jednostka\" aria-label=\"Jednostka\"><option value=\"m\" selected>m<\/option><option value=\"cm\">cm<\/option><option value=\"mm\">mm<\/option><option value=\"ft\">ft<\/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-6\">Obw\u00f3d \u2014 d\u0142ugo\u015b\u0107 linii okalaj\u0105cej ko\u0142o.<\/small><\/div><div class=\"field has-term\" id=\"input-5\" hidden><label for=\"field-8\">Pole<\/label><div class=\"term\">A<\/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=\"pole\" id=\"field-8\" aria-describedby=\"calc-info-8\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 78.5398\" min=\"0\" value=\"78.5398\"\/><div class=\"grid grid-cols-1\"><select id=\"field-9\" name=\"jednostka\" aria-label=\"Jednostka\"><option value=\"m2\" selected>m\u00b2<\/option><option value=\"cm2\">cm\u00b2<\/option><option value=\"mm2\">mm\u00b2<\/option><option value=\"ft2\">ft\u00b2<\/option><option value=\"in2\">in\u00b2<\/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-8\">Powierzchnia zawarta wewn\u0105trz ko\u0142a.<\/small><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Przelicz ponownie\" id=\"calculate-button\" data-post=\"2552\">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> Twoje ko\u0142o<\/h3><div class=\"result-box\"><div class=\"field-result\" id=\"output-1\"><span class=\"field-title\"><span>Promie\u0144<\/span><span class=\"result-term\">r<\/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>\u015arednica<\/span><span class=\"result-term\">d<\/span><\/span><span class=\"field-value\" id=\"result-2\"><\/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>Obw\u00f3d<\/span><span class=\"result-term\">C<\/span><\/span><span class=\"field-value\" id=\"result-3\"><\/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>Pole<\/span><span class=\"result-term\">A<\/span><\/span><span class=\"field-value\" id=\"result-4\"><\/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=\"2552\" 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>Wzory na ko\u0142o<\/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\\[ d = 2r, \\quad C = 2\\pi r, \\quad A = \\pi r^2 \\]\n\\[ r = \\frac{d}{2}, \\quad r = \\frac{C}{2\\pi}, \\quad r = \\sqrt{\\frac{A}{\\pi}} \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>gdzie:<\/strong><\/p>\n<ul>\n<li>\\(r\\) \u2014 promie\u0144 (odleg\u0142o\u015b\u0107 od \u015brodka do brzegu ko\u0142a)<\/li>\n<li>\\(d\\) \u2014 \u015brednica (odleg\u0142o\u015b\u0107 przez \u015brodek ko\u0142a od brzegu do brzegu)<\/li>\n<li>\\(C\\) \u2014 obw\u00f3d (d\u0142ugo\u015b\u0107 okr\u0119gu)<\/li>\n<li>\\(A\\) \u2014 pole (powierzchnia zawarta wewn\u0105trz ko\u0142a)<\/li>\n<li>\\(\\pi \\approx 3{,}14159\\) \u2014 sta\u0142a \u03c0<\/li>\n<\/ul>\n<p>Wszystkie cztery wielko\u015bci opisuj\u0105ce ko\u0142o zale\u017c\u0105 od jednej warto\u015bci \u2014 promienia. Pierwszy wiersz wzor\u00f3w pozwala obliczy\u0107 \u015brednic\u0119, obw\u00f3d i pole, gdy znany jest promie\u0144; drugi wiersz wyznacza promie\u0144 ze \u015brednicy, obwodu lub pola, a z niego wynikaj\u0105 ju\u017c wszystkie pozosta\u0142e warto\u015bci.<\/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>Ko\u0142o \u2013 przyk\u0142ad obliczenia<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Przyk\u0142ad:<\/strong> ko\u0142o ma promie\u0144 r\u00f3wny 5 m. Oblicz jego \u015brednic\u0119, obw\u00f3d i pole.<\/p>\n<p>\\[ d = 2r = 2 \\times 5 = 10 \\ \\text{m} \\]<\/p>\n<p>\\[ C = 2\\pi r = 2\\pi \\times 5 \\approx 31.4159 \\ \\text{m} \\]<\/p>\n<p>\\[ A = \\pi r^2 = \\pi \\times 5^2 \\approx 78.5398 \\ \\text{m}^2 \\]<\/p>\n<p><strong>Wynik:<\/strong> \u015brednica \\(d = 10\\) m, obw\u00f3d \\(C \\approx 31{,}4159\\) m, pole \\(A \\approx 78{,}5398\\) m\u00b2.<\/p>\n<p>\n\r\n<\/section>\n<h2>Jak korzysta\u0107 z kalkulatora ko\u0142a<\/h2>\n<ol>\n<li>Na li\u015bcie rozwijanej <strong>\u201eZnam\u201d<\/strong> wybierz warto\u015b\u0107, kt\u00f3r\u0105 ju\u017c znasz: promie\u0144, \u015brednic\u0119, obw\u00f3d lub pole.<\/li>\n<li>Wpisz znan\u0105 warto\u015b\u0107 w pojawiaj\u0105cym si\u0119 polu \u2014 promie\u0144, \u015brednic\u0119, obw\u00f3d lub pole.<\/li>\n<li>Wybierz <strong>jednostk\u0119<\/strong> z listy obok pola wprowadzania: m, cm, mm, ft lub in (dla pola: m\u00b2, cm\u00b2, mm\u00b2, ft\u00b2 lub in\u00b2).<\/li>\n<li>Odczytaj wyniki w sekcji <strong>\u201eTwoje ko\u0142o\u201d<\/strong>: promie\u0144, \u015brednic\u0119, obw\u00f3d i pole, wszystkie wyra\u017cone w wybranej jednostce.<\/li>\n<\/ol>\n<h2>Czym jest ko\u0142o i dlaczego te warto\u015bci s\u0105 istotne<\/h2>\n<p>Ko\u0142o to zbi\u00f3r wszystkich punkt\u00f3w na p\u0142aszczy\u017anie, kt\u00f3re le\u017c\u0105 w sta\u0142ej odleg\u0142o\u015bci \u2014 r\u00f3wnej promieniowi \u2014 od punktu centralnego. Cztery wielko\u015bci opisuj\u0105 je w pe\u0142ni: promie\u0144 \\(r\\), \u015brednica \\(d\\), obw\u00f3d \\(C\\) i pole \\(A\\). Poniewa\u017c wszystkie s\u0105 ze sob\u0105 powi\u0105zane przez \\(\\pi\\), znajomo\u015b\u0107 dowolnej z nich wystarcza do wyznaczenia pozosta\u0142ych trzech. W\u0142a\u015bnie to robi ten kalkulator: zamienia jedn\u0105 znan\u0105 warto\u015b\u0107 na kompletny zestaw wymiar\u00f3w ko\u0142a.<\/p>\n<p>Te zale\u017cno\u015bci warto zapami\u0119ta\u0107. \u015arednica to po prostu podwojony promie\u0144, czyli \\(d = 2r\\). Obw\u00f3d \u2014 dystans, kt\u00f3ry pokonaliby\u015bmy, id\u0105c raz dooko\u0142a ko\u0142a \u2014 to \\(C = 2\\pi r\\). To zreszt\u0105 sama definicja \\(\\pi\\): stosunek obwodu ka\u017cdego ko\u0142a do jego \u015brednicy. Pole zawarte wewn\u0105trz ko\u0142a to \\(A = \\pi r^2\\), dlatego podwojenie promienia zwi\u0119ksza pole czterokrotnie \u2014 co wielu osobom zaskakuje przy planowaniu staw\u00f3w, doborze rur, pizzy czy okr\u0105g\u0142ych sto\u0142\u00f3w.<\/p>\n<p>Interpretacja wynik\u00f3w jest prosta, ale pami\u0119taj o jednostkach. Wielko\u015bci liniowe (promie\u0144, \u015brednica, obw\u00f3d) wyra\u017cane s\u0105 w wybranej jednostce, a pole \u2014 w jej kwadracie. Na przyk\u0142ad przy promieniu podanym w cm pole wyjdzie w cm\u00b2. Kalkulator przelicza wszystko wewn\u0119trznie, wi\u0119c mo\u017cesz poda\u0107 obw\u00f3d w calach i nadal otrzyma\u0107 wszystkie wyniki w calach.<\/p>\n<h2>Obliczenia wstecz na podstawie obwodu lub pola<\/h2>\n<p>Dwa z wzor\u00f3w \u201ewstecznych\u201d zas\u0142uguj\u0105 na bli\u017csze spojrzenie. Je\u015bli znasz obw\u00f3d \u2014 powiedzmy, \u017ce zmierzy\u0142e\u015b miark\u0105 obw\u00f3d pnia drzewa albo rury \u2014 promie\u0144 wynosi \\(r = C\/(2\\pi)\\), czyli to jedno <a href=\"https:\/\/wpcalc.com\/pl\/matematyka\/kalkulator-dzielenia\/\">dzielenie<\/a> przez oko\u0142o 6,2832. Je\u015bli znasz pole, promie\u0144 to \\(r = \\sqrt{A\/\\pi}\\); a gdy potrzebujesz og\u00f3lnego pierwiastka z liczby, a nie tylko pierwiastka kwadratowego, przyda si\u0119 <a href=\"https:\/\/wpcalc.com\/pl\/matematyka\/pierwiastek-n-stopnia\/\">kalkulator pierwiastka n-tego stopnia<\/a>. Kalkulator ko\u0142a stosuje te wzory automatycznie, a nast\u0119pnie wyznacza pozosta\u0142e warto\u015bci.<\/p>\n<h2>Za\u0142o\u017cenia i praktyczne wskaz\u00f3wki<\/h2>\n<ul>\n<li><strong>Tylko idealne ko\u0142a.<\/strong> Wzory zak\u0142adaj\u0105 idealne ko\u0142o. Owale, elipsy i \u201emniej wi\u0119cej okr\u0105g\u0142e\u201d przedmioty z \u017cycia codziennego daj\u0105 jedynie wyniki przybli\u017cone.<\/li>\n<li><strong>Warto\u015bci dodatnie.<\/strong> Promie\u0144, \u015brednica, obw\u00f3d i pole musz\u0105 by\u0107 wi\u0119ksze od zera; kalkulator odrzuca zera i warto\u015bci ujemne.<\/li>\n<li><strong>Precyzja.<\/strong> Wyniki s\u0105 zaokr\u0105glane do 4 miejsc po przecinku. Kalkulator u\u017cywa wewn\u0119trznie pe\u0142nej precyzji \\(\\pi\\), wi\u0119c zaokr\u0105glenie dotyczy tylko wy\u015bwietlanych warto\u015bci, a nie samych oblicze\u0144.<\/li>\n<li><strong>Zgodno\u015b\u0107 jednostek.<\/strong> Wszystkie wyniki podawane s\u0105 w tej samej jednostce co wpisana warto\u015b\u0107. Je\u015bli potrzebujesz wyniku w innej jednostce, zmie\u0144 j\u0105 na li\u015bcie i wpisz warto\u015b\u0107 ponownie.<\/li>\n<li><strong>Wskaz\u00f3wka pomiarowa.<\/strong> Przy fizycznych obiektach cz\u0119sto \u0142atwiej zmierzy\u0107 obw\u00f3d (obwijaj\u0105c miar\u0105) albo \u015brednic\u0119 (na wprost) ni\u017c promie\u0144, bo \u015brodek bywa niedost\u0119pny. Wybierz t\u0119 warto\u015b\u0107, kt\u00f3r\u0105 jeste\u015b w stanie zmierzy\u0107 najdok\u0142adniej.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Wpisz jedn\u0105 znan\u0105 warto\u015b\u0107 \u2013 promie\u0144, \u015brednic\u0119, obw\u00f3d lub pole \u2013 i natychmiast otrzymaj wszystkie pozosta\u0142e wymiary ko\u0142a. Wybierz odpowiedni\u0105 jednostk\u0119, a reszt\u0105 zajmie si\u0119 kalkulator.<\/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-2552","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\/2552","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=2552"}],"version-history":[{"count":1,"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/posts\/2552\/revisions"}],"predecessor-version":[{"id":2734,"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/posts\/2552\/revisions\/2734"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/media?parent=2552"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/categories?post=2552"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/tags?post=2552"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}