{"id":2665,"date":"2026-10-15T02:12:56","date_gmt":"2026-10-15T01:12:56","guid":{"rendered":"https:\/\/wpcalc.com\/pl\/matematyka\/pole-wycinka-kola\/"},"modified":"2026-10-15T02:12:56","modified_gmt":"2026-10-15T01:12:56","slug":"pole-wycinka-kola","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/pl\/matematyka\/pole-wycinka-kola\/","title":{"rendered":"Kalkulator pola wycinka 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\">Obliczanie pola wycinka ko\u0142a z promienia i k\u0105ta<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"2665\" data-favorite-title=\"Pole wycinka ko\u0142a\" data-favorite-url=\"https:\/\/wpcalc.com\/pl\/matematyka\/pole-wycinka-kola\/\" data-favorite-excerpt=\"Oblicz pole wycinka ko\u0142a na podstawie promienia i k\u0105ta \u015brodkowego. Wpisz promie\u0144, wybierz jednostk\u0119 (deg, rad lub grad) i otrzymaj pole wycinka, d\u0142ugo\u015b\u0107 \u0142uku, obw\u00f3d oraz u\u0142amek pe\u0142nego ko\u0142a.\" 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\/pole-wycinka-kola\/\" method=\"POST\" class=\"calculator\" id=\"calculator-2665\" data-post=\"2665\"><fieldset class=\"fieldset-input is-2\"><legend class=\"sr-only\">Pola danych<\/legend><div class=\"field has-term\" id=\"input-1\"><label for=\"field-1\">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-1\" aria-describedby=\"calc-info-1\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"5\" min=\"0\" value=\"5\"\/><div class=\"grid grid-cols-1\"><select id=\"field-2\" 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-1\">Odleg\u0142o\u015b\u0107 od \u015brodka okr\u0119gu do \u0142uku.<\/small><\/div><div class=\"field has-term\" id=\"input-2\"><label for=\"field-3\">K\u0105t \u015brodkowy<\/label><div class=\"term\">\u03b8<\/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=\"kt_rodkowy\" id=\"field-3\" aria-describedby=\"calc-info-3\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"60\" min=\"0\" value=\"60\"\/><div class=\"grid grid-cols-1\"><select id=\"field-4\" name=\"jednostka\" aria-label=\"Jednostka\"><option value=\"deg\" selected>deg<\/option><option value=\"rad\">rad<\/option><option value=\"grad\">grad<\/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\">K\u0105t mi\u0119dzy dwoma promieniami wyznaczaj\u0105cymi wycinek. Dozwolone s\u0105 warto\u015bci powy\u017cej 360\u00b0 (kilka pe\u0142nych obrot\u00f3w).<\/small><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Przelicz ponownie\" id=\"calculate-button\" data-post=\"2665\">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> Tw\u00f3j wycinek ko\u0142a<\/h3><div class=\"result-box\"><div class=\"field-result is-column\" id=\"output-1\"><span class=\"field-title\"><span>Pole wycinka ko\u0142a<\/span><span class=\"result-term\">A<\/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>D\u0142ugo\u015b\u0107 \u0142uku<\/span><span class=\"result-term\">L<\/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\">P<\/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 is-column\" id=\"output-4\"><span class=\"field-title\"><span>U\u0142amek ko\u0142a<\/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 class=\"field-result is-column\" id=\"output-5\"><span class=\"field-title\"><span>Kroki oblicze\u0144<\/span><\/span><span class=\"field-value\" id=\"result-5\"><\/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=\"2665\" 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>Pole wycinka ko\u0142a<\/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\">\\[ A = \\frac{\\theta}{2}\\, r^2 \\qquad L = \\theta\\, r \\qquad P = 2r + L \\]<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Gdzie:<\/strong><\/p>\n<ul>\n<li>\\(A\\) \u2014 pole wycinka (jednostki kwadratowe, np. m\u00b2)<\/li>\n<li>\\(L\\) \u2014 d\u0142ugo\u015b\u0107 \u0142uku wycinka (ta sama jednostka co promie\u0144)<\/li>\n<li>\\(P\\) \u2014 obw\u00f3d wycinka (dwa promienie plus \u0142uk)<\/li>\n<li>\\(r\\) \u2014 promie\u0144 ko\u0142a<\/li>\n<li>\\(\\theta\\) \u2014 k\u0105t \u015brodkowy w <strong>radianach<\/strong><\/li>\n<\/ul>\n<p>Pole wycinka to po prostu ta cz\u0119\u015b\u0107 ca\u0142ego pola ko\u0142a \\(\\pi r^2\\), kt\u00f3r\u0105 obejmuje k\u0105t \\(\\theta\\): pe\u0142ne ko\u0142o odpowiada \\(2\\pi\\) radian\u00f3w, wi\u0119c wycinek zajmuje \\(\\theta \/ 2\\pi\\) tej powierzchni.<\/p>\n<p>Je\u015bli k\u0105t masz podany w stopniach, najpierw przelicz go na radiany: \\(\\theta_{\\text{rad}} = \\theta_{\\text{deg}} \\cdot \\pi \/ 180\\). Kalkulator wykonuje t\u0119 zamian\u0119 automatycznie.<\/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>Pole wycinka ko\u0142a \u2013 przyk\u0142ad obliczenia<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Przyk\u0142ad:<\/strong> wycinek ko\u0142a ma promie\u0144 5 m i k\u0105t \u015brodkowy 60\u00b0. Oblicz jego pole, d\u0142ugo\u015b\u0107 \u0142uku i obw\u00f3d.<\/p>\n<p>\\[ \\theta = 60\u00b0 \\cdot \\frac{\\pi}{180} = \\frac{\\pi}{3} \\approx 1.047 \\text{ rad} \\]<\/p>\n<p>\\[ A = \\frac{\\theta}{2} r^2 = \\frac{1.047}{2} \\cdot 5^2 \\approx 13.09 \\text{ m}^2 \\]<\/p>\n<p>\\[ L = \\theta r = 1.047 \\cdot 5 \\approx 5.236 \\text{ m}, \\qquad P = 2 \\cdot 5 + 5.236 \\approx 15.236 \\text{ m} \\]<\/p>\n<p><strong>Wynik:<\/strong> pole wycinka wynosi oko\u0142o 13,09 m\u00b2, d\u0142ugo\u015b\u0107 \u0142uku 5,236 m, a obw\u00f3d 15,236 m. Wycinek obejmuje \\(60\/360 = 1\/6 \\approx 0.167\\) pe\u0142nego ko\u0142a.<\/p>\n<p>\n\r\n<\/section>\n<h2>Jak korzysta\u0107 z kalkulatora<\/h2>\n<ol>\n<li>Wpisz <strong>Promie\u0144<\/strong> ko\u0142a i wybierz jego jednostk\u0119 (m, cm, mm, ft lub in). Pole zostanie podane w odpowiedniej jednostce kwadratowej.<\/li>\n<li>Wpisz <strong>K\u0105t \u015brodkowy<\/strong> mi\u0119dzy dwoma promieniami i wybierz jego jednostk\u0119: stopnie (deg), radiany (rad) lub grady (grad).<\/li>\n<li>Odczytaj wyniki: <strong>Pole wycinka<\/strong> (z polem pe\u0142nego ko\u0142a do por\u00f3wnania), <strong>D\u0142ugo\u015b\u0107 \u0142uku<\/strong>, <strong>Obw\u00f3d<\/strong>, <strong>U\u0142amek ko\u0142a<\/strong> oraz rozwini\u0119cie oblicze\u0144 krok po kroku.<\/li>\n<\/ol>\n<p>Promie\u0144 i k\u0105t musz\u0105 by\u0107 wi\u0119ksze od zera. K\u0105ty powy\u017cej 360\u00b0 s\u0105 dopuszczalne \u2014 wycinek okr\u0105\u017ca wtedy \u015brodek wi\u0119cej ni\u017c raz, a pole odpowiednio ro\u015bnie.<\/p>\n<h2>Czym jest wycinek ko\u0142a?<\/h2>\n<p>Wycinek ko\u0142a to obszar ko\u0142a ograniczony dwoma promieniami i rozpi\u0119tym mi\u0119dzy nimi \u0142ukiem \u2014 kszta\u0142t kawa\u0142ka pizzy, fragmentu wykresu ko\u0142owego albo wachlarza. Ka\u017cdy wycinek jest w pe\u0142ni okre\u015blony dwiema wielko\u015bciami: promieniem \\(r\\) ko\u0142a, do kt\u00f3rego nale\u017cy, oraz k\u0105tem \u015brodkowym \\(\\theta\\), kt\u00f3ry decyduje o tym, jak szeroko \u201ekawa\u0142ek\u201d otwiera si\u0119 przy \u015brodku.<\/p>\n<p>Sercem wzoru jest proporcjonalno\u015b\u0107. Pe\u0142ne ko\u0142o o k\u0105cie \\(2\\pi\\) radian\u00f3w ma pole \\(\\pi r^2\\); wycinek o k\u0105cie \\(\\theta\\) obejmuje dok\u0142adnie \\(\\theta\/2\\pi\\) tego pola. Skr\u00f3cenie \\(\\pi\\) daje zwi\u0119z\u0142y wz\u00f3r \\(A = \\frac{\\theta}{2} r^2\\). Przy sta\u0142ym promieniu pole ro\u015bnie <a href=\"https:\/\/wpcalc.com\/pl\/matematyka\/proporcjonalnosc-prosta\/\">proporcjonalnie<\/a> do k\u0105ta: podw\u00f3jny k\u0105t to podw\u00f3jne pole. Podwojenie promienia zwi\u0119ksza natomiast pole czterokrotnie, poniewa\u017c \\(r\\) wyst\u0119puje w drugiej pot\u0119dze.<\/p>\n<p>Interpretacja wynik\u00f3w jest prosta: <strong>d\u0142ugo\u015b\u0107 \u0142uku<\/strong> pokazuje, jak d\u0142uga jest zakrzywiona kraw\u0119d\u017a wycinka \u2014 przydaje si\u0119 przy szacowaniu materia\u0142u (listwy, ogrodzenia, gi\u0119te rury). <strong>Obw\u00f3d<\/strong> to \u0142uk plus dwa proste promienie \u2014 ca\u0142a d\u0142ugo\u015b\u0107 granicy \u201ekawa\u0142ka\u201d. <strong>U\u0142amek ko\u0142a<\/strong> pozwala spojrze\u0107 na rozmiar z perspektywy: wycinek o k\u0105cie 90\u00b0 to \u0107wiartka ko\u0142a, 60\u00b0 \u2014 jedna sz\u00f3sta i tak dalej, a dok\u0142adnie na tej zasadzie dzia\u0142aj\u0105 proporcje na wykresach ko\u0142owych.<\/p>\n<h2>Jednostki, za\u0142o\u017cenia i wskaz\u00f3wki<\/h2>\n<ul>\n<li><strong>Jednostka k\u0105ta ma znaczenie.<\/strong> Wz\u00f3r wymaga radian\u00f3w. Je\u015bli liczysz r\u0119cznie w stopniach, najpierw przemn\u00f3\u017c k\u0105t przez \\(\\pi\/180\\). Kalkulator sam zamienia stopnie, radiany i grady. Jeden grad to 0,9\u00b0, a pe\u0142ny obr\u00f3t to 400 grad\u00f3w.<\/li>\n<li><strong>Pole wymaga jednostki kwadratowej.<\/strong> Promie\u0144 w metrach daje pole w m\u00b2; promie\u0144 w centymetrach \u2014 w cm\u00b2. Mieszanie jednostek (np. promie\u0144 w metrach, a oczekiwanie cm\u00b2) to cz\u0119ste \u017ar\u00f3d\u0142o b\u0142\u0119d\u00f3w.<\/li>\n<li><strong>Wycinek to figura p\u0142aska.<\/strong> Obliczenia zak\u0142adaj\u0105 p\u0142aski wycinek ko\u0142a; nie dotycz\u0105 wycink\u00f3w sferycznych ani sto\u017ckowych (np. powierzchni bocznej sto\u017cka).<\/li>\n<li><strong>K\u0105ty powy\u017cej 360\u00b0<\/strong> tworz\u0105 nak\u0142adaj\u0105ce si\u0119 wycinki obejmuj\u0105ce wi\u0119cej ni\u017c pe\u0142ny obr\u00f3t \u2014 pole jest wtedy wi\u0119ksze ni\u017c ca\u0142e ko\u0142o. U\u017cywaj ich tylko wtedy, gdy faktycznie tego potrzebujesz.<\/li>\n<li><strong>Przypadki szczeg\u00f3lne:<\/strong> dla \\(\\theta = 2\\pi\\) wycinek staje si\u0119 pe\u0142nym ko\u0142em o polu \\(\\pi r^2\\); dla \\(\\theta = \\pi\\) jest to p\u00f3\u0142kole o polu \\(\\pi r^2\/2\\) i obwodzie \\(P = 2r + \\pi r\\).<\/li>\n<\/ul>\n<h2>Tabela pomocnicza<\/h2>\n<p>U\u0142amek ko\u0142a dla typowych k\u0105t\u00f3w:<\/p>\n<table>\n<thead>\n<tr>\n<th>K\u0105t \u015brodkowy<\/th>\n<th>W radianach<\/th>\n<th>U\u0142amek ko\u0142a<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>30\u00b0<\/td>\n<td>\\(\\pi\/6 \\approx 0.524\\)<\/td>\n<td>1\/12<\/td>\n<\/tr>\n<tr>\n<td>45\u00b0<\/td>\n<td>\\(\\pi\/4 \\approx 0.785\\)<\/td>\n<td>1\/8<\/td>\n<\/tr>\n<tr>\n<td>60\u00b0<\/td>\n<td>\\(\\pi\/3 \\approx 1.047\\)<\/td>\n<td>1\/6<\/td>\n<\/tr>\n<tr>\n<td>90\u00b0<\/td>\n<td>\\(\\pi\/2 \\approx 1.571\\)<\/td>\n<td>1\/4<\/td>\n<\/tr>\n<tr>\n<td>180\u00b0<\/td>\n<td>\\(\\pi \\approx 3.142\\)<\/td>\n<td>1\/2<\/td>\n<\/tr>\n<tr>\n<td>270\u00b0<\/td>\n<td>\\(3\\pi\/2 \\approx 4.712\\)<\/td>\n<td>3\/4<\/td>\n<\/tr>\n<tr>\n<td>360\u00b0<\/td>\n<td>\\(2\\pi \\approx 6.283\\)<\/td>\n<td>1<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Aby odczyta\u0107 z tabeli pole, wystarczy <a href=\"https:\/\/wpcalc.com\/pl\/matematyka\/kalkulator-mnozenia\/\">pomno\u017cy\u0107<\/a> u\u0142amek przez pole pe\u0142nego ko\u0142a \\(\\pi r^2\\) \u2014 albo pozwoli\u0107 zrobi\u0107 to kalkulatorowi.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Oblicz pole wycinka ko\u0142a na podstawie promienia i k\u0105ta \u015brodkowego. Wpisz promie\u0144, wybierz jednostk\u0119 (deg, rad lub grad) i otrzymaj pole wycinka, d\u0142ugo\u015b\u0107 \u0142uku, obw\u00f3d oraz u\u0142amek pe\u0142nego ko\u0142a.<\/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-2665","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\/2665","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=2665"}],"version-history":[{"count":1,"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/posts\/2665\/revisions"}],"predecessor-version":[{"id":2766,"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/posts\/2665\/revisions\/2766"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/media?parent=2665"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/categories?post=2665"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/tags?post=2665"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}