{"id":2955,"date":"2026-11-04T08:16:41","date_gmt":"2026-11-04T08:16:41","guid":{"rendered":"https:\/\/wpcalc.com\/pl\/matematyka\/kalkulator-pola-powierzchni\/"},"modified":"2026-11-04T08:16:41","modified_gmt":"2026-11-04T08:16:41","slug":"kalkulator-pola-powierzchni","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/pl\/matematyka\/kalkulator-pola-powierzchni\/","title":{"rendered":"Kalkulator pola powierzchni"},"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 pole dowolnej figury p\u0142askiej<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"2955\" data-favorite-title=\"Pole powierzchni\" data-favorite-url=\"https:\/\/wpcalc.com\/pl\/matematyka\/kalkulator-pola-powierzchni\/\" data-favorite-excerpt=\"Policz pole kwadratu, prostok\u0105ta, tr\u00f3jk\u0105ta, ko\u0142a, elipsy, trapezu, wielok\u0105ta foremnego, pier\u015bcienia i innych figur. Wybierz kszta\u0142t, wpisz wymiary i otrzymaj wynik w metrach kwadratowych, stopach kwadratowych, akrach lub hektarach.\" 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-pola-powierzchni\/\" method=\"POST\" class=\"calculator\" id=\"calculator-2955\" data-post=\"2955\"><fieldset class=\"fieldset-input is-2\"><legend class=\"sr-only\">Pola danych<\/legend><div class=\"field is-single\" id=\"input-1\"><label for=\"field-1\">Figura<\/label><div class=\"grid grid-cols-1\"><select id=\"field-1\" name=\"figura\"><option value=\"square\">Kwadrat<\/option><option value=\"rectangle\" selected>Prostok\u0105t<\/option><option value=\"triangle\">Tr\u00f3jk\u0105t<\/option><option value=\"circle\">Ko\u0142o<\/option><option value=\"semicircle\">P\u00f3\u0142kole<\/option><option value=\"ellipse\">Elipsa<\/option><option value=\"parallelogram\">R\u00f3wnoleg\u0142obok<\/option><option value=\"trapezoid\">Trapez<\/option><option value=\"rhombus\">Romb (przek\u0105tne)<\/option><option value=\"sector\">Wycinek ko\u0142a<\/option><option value=\"polygon\">Wielok\u0105t foremny<\/option><option value=\"annulus\">Pier\u015bcie\u0144 ko\u0142owy<\/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 is-single\" id=\"input-2\"><label for=\"field-2\">Jednostka d\u0142ugo\u015bci<\/label><div class=\"grid grid-cols-1\"><select id=\"field-2\" name=\"jednostka_dugoci\"><option value=\"mm\">mm<\/option><option value=\"cm\" selected>cm<\/option><option value=\"m\">m<\/option><option value=\"km\">km<\/option><option value=\"in\">in<\/option><option value=\"ft\">ft<\/option><option value=\"yd\">yd<\/option><option value=\"mi\">mi<\/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=\"is-single field\" id=\"input-3\"><span class=\"font-semibold\">Wymiary<\/span><\/div><div class=\"field has-term\" id=\"input-4\"><label for=\"field-4\">Bok a<\/label><div class=\"term\">a<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"bok_a\" id=\"field-4\" aria-describedby=\"calc-info-4\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0\" value=\"6\"\/><small id=\"calc-info-4\">Bok kwadratu lub prostok\u0105ta, p\u00f3\u0142os elipsy albo bok a trapezu.<\/small><\/div><div class=\"field has-term\" id=\"input-5\"><label for=\"field-5\">Bok b<\/label><div class=\"term\">b<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"bok_b\" id=\"field-5\" aria-describedby=\"calc-info-5\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0\" value=\"4\"\/><small id=\"calc-info-5\">Drugi bok prostok\u0105ta lub trapezu, druga p\u00f3\u0142os elipsy.<\/small><\/div><div class=\"field\" id=\"input-6\" hidden><label for=\"field-6\">Dane tr\u00f3jk\u0105ta<\/label><div class=\"grid grid-cols-1\"><select id=\"field-6\" name=\"dane_trjkta\"><option value=\"bh\" selected>Podstawa i wysoko\u015b\u0107<\/option><option value=\"sss\">Trzy boki (wz\u00f3r Herona)<\/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-7\" hidden><label for=\"field-7\">Podstawa<\/label><div class=\"term\">b<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"podstawa\" id=\"field-7\" aria-describedby=\"calc-info-7\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0\" value=\"8\"\/><small id=\"calc-info-7\">Podstawa tr\u00f3jk\u0105ta lub r\u00f3wnoleg\u0142oboku.<\/small><\/div><div class=\"field has-term\" id=\"input-8\" hidden><label for=\"field-8\">Wysoko\u015b\u0107<\/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\" id=\"field-8\" aria-describedby=\"calc-info-8\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0\" value=\"5\"\/><small id=\"calc-info-8\">Wysoko\u015b\u0107 prostopad\u0142a do podstawy.<\/small><\/div><div class=\"field has-term\" id=\"input-9\" hidden><label for=\"field-9\">Bok a (tr\u00f3jk\u0105t)<\/label><div class=\"term\">a<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"bok_a_trjkt\" id=\"field-9\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0\" value=\"3\"\/><\/div><div class=\"field has-term\" id=\"input-10\" hidden><label for=\"field-10\">Bok b (tr\u00f3jk\u0105t)<\/label><div class=\"term\">b<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"bok_b_trjkt\" id=\"field-10\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0\" value=\"4\"\/><\/div><div class=\"field has-term\" id=\"input-11\" hidden><label for=\"field-11\">Bok c<\/label><div class=\"term\">c<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"bok_c\" id=\"field-11\" aria-describedby=\"calc-info-11\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0\" value=\"5\"\/><small id=\"calc-info-11\">Ka\u017cdy bok musi by\u0107 kr\u00f3tszy od sumy dw\u00f3ch pozosta\u0142ych.<\/small><\/div><div class=\"field has-term\" id=\"input-12\" hidden><label for=\"field-12\">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><input type=\"text\" name=\"promie\" id=\"field-12\" aria-describedby=\"calc-info-12\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0\" value=\"5\"\/><small id=\"calc-info-12\">Promie\u0144 ko\u0142a, p\u00f3\u0142kola lub wycinka; promie\u0144 zewn\u0119trzny pier\u015bcienia.<\/small><\/div><div class=\"field has-term\" id=\"input-13\" hidden><label for=\"field-13\">Promie\u0144 wewn\u0119trzny<\/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_wewntrzny\" id=\"field-13\" aria-describedby=\"calc-info-13\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0\" value=\"3\"\/><small id=\"calc-info-13\">Promie\u0144 otworu; musi by\u0107 mniejszy ni\u017c promie\u0144 podany powy\u017cej.<\/small><\/div><div class=\"field has-term\" id=\"input-14\" hidden><label for=\"field-14\">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><input type=\"text\" name=\"kt_rodkowy\" id=\"field-14\" aria-describedby=\"calc-info-14\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0\" max=\"360\" value=\"90\"\/><small id=\"calc-info-14\">K\u0105t mi\u0119dzy dwoma promieniami wycinka.<\/small><\/div><div class=\"field\" id=\"input-15\" hidden><label for=\"field-15\">Jednostka k\u0105ta<\/label><div class=\"grid grid-cols-1\"><select id=\"field-15\" name=\"jednostka_kta\"><option value=\"deg\" selected>stopnie (\u00b0)<\/option><option value=\"rad\">radiany (rad)<\/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-16\" hidden><label for=\"field-16\">Liczba bok\u00f3w<\/label><div class=\"term\">n<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"liczba_bokw\" id=\"field-16\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"3\" max=\"1000\" value=\"6\"\/><\/div><div class=\"field has-term\" id=\"input-17\" hidden><label for=\"field-17\">D\u0142ugo\u015b\u0107 boku<\/label><div class=\"term\">s<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"dugo_boku\" id=\"field-17\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0\" value=\"10\"\/><\/div><div class=\"field has-term\" id=\"input-18\" hidden><label for=\"field-18\">Przek\u0105tna 1<\/label><div class=\"term\">d\u2081<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"przektna_1\" id=\"field-18\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0\" value=\"10\"\/><\/div><div class=\"field has-term\" id=\"input-19\" hidden><label for=\"field-19\">Przek\u0105tna 2<\/label><div class=\"term\">d\u2082<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"przektna_2\" id=\"field-19\" aria-describedby=\"calc-info-19\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0\" value=\"8\"\/><small id=\"calc-info-19\">Przek\u0105tne rombu przecinaj\u0105 si\u0119 pod k\u0105tem prostym.<\/small><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Przelicz ponownie\" id=\"calculate-button\" data-post=\"2955\">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: pole powierzchni<\/h3><div class=\"result-box\"><div class=\"field-result\" id=\"output-1\"><span class=\"field-title\"><span>Pole<\/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>Pole w metrach kwadratowych<\/span><\/span><span class=\"field-value\" id=\"result-2\" data-unit=\"m\u00b2\"><\/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>Pole w stopach kwadratowych<\/span><\/span><span class=\"field-value\" id=\"result-3\" data-unit=\"ft\u00b2\"><\/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 w jardach kwadratowych<\/span><\/span><span class=\"field-value\" id=\"result-4\" data-unit=\"yd\u00b2\"><\/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>Pole w akrach<\/span><\/span><span class=\"field-value\" id=\"result-5\" data-unit=\"ac\"><\/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 w hektarach<\/span><\/span><span class=\"field-value\" id=\"result-6\" data-unit=\"ha\"><\/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>Obw\u00f3d<\/span><span class=\"result-term\">P<\/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 is-column\" id=\"output-8\"><span class=\"field-title\"><span>Wz\u00f3r z podstawionymi warto\u015bciami<\/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 is-column\" id=\"output-9\"><span class=\"field-title\"><span>Schemat figury<\/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><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=\"2955\" 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 pole powierzchni<\/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} \\text{Kwadrat \/ prostok\u0105t:} \\quad &amp; A = a^2 \\;\\;(a = b) \\qquad A = ab \\\\ \\text{Tr\u00f3jk\u0105t:} \\quad &amp; A = \\tfrac{1}{2}\\,b\\,h \\qquad A = \\sqrt{s(s-a)(s-b)(s-c)},\\; s = \\tfrac{a+b+c}{2} \\\\ \\text{Ko\u0142o:} \\quad &amp; A = \\pi r^2 \\qquad \\text{P\u00f3\u0142kole: } A = \\tfrac{1}{2}\\pi r^2 \\\\ \\text{Elipsa:} \\quad &amp; A = \\pi a b \\\\ \\text{R\u00f3wnoleg\u0142obok:} \\quad &amp; A = b\\,h \\qquad \\text{Trapez: } A = \\tfrac{1}{2}(a+b)h \\\\ \\text{Romb:} \\quad &amp; A = \\tfrac{1}{2}\\,d_1 d_2 \\\\ \\text{Wycinek ko\u0142a:} \\quad &amp; A = \\tfrac{1}{2}\\,r^2\\theta \\quad (\\theta \\text{ w radianach}) \\\\ \\text{Wielok\u0105t foremny:} \\quad &amp; A = \\frac{n\\,s^2}{4\\tan(\\pi\/n)} \\\\ \\text{Pier\u015bcie\u0144 ko\u0142owy:} \\quad &amp; A = \\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>\\(a\\), \\(b\\) \u2014 d\u0142ugo\u015bci bok\u00f3w, p\u00f3\u0142osie albo boki r\u00f3wnoleg\u0142e, w zale\u017cno\u015bci od figury<\/li>\n<li>\\(h\\) \u2014 wysoko\u015b\u0107 prostopad\u0142a do podstawy<\/li>\n<li>\\(r\\), \\(R\\) \u2014 promie\u0144 wewn\u0119trzny i promie\u0144 zewn\u0119trzny<\/li>\n<li>\\(d_1\\), \\(d_2\\) \u2014 przek\u0105tne rombu<\/li>\n<li>\\(\\theta\\) \u2014 k\u0105t \u015brodkowy wycinka<\/li>\n<li>\\(n\\), \\(s\\) \u2014 liczba bok\u00f3w i d\u0142ugo\u015b\u0107 boku wielok\u0105ta foremnego<\/li>\n<\/ul>\n<p>Ka\u017cdy z tych wzor\u00f3w mno\u017cy dwie prostopad\u0142e d\u0142ugo\u015bci, wi\u0119c pole zawsze wychodzi w kwadracie wybranej jednostki d\u0142ugo\u015bci (na przyk\u0142ad \\(\\text{cm}^2\\)). Dla wycinka ko\u0142a k\u0105t trzeba najpierw przeliczy\u0107 ze stopni na radiany: \\(\\theta = \\theta_{\\text{stopn}} \\cdot \\pi\/180\\).<\/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 powierzchni \u2013 przyk\u0142ad oblicze\u0144<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Przyk\u0142ad:<\/strong> prostok\u0105tny pok\u00f3j ma na planie 6 cm d\u0142ugo\u015bci i 4 cm szeroko\u015bci (domy\u015blne warto\u015bci kalkulatora), a jednostk\u0105 jest cm.<\/p>\n<p>\\[ A = a \\times b = 6 \\times 4 = 24 \\;\\text{cm}^2 \\]<\/p>\n<p>\\[ P = 2(a + b) = 2 \\times (6 + 4) = 20 \\;\\text{cm} \\]<\/p>\n<p><strong>Wynik:<\/strong> pole wynosi 24 cm\u00b2 (0,0024 m\u00b2, czyli ok. 0,258 ft\u00b2), a obw\u00f3d 20 cm. Te same liczby podane w metrach zamiast centymetr\u00f3w da\u0142yby pole 24 m\u00b2 \u2014 i dlatego wyb\u00f3r jednostki ma takie znaczenie.<\/p>\n<p>\n\r\n<\/section>\n<h2>Jak korzysta\u0107 z kalkulatora<\/h2>\n<ol>\n<li>Wybierz <strong>Kszta\u0142t<\/strong> z listy rozwijanej \u2014 kwadrat, prostok\u0105t, tr\u00f3jk\u0105t, ko\u0142o, p\u00f3\u0142kole, elipsa, r\u00f3wnoleg\u0142obok, trapez, romb, wycinek ko\u0142a, wielok\u0105t foremny lub pier\u015bcie\u0144 ko\u0142owy.<\/li>\n<li>Wybierz <strong>Jednostk\u0119 d\u0142ugo\u015bci<\/strong> (mm, cm, m, km, in, ft, yd lub mi). Ka\u017cdy wymiar, kt\u00f3ry wpiszesz, interpretowany jest w tej jednostce, a pole zwracane jest w jej kwadracie.<\/li>\n<li>Pod pozycj\u0105 <strong>Wymiary<\/strong> pokazuj\u0105 si\u0119 tylko te pola, kt\u00f3rych potrzebuje wybrana figura. Wpisuj liczby dodatnie \u2014 np. <strong>Bok a<\/strong> i <strong>Bok b<\/strong> dla prostok\u0105ta albo <strong>Promie\u0144<\/strong> i <strong>K\u0105t \u015brodkowy<\/strong> dla wycinka ko\u0142a.<\/li>\n<li>Dla tr\u00f3jk\u0105ta najpierw wybierz spos\u00f3b podania danych w polu <strong>Dane tr\u00f3jk\u0105ta<\/strong>: podstawa i wysoko\u015b\u0107 albo trzy boki (wz\u00f3r Herona).<\/li>\n<li>Odczytaj wyniki: pole w wybranej jednostce, przeliczenia na metry kwadratowe, stopy kwadratowe, jardy kwadratowe, akry i hektary, a tak\u017ce obw\u00f3d \u2014 o ile wymiary figury jednoznacznie go okre\u015blaj\u0105. Na dole pojawia si\u0119 wz\u00f3r z podstawionymi warto\u015bciami oraz rysunek w skali.<\/li>\n<\/ol>\n<h2>Czym jest pole powierzchni i jak odczyta\u0107 wynik<\/h2>\n<p>Pole powierzchni okre\u015bla rozmiar figury: ile p\u0142askiej przestrzeni ona zajmuje. Spotykasz je wsz\u0119dzie \u2014 pod\u0142oga w pokoju, farba potrzebna do \u015bciany, dzia\u0142ka opisana w akcie, materia\u0142 na plandek\u0119 albo grz\u0105dk\u0119. Niezale\u017cnie od figury idea jest zawsze ta sama: trzeba policzy\u0107, ile kwadracik\u00f3w jednostkowych mie\u015bci si\u0119 w \u015brodku. Prostok\u0105t o wymiarach 6 na 4 jednostki zawiera dok\u0142adnie 24 takie kwadraty, st\u0105d \\(A = 24\\) jednostek kwadratowych.<\/p>\n<p>Powy\u017csze wzory to skr\u00f3ty tego liczenia. Poniewa\u017c ka\u017cdy z nich \u0142\u0105czy dwie d\u0142ugo\u015bci, wynik zawsze nosi jednostk\u0119 do kwadratu: centymetry daj\u0105 cm\u00b2, stopy ft\u00b2, kilometry km\u00b2. Mieszanie jednostek bez ich przeliczenia to najcz\u0119stszy b\u0142\u0105d \u2014 dlatego kalkulator narzuca jedn\u0105 jednostk\u0119 wszystkim danym, a wynik przelicza za Ciebie na m\u00b2, ft\u00b2, yd\u00b2, akry i hektary, czyli pi\u0119\u0107 jednostek najcz\u0119\u015bciej u\u017cywanych w budownictwie, urz\u0105dzaniu ogrod\u00f3w i geodezji.<\/p>\n<p>Obw\u00f3d, gdy jest pokazany, odpowiada na inne pytanie: nie to, ile miejsca figura zajmuje, ale to, jak d\u0142uga jest jej granica. D\u0142ugo\u015b\u0107 ogrodzenia to zadanie na obw\u00f3d; ilo\u015b\u0107 trawy, farby czy p\u0142ytek to zadanie na pole. D\u0142ugi w\u0105ski prostok\u0105t i zwarty kwadrat mog\u0105 obejmowa\u0107 to samo pole przy zupe\u0142nie r\u00f3\u017cnych obwodach.<\/p>\n<p>Zwr\u00f3\u0107 uwag\u0119, \u017ce dla niekt\u00f3rych figur, np. ko\u0142a, obw\u00f3d to po prostu d\u0142ugo\u015b\u0107 okr\u0119gu \\(C = 2\\pi r\\), a dla wycinka \u2014 \u0142uk plus dwa promienie. Je\u015bli chcesz wej\u015b\u0107 g\u0142\u0119biej, mamy narz\u0119dzia wyspecjalizowane: <a href=\"https:\/\/wpcalc.com\/en\/mathematics\/triangle-area-calculator\/\">kalkulator pola tr\u00f3jk\u0105ta<\/a> obejmuje wi\u0119cej przypadk\u00f3w tr\u00f3jk\u0105t\u00f3w, <a href=\"https:\/\/wpcalc.com\/pl\/matematyka\/kalkulator-kola\/\">kalkulator ko\u0142a<\/a> wylicza promie\u0144, \u015brednic\u0119 i obw\u00f3d, a <a href=\"https:\/\/wpcalc.com\/pl\/matematyka\/pole-wycinka-kola\/\">kalkulator pola wycinka ko\u0142a<\/a> i <a href=\"https:\/\/wpcalc.com\/pl\/matematyka\/pole-wielokata-foremnego\/\">kalkulator pola wielok\u0105ta foremnego<\/a> szczeg\u00f3\u0142owo opisuj\u0105 te dwie figury.<\/p>\n<h2>Za\u0142o\u017cenia, ograniczenia i praktyczne wskaz\u00f3wki<\/h2>\n<ul>\n<li><strong>Wszystkie dane dziel\u0105 jedn\u0105 jednostk\u0119.<\/strong> Je\u015bli plan miesza metry i centymetry, przelicz wszystko na jedn\u0105 jednostk\u0119 \u2014 albo skorzystaj z <a href=\"https:\/\/wpcalc.com\/en\/mathematics\/scientific-calculator\/\">kalkulatora naukowego<\/a>, \u017ceby zrobi\u0107 to szybko.<\/li>\n<li><strong>Wysoko\u015b\u0107 musi by\u0107 prostopad\u0142a.<\/strong> Dla tr\u00f3jk\u0105ta, r\u00f3wnoleg\u0142oboku i trapezu podaj wysoko\u015b\u0107 zmierzon\u0105 pod k\u0105tem prostym do podstawy, a nie sko\u015bny bok.<\/li>\n<li><strong>Tr\u00f3jk\u0105t zadany podstaw\u0105 i wysoko\u015bci\u0105 nie ma jednoznacznego obwodu.<\/strong> Pole jest wyznaczone, ale boki boczne mog\u0105 by\u0107 r\u00f3\u017cne, wi\u0119c kalkulator ukrywa obw\u00f3d przy tej metodzie. Przy trzech bokach (wz\u00f3r Herona) obw\u00f3d to po prostu \\(a + b + c\\).<\/li>\n<li><strong>Boki tr\u00f3jk\u0105ta musz\u0105 spe\u0142nia\u0107 nier\u00f3wno\u015b\u0107 tr\u00f3jk\u0105ta<\/strong>: ka\u017cdy bok kr\u00f3tszy od sumy dw\u00f3ch pozosta\u0142ych. Kalkulator poinformuje Ci\u0119, gdy tak nie jest.<\/li>\n<li><strong>Romb podajemy przez przek\u0105tne<\/strong>, kt\u00f3re musz\u0105 przecina\u0107 si\u0119 pod k\u0105tem prostym \u2014 w rombie zawsze tak jest. K\u0105t wycinka musi mie\u015bci\u0107 si\u0119 mi\u0119dzy 0\u00b0 a 360\u00b0 (0 i 2\u03c0 rad).<\/li>\n<li><strong>Wielok\u0105t musi by\u0107 foremny<\/strong> (wszystkie boki i k\u0105ty r\u00f3wne). Czworok\u0105t nieregularny podziel na tr\u00f3jk\u0105ty i dodaj ich pola.<\/li>\n<li><strong>Pier\u015bcie\u0144 wymaga promienia wewn\u0119trznego mniejszego od zewn\u0119trznego.<\/strong> Wynikiem jest pole pier\u015bcienia mi\u0119dzy dwoma okr\u0119gami.<\/li>\n<li><strong>Obw\u00f3d elipsy jest przybli\u017cony<\/strong> (wz\u00f3r Ramanujana) \u2014 bardzo dok\u0142adny dla typowych kszta\u0142t\u00f3w, ale nie istnieje dok\u0142adny wz\u00f3r elementarny.<\/li>\n<li><strong>Przeliczenia na akry i hektary<\/strong> pojawiaj\u0105 si\u0119 automatycznie, co przydaje si\u0119 przy gruntach: 1 ha = 10 000 m\u00b2, a 1 akr \u2248 4046,86 m\u00b2.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Policz pole kwadratu, prostok\u0105ta, tr\u00f3jk\u0105ta, ko\u0142a, elipsy, trapezu, wielok\u0105ta foremnego, pier\u015bcienia i innych figur. Wybierz kszta\u0142t, wpisz wymiary i otrzymaj wynik w metrach kwadratowych, stopach kwadratowych, akrach lub hektarach.<\/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-2955","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\/2955","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=2955"}],"version-history":[{"count":0,"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/posts\/2955\/revisions"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/media?parent=2955"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/categories?post=2955"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/tags?post=2955"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}