{"id":2963,"date":"2026-04-24T13:29:02","date_gmt":"2026-04-24T11:29:02","guid":{"rendered":"https:\/\/science-x.net\/?page_id=2963"},"modified":"2026-04-24T13:29:02","modified_gmt":"2026-04-24T11:29:02","slug":"projectile-motion-calculator","status":"publish","type":"page","link":"https:\/\/science-x.net\/?page_id=2963","title":{"rendered":"Projectile Motion Calculator"},"content":{"rendered":"\n<div class=\"eco-tool wp-block-group\" id=\"eco-tool-projectile-72e4c\">\n  <div class=\"eco-tool__header\">\n    <h2 class=\"eco-tool__title\">Projectile Motion Calculator<\/h2>\n    <p class=\"eco-tool__lead\">\n      Estimate range, maximum height, and flight time based on launch speed and angle.\n    <\/p>\n  <\/div>\n\n  <form class=\"eco-tool__form\" id=\"eco-projectile-form-72e4c\" novalidate>\n    <div class=\"eco-tool__grid3\">\n      <div class=\"eco-tool__field\">\n        <label class=\"eco-tool__label\" for=\"eco-proj-speed-72e4c\">Launch speed<br>(m\/s)<\/label>\n        <input class=\"eco-tool__input\" id=\"eco-proj-speed-72e4c\" type=\"number\" min=\"0.1\" step=\"0.1\" value=\"20\" inputmode=\"decimal\" \/>\n        <div class=\"eco-tool__hint\">Initial speed at launch.<\/div>\n      <\/div>\n\n      <div class=\"eco-tool__field\">\n        <label class=\"eco-tool__label\" for=\"eco-proj-angle-72e4c\">Launch angle<br>(degrees)<\/label>\n        <input class=\"eco-tool__input\" id=\"eco-proj-angle-72e4c\" type=\"number\" min=\"1\" max=\"89\" step=\"1\" value=\"45\" inputmode=\"numeric\" \/>\n        <div class=\"eco-tool__hint\">Angle above horizontal.<\/div>\n      <\/div>\n\n      <div class=\"eco-tool__field\">\n        <label class=\"eco-tool__label\" for=\"eco-proj-gravity-72e4c\">Gravity<br>(m\/s\u00b2)<\/label>\n        <input class=\"eco-tool__input\" id=\"eco-proj-gravity-72e4c\" type=\"number\" min=\"0.1\" step=\"0.01\" value=\"9.81\" inputmode=\"decimal\" \/>\n        <div class=\"eco-tool__hint\">Use 9.81 for Earth.<\/div>\n      <\/div>\n    <\/div>\n\n    <div class=\"eco-tool__actions\">\n      <button type=\"button\" class=\"wp-element-button eco-tool__btn\" id=\"eco-proj-calc-72e4c\">Calculate<\/button>\n      <button type=\"button\" class=\"wp-element-button eco-tool__btn eco-tool__btn--ghost\" id=\"eco-proj-reset-72e4c\">Reset<\/button>\n      <div class=\"eco-tool__error\" id=\"eco-proj-error-72e4c\" aria-live=\"polite\"><\/div>\n    <\/div>\n  <\/form>\n\n  <div class=\"eco-tool__result\" id=\"eco-proj-result-72e4c\" hidden>\n    <h3 class=\"eco-tool__subtitle\">Result<\/h3>\n\n    <div class=\"eco-tool__cards eco-tool__cards--3\">\n      <div class=\"eco-tool__card\">\n        <div class=\"eco-tool__metric-label\">Horizontal range<\/div>\n        <div class=\"eco-tool__metric-value\" id=\"eco-proj-range-72e4c\">\u2014<\/div>\n      <\/div>\n\n      <div class=\"eco-tool__card\">\n        <div class=\"eco-tool__metric-label\">Maximum height<\/div>\n        <div class=\"eco-tool__metric-value\" id=\"eco-proj-height-72e4c\">\u2014<\/div>\n      <\/div>\n\n      <div class=\"eco-tool__card\">\n        <div class=\"eco-tool__metric-label\">Flight time<\/div>\n        <div class=\"eco-tool__metric-value\" id=\"eco-proj-time-72e4c\">\u2014<\/div>\n      <\/div>\n    <\/div>\n\n    <div class=\"eco-tool__card eco-tool__card--wide\">\n      <div class=\"eco-tool__metric-label\">Launch components<\/div>\n      <div class=\"eco-tool__bars\" id=\"eco-proj-bars-72e4c\"><\/div>\n      <div class=\"eco-tool__metric-sub eco-tool__muted\" id=\"eco-proj-tip-72e4c\"><\/div>\n    <\/div>\n\n    <p class=\"eco-tool__note\">\n      Idealized estimate only. This calculator ignores air resistance, wind, spin, and launch height differences.\n    <\/p>\n  <\/div>\n\n  <details class=\"eco-tool__details\">\n    <summary class=\"eco-tool__summary\">How we calculate<\/summary>\n    <div class=\"eco-tool__details-body\">\n      <p class=\"eco-tool__text\">\n        We use standard projectile motion equations with no air resistance: range = v\u00b2\u00b7sin(2\u03b8)\/g, maximum height = v\u00b2\u00b7sin\u00b2(\u03b8)\/(2g), flight time = 2v\u00b7sin(\u03b8)\/g.\n      <\/p>\n      <ul class=\"eco-tool__list\" id=\"eco-proj-factors-72e4c\"><\/ul>\n    <\/div>\n  <\/details>\n<\/div>\n\n<style>\n.eco-tool{border:1px solid rgba(0,0,0,.12);border-radius:12px;padding:16px}\n.eco-tool__header{margin-bottom:12px}\n.eco-tool__title{margin:0 0 8px}\n.eco-tool__lead{margin:0;opacity:.9}\n.eco-tool__form{margin-top:12px}\n.eco-tool__grid3{display:grid;grid-template-columns:1fr;gap:16px}\n@media (min-width:860px){.eco-tool__grid3{grid-template-columns:1fr 1fr 1fr}}\n.eco-tool__field{display:flex;flex-direction:column;gap:6px}\n.eco-tool__label{font-weight:600}\n.eco-tool__input{width:100%;height:44px;padding:0 12px;border:1px solid rgba(0,0,0,.20);border-radius:10px;background:#fff;box-sizing:border-box;font:inherit}\n.eco-tool__hint{font-size:.92em;opacity:.78;min-height:38px}\n.eco-tool__actions{display:flex;flex-wrap:wrap;gap:10px;align-items:center;margin-top:16px}\n.eco-tool__btn{padding:10px 22px}\n.eco-tool__btn--ghost{background:transparent!important;border:1px solid rgba(0,0,0,.20)!important}\n.eco-tool__btn--ghost:hover,.eco-tool__btn--ghost:focus{background:rgba(0,0,0,.06)!important;border-color:rgba(0,0,0,.35)!important}\n.eco-tool__error{min-height:1.2em;font-weight:600;flex:1 1 240px}\n.eco-tool__result{margin-top:16px}\n.eco-tool__subtitle{margin:0 0 10px}\n.eco-tool__cards{display:grid;gap:10px;grid-template-columns:1fr}\n@media (min-width:860px){.eco-tool__cards{grid-template-columns:1fr 1fr}}\n.eco-tool__cards--3{grid-template-columns:1fr}\n@media (min-width:860px){.eco-tool__cards--3{grid-template-columns:1fr 1fr 1fr}}\n.eco-tool__card{border:1px solid rgba(0,0,0,.12);border-radius:12px;padding:12px}\n.eco-tool__card--wide{margin-top:10px}\n.eco-tool__metric-label{opacity:.85;font-weight:600}\n.eco-tool__metric-value{font-size:1.6em;font-weight:800;margin-top:6px;line-height:1.1}\n.eco-tool__metric-sub{opacity:.85;margin-top:6px}\n.eco-tool__bars{display:grid;gap:10px;margin-top:12px}\n.eco-tool__barrow{display:grid;grid-template-columns:160px 1fr 90px;gap:10px;align-items:center}\n@media (max-width:480px){.eco-tool__barrow{grid-template-columns:120px 1fr 70px}}\n.eco-tool__barlabel{font-weight:600;opacity:.9}\n.eco-tool__bartrack{border:1px solid rgba(0,0,0,.12);border-radius:999px;height:12px;overflow:hidden;background:rgba(0,0,0,.03)}\n.eco-tool__barfill{height:100%;width:0%;background:rgba(0,0,0,.25)}\n.eco-tool__barval{text-align:right;opacity:.85;white-space:nowrap}\n.eco-tool__note{margin:10px 0 0;opacity:.9}\n.eco-tool__muted{opacity:.8}\n.eco-tool__details{margin-top:14px}\n.eco-tool__summary{cursor:pointer;font-weight:700}\n.eco-tool__details-body{margin-top:10px}\n.eco-tool__text{margin:0 0 10px}\n.eco-tool__list{margin:0;padding-left:18px}\n<\/style>\n\n<script>\n(function(){\n  const S = \"72e4c\";\n  const el = (id) => document.getElementById(id + \"-\" + S);\n\n  const speedEl = el(\"eco-proj-speed\");\n  const angleEl = el(\"eco-proj-angle\");\n  const gravityEl = el(\"eco-proj-gravity\");\n\n  const calcBtn = el(\"eco-proj-calc\");\n  const resetBtn = el(\"eco-proj-reset\");\n  const errorEl = el(\"eco-proj-error\");\n  const resultEl = el(\"eco-proj-result\");\n\n  const rangeEl = el(\"eco-proj-range\");\n  const heightEl = el(\"eco-proj-height\");\n  const timeEl = el(\"eco-proj-time\");\n  const barsEl = el(\"eco-proj-bars\");\n  const tipEl = el(\"eco-proj-tip\");\n  const factorsEl = el(\"eco-proj-factors\");\n\n  function setError(msg){ errorEl.textContent = msg || \"\"; }\n  function fmt(x){ return (Math.round(x * 100) \/ 100).toLocaleString(undefined,{minimumFractionDigits:2,maximumFractionDigits:2}); }\n  function degToRad(d){ return d * Math.PI \/ 180; }\n\n  function fillFactors(){\n    factorsEl.innerHTML = [\n      `<li><strong>Range:<\/strong> v\u00b2 \u00d7 sin(2\u03b8) \/ g<\/li>`,\n      `<li><strong>Max height:<\/strong> v\u00b2 \u00d7 sin\u00b2(\u03b8) \/ (2g)<\/li>`,\n      `<li><strong>Flight time:<\/strong> 2v \u00d7 sin(\u03b8) \/ g<\/li>`,\n      `<li><strong>Horizontal speed:<\/strong> v \u00d7 cos(\u03b8)<\/li>`,\n      `<li><strong>Vertical speed:<\/strong> v \u00d7 sin(\u03b8)<\/li>`\n    ].join(\"\");\n  }\n\n  function barRow(label, pct, value){\n    const p = Math.max(0, Math.min(100, pct));\n    return `\n      <div class=\"eco-tool__barrow\">\n        <div class=\"eco-tool__barlabel\">${label}<\/div>\n        <div class=\"eco-tool__bartrack\"><div class=\"eco-tool__barfill\" style=\"width:${p}%;\"><\/div><\/div>\n        <div class=\"eco-tool__barval\">${value}<\/div>\n      <\/div>\n    `;\n  }\n\n  function calculate(){\n    setError(\"\");\n\n    const speed = Number(speedEl.value);\n    const angle = Number(angleEl.value);\n    const gravity = Number(gravityEl.value);\n\n    if (!Number.isFinite(speed) || speed <= 0 ||\n        !Number.isFinite(angle) || angle <= 0 || angle >= 90 ||\n        !Number.isFinite(gravity) || gravity <= 0) {\n      setError(\"Please enter valid values in all fields.\");\n      resultEl.hidden = true;\n      return;\n    }\n\n    const rad = degToRad(angle);\n    const sin = Math.sin(rad);\n    const cos = Math.cos(rad);\n\n    const range = (speed * speed * Math.sin(2 * rad)) \/ gravity;\n    const height = (speed * speed * sin * sin) \/ (2 * gravity);\n    const time = (2 * speed * sin) \/ gravity;\n\n    const vx = speed * cos;\n    const vy = speed * sin;\n    const max = Math.max(vx, vy, speed);\n\n    rangeEl.textContent = `${fmt(range)} m`;\n    heightEl.textContent = `${fmt(height)} m`;\n    timeEl.textContent = `${fmt(time)} s`;\n\n    barsEl.innerHTML = [\n      barRow(\"Launch speed\", (speed \/ max) * 100, `${fmt(speed)} m\/s`),\n      barRow(\"Horizontal\", (vx \/ max) * 100, `${fmt(vx)} m\/s`),\n      barRow(\"Vertical\", (vy \/ max) * 100, `${fmt(vy)} m\/s`)\n    ].join(\"\");\n\n    tipEl.textContent =\n      Math.abs(angle - 45) < 1\n        ? \"Tip: Around 45\u00b0 gives the maximum range in this idealized model.\"\n        : angle < 45\n        ? \"Tip: Lower angles usually reduce height and can reduce range if too low.\"\n        : \"Tip: Higher angles increase height but usually reduce range above 45\u00b0.\";\n\n    resultEl.hidden = false;\n  }\n\n  function reset(){\n    setError(\"\");\n    speedEl.value = \"20\";\n    angleEl.value = \"45\";\n    gravityEl.value = \"9.81\";\n    resultEl.hidden = true;\n  }\n\n  fillFactors();\n  calcBtn.addEventListener(\"click\", calculate);\n  resetBtn.addEventListener(\"click\", reset);\n})();\n<\/script>\n","protected":false},"excerpt":{"rendered":"<p>Projectile Motion Calculator Estimate range, maximum height, and flight time based on launch speed and angle. Launch speed(m\/s) Initial speed at launch. Launch angle(degrees) Angle above horizontal. Gravity(m\/s\u00b2) Use 9.81&hellip;<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":2354,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_sitemap_exclude":false,"_sitemap_priority":"","_sitemap_frequency":"","footnotes":""},"_links":{"self":[{"href":"https:\/\/science-x.net\/index.php?rest_route=\/wp\/v2\/pages\/2963"}],"collection":[{"href":"https:\/\/science-x.net\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/science-x.net\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/science-x.net\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/science-x.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2963"}],"version-history":[{"count":1,"href":"https:\/\/science-x.net\/index.php?rest_route=\/wp\/v2\/pages\/2963\/revisions"}],"predecessor-version":[{"id":2964,"href":"https:\/\/science-x.net\/index.php?rest_route=\/wp\/v2\/pages\/2963\/revisions\/2964"}],"up":[{"embeddable":true,"href":"https:\/\/science-x.net\/index.php?rest_route=\/wp\/v2\/pages\/2354"}],"wp:attachment":[{"href":"https:\/\/science-x.net\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2963"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}