📐 幾何工具

📐 圓周長（C = 2π·r）Circle Circumference 圓周長計算器。輸入半徑 r，按 C = 2π·r 求圓周長，用於管道周長、輪緣長度與圓環尺寸的快速換算。Circle Circumference - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Geometry tools. 📐 圓柱體積（V = π·r²·h）Cylinder Volume 圓柱體積計算器。輸入底面半徑與高，按 V = πr²h 求圓柱體積，用於罐體、管道與柱體容積的即時計算。Cylinder Volume - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Geometry tools. 📐 圓錐體積（V = π·r²·h / 3）Cone Volume 圓錐體積計算器。輸入底面半徑與高，按 V = πr²h/3 求圓錐體積，用於容器容量、填料量與幾何建模的體積估算。Cone Volume - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Geometry tools. 📐 圓面積（A = π·r²）Circle Area 圓面積計算器。輸入半徑 r，按 A = π·r² 求圓面積，用於平面幾何、材料下料與截面積等常見面積估算。Circle Area - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Geometry tools. 📐 對角線（d = √(w² + h²)）Rectangle Diagonal 矩形對角線計算器。輸入寬 w 與高 h，按 d = √(w²+h²) 求對角線長度，用於屏幕、板材與邊框的尺寸換算。Rectangle Diagonal - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Geometry tools. 📐 弦長（c = 2r·sin(θ/2)）Chord Length 弦長計算器。輸入半徑與圓心角（弧度），按 c = 2r·sin(θ/2) 求弦長，用於圓內線段、弓形與齒輪等幾何設計的長度計算。Chord Length - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Geometry tools. 📐 弧長（L = r·θ，θ 為弧度）Arc Length 弧長計算器。輸入半徑 r 與圓心角 θ（弧度），按 L = r·θ 求圓弧長，支持度轉弧度，用於幾何、機械與工程製圖中的弧段長度計算。Arc Length - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Geometry tools. 📐 扇形面積（A = r²·θ / 2，θ 為弧度）Sector Area 扇形面積計算器。輸入半徑與圓心角（弧度），按 A = r²θ/2 求扇形面積，用於圓扇區、餅圖扇區與幾何建模的面積計算。Sector Area - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Geometry tools. 📐 斜邊（c = √(a² + b²)）Pythagorean 勾股定理計算器。輸入直角邊 a、b，按 c = √(a²+b²) 求斜邊長度，用於直角三角形、距離與尺寸的快速求解。Pythagorean - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Geometry tools. 📐 梯形面積（A = (a + b)·h / 2）Trapezoid Area 梯形面積計算器。輸入上下底 a、b 與高 h，按 A = (a+b)h/2 求梯形面積，用於土地、截面與圖形面積估算。Trapezoid Area - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Geometry tools. 📐 正多邊形面積（A = n·s² / (4·tan(π/n))）Regular Polygon Area 輸入邊數 n（n≥3）與邊長 s，使用公式 A=n·s²/(4·tan(π/n)) 計算正多邊形面積，用於地磚、螺母截面、花壇等邊數規則形狀的面積估算與設計。Regular Polygon Area - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Geometry tools. 📐 海倫公式（A = √(s(s−a)(s−b)(s−c))）Triangle Heron 三角形面積計算器（海倫公式）。輸入三邊長 a、b、c，按半周長 s 求面積 A = √(s(s−a)(s−b)(s−c))，適用於已知三邊而不知高的情況。Triangle Heron - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Geometry tools. 🥚 由三半軸求橢球體積Ellipsoid Volume 輸入橢球的三個半軸 a、b、c，使用公式 V=4/3·π·a·b·c 計算其體積，用於天體、細胞、藥丸或儲罐等橢球形體的容積估算與三維建模。Ellipsoid Volume - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Geometry tools. 🔺 由上下底半徑與高求圓台體積Cone Frustum Volume 輸入圓台的上底面半徑 r、下底面半徑 R 與高 h，使用公式 V = πh/3·(R²+Rr+r²) 計算其體積，用於土建、容器設計或數學學習中圓台形體的容積估算。Cone Frustum Volume - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Geometry tools. 🧭 由兩向量求夾角Angle Between Vectors 兩向量夾角計算器。輸入兩個向量的分量，按 θ = arccos(a·b/(|a||b|)) 求夾角（弧度/角度），用於幾何、物理與機器學習中的方向關係計算。Angle Between Vectors - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Geometry tools. 🎯 由兩向量求數量積與投影Dot Product 2d 輸入兩個二維向量的分量，計算它們的點積 a·b=a_x·b_x+a_y·b_y，以及向量 a 在 b 上的投影長度，用於力學分解、圖形學與向量夾角的幾何分析。Dot Product 2d - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Geometry tools. 🔲 由兩點座標求空間距離Distance 3d 輸入兩點 (x1,y1,z1) 與 (x2,y2,z2)，求三維距離。Distance 3d - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Geometry tools. 📍 由兩點求線段中點Midpoint 2d 線段中點計算器。輸入兩點座標 (x₁,y₁)、(x₂,y₂)，按 M = ((x₁+x₂)/2, (y₁+y₂)/2) 求中點座標，用於幾何、圖形處理與座標定位。Midpoint 2d - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Geometry tools. 🍩 由主半徑與管半徑求環體體積Torus Volume 輸入環面的主半徑 R（到管中心距離）與管半徑 r，使用公式 V=2·π²·R·r² 計算環體體積，用於甜甜圈形零件、管道彎頭或數學模型中環面體的容積估算。Torus Volume - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Geometry tools. ⭕ 由半徑求球的體積Sphere Volume 球體積計算器。輸入球半徑，按 V = (4/3)πr³ 求體積，用於球罐容量、球體物料與幾何建模的體積計算。Sphere Volume - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Geometry tools. ⭕ 由半徑求球的表面積Sphere Surface Area 球表面積計算器。輸入球半徑，按 A = 4πr² 求表面積，用於球體包裝、熱傳導面積與幾何建模的表面積估算。Sphere Surface Area - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Geometry tools. 🔺 由底面積與高求稜錐體積Pyramid Volume 稜錐體積計算器。輸入底面積與高，按 V = (1/3)·底面積·高 求稜錐體積，用於稜錐、帳篷與錐台類幾何體的體積估算。Pyramid Volume - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Geometry tools. ⬡ 由邊數求正多邊形每個內角Polygon Interior Angle 正多邊形內角計算器。輸入邊數 n，按 θ = (n−2)·180°/n 求正多邊形每個內角，用於多邊形繪圖、鋪磚與幾何教學。Polygon Interior Angle - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Geometry tools. 📦 由邊長求體積、表面積、體對角線Cube Properties 輸入立方體邊長 a，計算其體積 V=a³、表面積 A=6a² 與體對角線 d=a√3，用於幾何教學、包裝箱設計或三維空間尺寸與材料用量的快速估算。Cube Properties - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Geometry tools. 📦 由長、寬、高求體積Rectangular Prism Volume 輸入長方體的長、寬、高，計算其體積 V=l·w·h 與表面積，用於裝箱、房間容積、倉儲空間等矩形體對象的尺寸估算與材料用量核算。Rectangular Prism Volume - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Geometry tools. 🥚 由長短半軸求橢圓面積Ellipse Area 輸入橢圓的長半軸 a 與短半軸 b，使用公式 A=π·a·b 計算其面積，用於機械零件、花壇、軌道截面等橢圓形狀的面積估算與圖紙標註核對。Ellipse Area - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Geometry tools. 📐 距離（d = |Ax₀+By₀+C| / √(A²+B²)）Point Line Distance 輸入點 (x₀,y₀) 與直線 Ax+By+C=0 的係數，使用公式 d=|Ax₀+By₀+C|/√(A²+B²) 計算二者最短距離，用於幾何作圖、碰撞檢測與路徑規劃中的距離判定。Point Line Distance - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Geometry tools. 📐 頂點（x_v = −b/2a，y_v = f(x_v)）Parabola Vertex 輸入二次函數 y=ax²+bx+c 的係數，計算其頂點座標（x_v=−b/2a，y_v=f(x_v)）與對稱軸，用於拋物線軌跡、最值問題與函數圖像的教學分析與繪圖。Parabola Vertex - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Geometry tools.