🧮 數學計算工具

🧮 GCD / LCM 計算器Gcd Lcm 輸入兩個或多個整數，用輾轉相除法求最大公約數（GCD）並據此求最小公倍數（LCM），用於約分與通分。Gcd Lcm - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Math Calculation tools. 🧮 一元二次方程求根計算器Quadratic Solver 一元二次方程求根計算器依據判別式 Δ=b²−4ac 求解 ax²+bx+c=0 的兩個根，支持實根與復根，適合代數作業與工程方程求解。Quadratic Solver - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Math Calculation tools. 🧮 與 ∛xRoot Calc 開方計算器求平方根、立方根及任意次方根，支持正負輸入，適合數學、幾何與工程中的根式運算與尺寸推導。Root Calc - calculate online, free and accurate. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Math Calculation... 🧮 任意底數對數計算器Log Base 任意底數對數計算器依據換底公式求以任意底數為底的對數，適合數學、信息論與工程中的對數換算與指數反解。Log Base - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Math Calculation tools. 📏 幾何計算器Geometry Calculator 幾何計算器支持常見 2D/3D 圖形的面積、體積與周長計算，覆蓋圓、三角形、球、柱等，適合學習、工程與日常幾何量求解。Geometry Calculator - calculate online, free and accurate. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Math C... 📐 勾股定理Pythagorean Theorem Calculator 輸入直角三角形任意兩條邊長，自動計算第三條邊及兩個鋭角度數，用於幾何與工程測量。Compute sides of a right triangle (a^2 + b^2 = c^2). Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Math Calcula... 🧮 取模運算Modulo Calc 取模運算計算器求 a 除以 b 的餘數，支持正負數，適合編程、哈希與週期問題中的模運算驗證。Modulo Calc - calculate online, free and accurate. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Math Calculati... ⭕ 圓的面積/周長Circle Area / Circumference Calculator 輸入半徑、直徑、面積或周長中的任意一項，自動計算其餘三項，用於圓的幾何參數換算。Compute area and circumference of a circle. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Math Calculation tools. 📋 常用公式速查Formula Calculator 常用公式速查：內置數學、物理、化學、幾何公式，填參數即算，附單位口徑提示。Formula Calculator - calculate online, free and accurate. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Math Ca... 🧮 冪運算Power Calc 冪運算計算器求底數 x 的 y 次冪 x^y，支持整數與小數指數，適合數學、複利與科學計算中的指數運算。Power Calc - calculate online, free and accurate. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Math Calculatio... 🧮 平面兩點距離計算器Distance 2d 平面兩點距離計算器依據座標求二維平面上兩點間的歐氏距離，支持批量，適合幾何、地圖與圖形處理中的距離測算。Distance 2d - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Math Calculation tools. 📐 微積分工具Calculus Tools 微積分工具集支持函數求導、不定積分、極限與級數展開計算，輸入表達式實時輸出結果，適合高等數學學習、作業驗算與工程函數分析。Calculus Tools - calculate online, free and accurate. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Math Calcul... 🧮 排列數計算器Permutation 排列數計算器求從 n 個元素取 r 個的排列數 P(n,r)，適合組合數學、排班與概率問題中的有序選擇計算。Permutation - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Math Calculation tools. 🧮 斐波那契第 n 項計算器Fibonacci N 斐波那契第 n 項計算器用迭代法快速求出數列第 n 項，適合數列學習、算法演示與自然規律（如黃金分割）相關計算。Fibonacci N - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Math Calculation tools. 🧮 方程求解器Equation Solver 方程求解器支持一元一次/二次、二元及三元線性方程組求解，輸入係數實時輸出根或解，適合數學作業、工程計算與方程組驗證。Equation Solver - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Math Calculation tools. ⚖️ 比例計算Ratio Calculator 依據比例式 A:B=C:D，輸入任意三項求解第四項未知數，適用於配方縮放、地圖比例與相似圖形計算等比例換算場景。Solve for an unknown term in a proportion. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Math Calculation tools. 🔺 由三邊長求三角形面積Herons Area 輸入三角形三邊長a、b、c，按海倫公式 A = √[s(s−a)(s−b)(s−c)] 計算其面積，無需已知高。Herons Area - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Math Calculation tools. 📦 由兩三維向量求點積Dot Product 向量點積計算器求兩向量各分量乘積之和 A·B，支持三維，適合幾何、物理與機器學習中的投影、夾角與相似度計算。Dot Product - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Math Calculation tools. 🔺 由兩邊及夾角求第三邊Law of Cosines 輸入兩邊a、b及其夾角C（度），按 c = √(a²+b²−2ab·cosC) 計算第三邊，適用於非直角三角形求解。Law of Cosines - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Math Calculation tools. 🔢 由二次項係數求判別式Quadratic Discriminant 輸入一元二次方程係數a、b、c，計算判別式 Δ = b²−4ac，據此判斷方程實根的個數與性質。Quadratic Discriminant - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Math Calculation tools. 🔲 由二階矩陣四元素求行列式Determinant 2x2 輸入二階矩陣元素a、b、c、d，按 |A| = ad−bc 計算其行列式值，用於線性代數基礎運算。Determinant 2x2 - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Math Calculation tools. 🔄 由元素個數求環形排列數Circular Permutation 環形排列數計算器依據 P=(n−1)! 求 n 個元素圍成圓環的排列數，適合組合數學、座位編排與概率問題求解。Circular Permutation - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Math Calculation tools. 🔺 由已知邊角與對角求未知邊長Law of Sines 輸入已知邊 b、其對角 B 與待求邊對角 A(度)，按正弦定理 a=b·sinA/sinB 求解未知邊長，用於三角形邊角計算與測量。Law of Sines - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Math Calculation tools. 🔢 由底數與結果求指數Exponent Solve 輸入底數a與結果b，按 x = ln b/ln a 求解指數方程 a^x = b 中的指數x，用於對數與指數運算。Exponent Solve - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Math Calculation tools. 🔲 由總數與各類別數求多項式係數Multinomial Coefficient 輸入總數 n 與三個類別數 k₁、k₂、k₃（和為 n），求多項式係數。Multinomial Coefficient - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Math Calculation tools. ➗ 由數值序列求算術平均數Arithmetic Mean Math 輸入一組以逗號或空格分隔的數值，計算其算術平均數 x̄ = Σx/n，用於統計平均值快速求解。Arithmetic Mean Math - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Math Calculation tools. 🔁 由類型數與選取數求可重複組合數Combination Repetition 輸入類型數n與選取數r，計算允許元素重複的組合數 C(n+r−1, r)，用於抽樣、分配與組合計數問題。Combination Repetition - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Math Calculation tools. 📈 由項數、首末項求等差級數和Arithmetic Series Sum 輸入項數n、首項a₁與末項aₙ，按 S_n = n(a₁+aₙ)/2 計算等差數列前n項之和。Arithmetic Series Sum - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Math Calculation tools. 📈 由首項、公比與項數求等比級數和Geometric Series Sum 輸入首項a、公比r與項數n，按 S_n = a(1−rⁿ)/(1−r) 計算等比數列前n項之和（r≠1）。Geometric Series Sum - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Math Calculation tools. #️⃣ 由首項、公比與項數求通項Nth Term Geometric 輸入首項a₁、公比r與項數n，按 aₙ = a₁·r^(n−1) 計算等比數列的第n項值。Nth Term Geometric - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Math Calculation tools. 🧮 百分比變化計算器Percent Change Δ% = (新 − 舊) / 舊 × 100%Percent Change - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Math Calculation tools. 📊 百分比計算Percentage Calculator 支持多種常見百分比運算（求百分比、增減幅、佔比等），輸入任意兩個已知量即可自動算出第三個，用於日常與財務比例計算。Compute the four common percentage operations. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Math Calculation t... 🧮 直線斜率計算器Slope Line 直線斜率計算器由兩點座標求直線斜率 k，適合解析幾何、函數作圖與工程坡度（如道路、屋頂）的傾斜度計算。Slope Line - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Math Calculation tools. 🧮 組合數計算器Combination 組合數計算器求從 n 個元素中選取 r 個的組合數 C(n,r)，支持大數運算，適合概率統計、抽獎與組合問題計算。Combination - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Math Calculation tools. 🧮 試除法判定素數Prime Check 素數判定計算器用試除法判斷給定正整數是否為質數，輸出結果並展示因數，適合數論學習、密碼學基礎與算法練習。Prime Check - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Math Calculation tools. 🧮 階乘計算器Factorial Calculate 階乘計算器求非負整數的階乘 n!，定義 0!=1，支持大數，適合排列組合、概率與級數計算中的階乘運算。Factorial Calculate - calculate online, free and accurate. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Math C...