Math & Statistics数学与统计计算
Scientific Calculator科学计算器
Standard and scientific calculator with variables, history and DEG/RAD modes.标准与科学计算器，支持变量存储、历史记录与角度/弧度切换。
Function Grapher函数图像绘制器
Plot up to 5 functions with zoom, pan and a live value crosshair.同时绘制多达 5 条函数图像，支持平移缩放与十字准星实时取值。
3D Surface Plotter三维函数图像绘制器
Plot z = f(x, y) as a shaded 3D surface you can rotate, zoom and inspect.把 z = f(x, y) 绘制为可旋转缩放的三维曲面，支持等高配色与极值读数。
Percentage Calculator百分比计算器
What is P% of V, N as a percent of V, and value increased or decreased by a percent.快速计算数值的 P% 百分比、占比多少以及按百分比增减后的数值。
Percentage Increase Calculator百分比增减计算器
Percentage change between two values, with absolute change and multiplier.计算两个数值之间的相对增长/下降百分比、绝对差值与变化倍数。
Fraction Calculator分数计算器
Simplify fractions, convert to decimal and percent, and decimals back to exact fractions.分数约分最简式、转小数与百分比，支持小数利用连分数逆向还原为精确分数。
Ratio & Proportion Calculator比例与比例方程计算器
Simplify ratios, solve proportions A:B = C:x, and convert to decimal and percent.化简比值为最简整数比，求解 A:B = C:x 比例方程与小数百分比互转。
Prime Factorization质因数分解
Factor a whole number into primes as 2^3 × 3 × 5, with the divisor count.把一个整数分解为质因数（如 2^3 × 3 × 5），并给出约数个数。
Combinations & Permutations组合与排列计算器
Compute nCr (combinations), nPr (permutations) and n! with exact BigInt results.精确计算组合数 nCr、排列数 nPr 与阶乘 n!，大数使用 BigInt 无溢出。
Descriptive Statistics描述统计与线性回归
Sum, mean, median, mode, min/max and both sample & population standard deviation — plus optional simple linear regression.求和、均值、中位数、众数、极值、样本与总体标准差，并可对 y 关于 x 做一元线性回归。
Pi Calculator (π up to 1,000,000 Digits)圆周率 π 计算器（100 万位高精度）
Compute Pi (π) up to 1,000,000 decimal places using a high-precision Hybrid Engine (Machin & Chudnovsky) with real-time progress and CPU benchmark presets.采用分段混合引擎（低位数 Machin 秒开，1.5 万位以上自动切换 Chudnovsky 超高阶级数与二进制拆分）实时计算圆周率 π 至 100 万位（1,000,000）。
Matrix Calculator (Linear Algebra)矩阵计算器（线性代数）
Perform matrix arithmetic and linear algebra operations: Determinant, Inverse, Trace, Transpose, Addition, and Multiplication.线性代数常用矩阵运算工具：行列式求解、逆矩阵、矩阵的迹、转置矩阵以及矩阵加减与乘法。
Equation, Calculus & Limit Solver方程求解、微积分与极限计算器
Solve quadratic and cubic equations, 2x2 linear systems, calculate numerical derivatives, definite integrals, and function limits (e.g. sin(x)/x as x→0).一元二次与三次方程（含复数根）、二元一次线性方程组求解，以及数值微积分与极限求解（如 sin(x)/x 趋向 0 的极限）。
Complex Numbers Calculator复数计算器（代数与极坐标形式）
Perform complex arithmetic, rectangular to polar Euler form conversion, powers, roots, and complex functions.复数代数运算与极坐标/欧拉形式互转，支持模长辐角、共轭、乘方、开方及复指数对数。
Vector Calculator (2D & 3D)空间向量计算器（2D / 3D）
Calculate 2D and 3D vector magnitude, dot product, cross product, angle, projection, addition, and distance.计算二维与三维向量的模长、点积、叉积、向量夹角、投影向量、向量加减及空间距离。
Hypothesis Testing & p-Value Calculator假设检验与 p 值计算器 (Z-Test / t-Test)
Perform Z-test and Student’s t-test for sample means, calculate p-values, test statistics, and 95%/99% confidence intervals.支持单样本 Z 检验与 t 检验，精准计算检验统计量、单侧与双侧 p-value 显著性及置信区间。
Normal Distribution & Z-Score Calculator正态分布与 Z-Score 分位数计算器
Calculate Z-score, cumulative probability P(X ≤ x), interval probability P(x1 ≤ X ≤ x2), and percentiles for any mean μ and std dev σ.计算给定均值 μ 与标准差 σ 下的 Z-Score、累积分布概率 P(X ≤ x)、区间概率与标准百分位数。
Confidence Interval Calculator均值与比例置信区间计算器
Calculate 90%, 95%, or 99% confidence intervals for sample means (t / Z distribution) and sample proportions with margin of error.计算 90%、95% 或 99% 置信水平下的样本均值（t 分布 / Z 分布）与样本比例置信区间及抽样误差范围。
One-Way ANOVA Calculator (Analysis of Variance)单因素方差分析计算器 (One-Way ANOVA)
Perform One-Way ANOVA across 3 or 4 sample groups, with F-statistic, p-value, sum of squares (SSB/SSW), and mean squares.多组样本数据的单因素方差分析 (ANOVA)，计算 F 检验统计量、p-value 显著性概率、组间/组内平方和与均方。
Calculus Calculator (Derivative · Integral · Limit)微积分计算器（导数 · 定积分 · 极限）
Numerical derivative at a point, definite integral over an interval, and two-sided limits of any f(x) — powered by the site expression engine.对任意 f(x) 求某点的数值导数、区间定积分与双侧极限——由站内表达式引擎驱动。
Polynomial Regression多项式回归拟合
Fit a polynomial of degree 1–5 to (x, y) data by least squares: coefficients, R², RMSE and the fitted equation.对 (x, y) 数据做 1–5 次多项式最小二乘拟合：给出系数、R²、RMSE 与拟合方程。
Probability Distribution (Binomial · Poisson)概率分布（二项 · 泊松）
P(X = k), P(X ≤ k), mean and variance for binomial and Poisson distributions — computed in log space so huge n never overflows.二项分布与泊松分布的 P(X = k)、P(X ≤ k)、均值与方差——对数空间计算，超大 n 也不会溢出。
Linear Regression (OLS · WLS · GLS)线性回归（OLS · WLS · GLS）
Multiple linear regression with classical or robust standard errors (HC1–HC3, Newey–West HAC, cluster-robust) and AR(1) GLS — coefficients, t tests, R² and F.多元线性回归：经典或稳健标准误（HC1–HC3、Newey–West HAC、聚类稳健），支持 AR(1) 广义最小二乘——系数、t 检验、R² 与 F 检验。
OLS Regression DiagnosticsOLS 回归诊断
Heteroskedasticity (Breusch–Pagan, White), autocorrelation (Durbin–Watson, Breusch–Godfrey, Ljung–Box), normality (Jarque–Bera) and influence (leverage, Cook's distance, DFFITS) on a fitted regression.对回归残差做全面诊断：异方差（Breusch–Pagan、White）、自相关（Durbin–Watson、Breusch–Godfrey、Ljung–Box）、正态性（Jarque–Bera）与强影响点（杠杆值、Cook 距离、DFFITS）。
Quantile Regression分位数回归
Estimate conditional quantiles (median = τ 0.5) by minimising the check loss — robust to outliers and skewness that distort least squares.通过最小化检查损失估计条件分位数（τ = 0.5 即中位数回归）——对扭曲最小二乘的离群值与偏态更稳健。
Mixed Effects Model (Random Intercept)混合效应模型（随机截距）
Linear mixed model by maximum likelihood: fixed effects with random intercepts (and an optional random slope) across groups, plus ICC and variance components.极大似然线性混合模型：固定效应 + 跨组随机截距（可选随机斜率），给出 ICC 与方差分解。
Logistic Regression (Logit · Probit)逻辑回归（Logit · Probit）
Binary outcome regression by iteratively reweighted least squares: coefficients, z tests, likelihood-ratio test, AIC/BIC and average marginal effects.二分类结果的 IRLS 回归：系数、z 检验、似然比检验、AIC/BIC 与平均边际效应。
Count Regression (Poisson · NB · ZIP)计数回归（泊松 · 负二项 · 零膨胀）
Poisson, negative binomial (ML dispersion) and zero-inflated models for count outcomes, with overdispersion diagnostics and AIC comparison.针对计数型因变量的泊松、负二项（极大似然估计离散参数）与零膨胀模型，含过散度诊断与 AIC 比较。
Stationarity Tests (ADF · KPSS)平稳性检验（ADF · KPSS）
Augmented Dickey–Fuller (unit-root null) and KPSS (stationarity null) tests with MacKinnon and Kwiatkowski critical values — they confirm each other from opposite directions.增广 Dickey–Fuller 检验（单位根原假设）与 KPSS 检验（平稳原假设），附 MacKinnon 与 Kwiatkowski 临界值——两个方向互相印证。
ARIMA Forecast (SARIMAX)ARIMA 预测（SARIMAX）
Fit ARIMA/SARIMAX by conditional-sum-of-squares maximum likelihood (parameters constrained to be stable and invertible) and forecast with 95% intervals.以条件平方和极大似然拟合 ARIMA/SARIMAX（参数约束为稳定可逆），并给出带 95% 置信区间的预测。
VAR & Cointegration (Johansen)VAR 与协整（Johansen）
Vector autoregression with stability check, Granger causality F tests and Cholesky impulse responses, plus the Johansen reduced-rank trace statistics for cointegration.向量自回归：稳定性检验、Granger 因果 F 检验、Cholesky 脉冲响应，以及 Johansen 降秩迹统计量协整检验。
State Space & Kalman Filter状态空间与卡尔曼滤波
Local level / local drift / stationary AR(1) unobserved-component models: the Kalman filter and RTS smoother estimate the latent state and forecast with exact likelihood-based variances.局部水平 / 带漂移 / 平稳 AR(1) 不可观测分量模型：卡尔曼滤波与 RTS 平滑器估计潜状态，并以精确似然给出预测及方差。