Calculators
Signal Integrity Simulator
Interactive waveform simulator — model how R, L, C parasitics and transmission line effects distort SPI, I²C, UART, and PWM signals. Rise/fall time, overshoot, ringing, and reflection analysis.
Ohm's Law
Solve for voltage, current, or resistance given any two. Bonus: power (P = IV).
RC Circuit
Time constant τ = RC, cutoff frequency, and charge/discharge timing.
PCB Trace Width
Minimum trace width from IPC-2221 for a given current and copper weight.
Beam Deflection
Max deflection for simply-supported and cantilever beams under a point load.
Stress & Strain
Compute stress (MPa), strain, and Young's modulus from force, area, and elongation.
Gear Ratio
Output RPM, torque, and gear ratio from driver/driven tooth counts.
PWM Duty Cycle
Compare register value, on-time, and off-time from duty cycle and timer period.
UART Baud Rate
STM32 BRR register value, achieved baud rate, and error % for any clock/baud pair.
Timer Frequency
Timer output frequency and period from system clock, prescaler, and ARR.
Mean / Median / Mode
Descriptive stats for a data set: count, sum, mean, median, mode, range, min, max.
Standard Deviation
Population or sample standard deviation, variance, and standard error of the mean.
Percentile Calculator
Percentile rank of a value, quartiles (P25/P50/P75/P90), and IQR for a data set.
Probability Calculator
P(A∩B), P(A∪B), and conditional probabilities via Bayes — with Venn diagram.
Combinations & Permutations
C(n,r) and P(n,r) with or without repetition — formula display and large-number formatting.
Normal Distribution
Z-score, PDF, CDF, tail areas, and shaded bell curve for any μ, σ, and X.
Confidence Interval
Margin of error, lower/upper bounds, and interval for Z- or T-methods.
Sample Size
Required n for a proportion or mean estimate at a given confidence and margin of error.
Correlation Calculator
Pearson r, R², and Spearman ρ for paired data — with scatter plot and best-fit line.
Outlier Detector
IQR/Tukey fences and Z-score method run simultaneously — box plot and scored table.
Linear Regression
Slope, intercept, R², standard error, and Y prediction — scatter plot with fit line.
Hypothesis T-Test
One-sample, two-sample, and paired T-tests — t-stat, p-value, Cohen's d, rejection region.
Chi-Squared Test
Goodness-of-fit and test of independence up to 4×4 — χ² stat, df, p-value, per-cell contributions.
Descriptive Stats
All-in-one: mean, median, mode, SD, variance, IQR, skewness, kurtosis, and auto-binned histogram.
Odds Converter
Convert between decimal, fractional, American odds, and implied probability — live in any field.
Z-Test Calculator
One- and two-sample Z-tests — Z-stat, p-value, critical values at α = 0.05/0.01, rejection region curve.
One-Way ANOVA
Full ANOVA table: SS, df, MS, F-statistic, p-value, η², group means — dot plot by group.
Variance & Std Error
Population vs sample variance, SEM, confidence intervals, and how SEM shrinks as n grows.
Bayes' Theorem
Posterior from prior and likelihoods — expanded formula, natural frequency tree, and real-world presets.
Effect Size Calculator
Cohen's d, Cohen's h, and Eta Squared (η²) — magnitude bar with practical significance interpretation.
Poisson Distribution
P(X=k), cumulative CDF, tail probabilities, and PMF bar chart for any λ — with range mode and real-world presets.
Binomial Distribution
P(X=k), CDF, tail areas, and PMF bar chart for n trials at probability p — normal approximation overlay.
Multiple Linear Regression
OLS with up to 5 predictors — β coefficients, R², adjusted R², residuals plot, and prediction panel.
Mann-Whitney U Test
Nonparametric two-group test — U statistic, Z approximation, p-value, effect size r, rank-annotated dot plots.
Markov Chain Calculator
n-step state distribution, steady-state vector via power iteration, absorbing states — SVG state diagram.
Voltage Divider
Vout from R1/R2, or solve for R2 from desired Vout — power dissipation, E24 nearest standard value.
Op-Amp Gain
Inverting, non-inverting, and voltage follower gain — linear and dB, input impedance, op-amp schematic.
RC / RL Filter
Cutoff frequency, time constant, and attenuation for RC and RL low/high-pass filters — Bode plot.
Torque & Power
Solve for power, torque, or RPM from the power triangle P = τω — unit conversions and RPM gauge.
Compound Interest
Final balance, total interest, and EAR for any compounding frequency — with optional monthly contributions and year-by-year growth chart.
Loan Calculator
Monthly payment, total interest, and full amortization table — extra payments show months and interest saved.
Mortgage Calculator
P&I, tax, insurance breakdown and total monthly payment — LTV ratio, PMI flag, and equity growth curve.
Savings Goal
Months to reach a target, or required monthly contribution for a deadline — projected growth curve with goal marker.
ROI Calculator
Total ROI %, CAGR, real vs nominal return, and benchmark comparison against S&P 500 (7%) and bonds (4%).
NPV & IRR
Net present value, IRR via Newton-Raphson, simple and discounted payback periods, profitability index, and NPV sensitivity table.
Break-Even Analysis
Break-even units and revenue, contribution margin, CM ratio, margin of safety, target profit units — with break-even chart.
Project Budget Estimator
Dynamic line item builder by category — estimated vs actual, variance tracking, contingency reserve, burn rate, and clipboard export.
Depreciation Calculator
Straight-line, declining balance, and sum-of-years-digits schedules side by side — book value chart and annual depreciation table.
WACC Calculator
Weighted average cost of capital — equity, debt, preferred weights, after-tax cost of debt, CAPM helper, and ±2% sensitivity table.
Two-Way ANOVA
Full two-way ANOVA table with interaction term — η², F-tests, interaction plot for Factor A × B.
Repeated Measures ANOVA
Within-subjects ANOVA with Mauchly sphericity test and Greenhouse-Geisser correction — subject line plot.
Kruskal-Wallis Test
Non-parametric one-way ANOVA — H statistic with tie correction, Dunn post-hoc pairwise comparisons.
Friedman Test
Non-parametric RM-ANOVA — rank matrix heatmap, χ²_r statistic, Kendall W, Conover post-hoc.
Wilcoxon Signed-Rank Test
Non-parametric paired test — W⁺/W⁻, exact critical values (n≤25), normal approx, difference dot plot.
One-Sample Proportion Test
Z-test for a proportion against a known value — p-value, Wilson CI, reliability check, rejection-region curve.
Two-Sample Proportion Test
Compare two proportions — pooled Z-test, p-value, Wilson CI for difference, relative risk, odds ratio.
Chi-Squared Variance Test
Test a sample variance against a known population variance — χ² statistic, p-value, confidence interval for σ².
F-Test for Variances
Compare two sample variances — F statistic, p-value, F critical value, ratio CI, and F-distribution curve.
Levene's Test
Brown-Forsythe variance homogeneity test for 2–8 groups — W statistic, p-value, and box plots of deviations.
Kaplan-Meier Survival Analysis
Product-limit survival curve with Greenwood CI, median survival, and log-rank test for two groups.
DeLong Test — Independent ROC
Compare AUCs of two independent classifiers — DeLong variance, Z-statistic, p-value, CI, and ROC plot.
DeLong Test — Paired ROC
Compare AUCs of two classifiers on the same subjects — accounts for correlation via covariance term.
Kolmogorov-Smirnov Test
One-sample KS test against Normal, Uniform, Exponential, or Poisson — D statistic, p-value, ECDF vs theoretical CDF overlay.
Two-Sample Kolmogorov-Smirnov
Distribution-free two-sample test — D statistic, p-value at α=0.05/0.01, ECDF overlay with D arrow.
T-Distribution
Student's t-distribution — PDF, CDF, p-value, critical t±, CI bounds, normal overlay; handles df 1–1000.
F-Distribution
F-distribution — PDF, CDF, right-tail p-value, critical F at α=0.05/0.01; ANOVA and variance-test presets.
Chi-Squared Distribution
Chi-squared distribution — PDF, CDF, p-value, critical χ², tail selector; normal approximation for df > 200.
Exponential Distribution
Exponential distribution — PDF, CDF, survival function S(x), hazard rate, memoryless property explainer; λ or mean input.
Uniform Distribution
Continuous and discrete uniform distributions — PDF/PMF, CDF, range probability, random sample dot plot generator.
Shapiro-Wilk Normality Test
W statistic and p-value for normality — Q-Q plot, skewness/kurtosis, α=0.05/0.01 conclusions. Supports n = 3 to 50.
Geometric Mean
GM via log-sum, weighted GM, comparison with AM and HM — number line showing all three means with context panel.
Harmonic Mean
HM = n/Σ(1/xᵢ), weighted and rate-pairs mode, AM-GM-HM inequality check, parallel resistance easter egg.
Coefficient of Variation
CV = SD/Mean × 100%, SNR, index of dispersion — gauge SVG with variability bands, two-dataset comparison mode.
Measures of Dispersion
Range, IQR, variance, SD, SEM, skewness, kurtosis — box-and-whisker plot, strip plot, and SD ruler with empirical rule.
Weighted Average
Dynamic value/weight pair builder — weighted mean, effective sample size, weight distribution bar chart, GPA/portfolio/survey presets.
Betting Odds Calculator
Convert between decimal, fractional, American odds, and implied probability — parlay calculator, probability gauge, vig/overround analysis.
Mean Absolute Deviation
MAD = Σ|xᵢ−x̄|/n — mean-based and median-based modes, deviation table, MAD vs SD comparison, dot plot with deviation lines.
Median Absolute Deviation
Robust scale estimator MAD = median(|xᵢ−median|) — scaled MAD for σ estimation, outlier flagging, MAD-based box plot.
Hypergeometric Distribution
P(X=k) without replacement — CDF, tail probabilities, mean, variance, PMF bar chart with binomial approximation overlay.
Logistic Regression
Gradient descent logistic regression from scratch — log loss curve, confusion matrix, decision boundary (2-feature mode), accuracy, precision, recall, F1.
Classification Metrics
Full confusion matrix analysis — accuracy, precision, recall, F1, F-beta, MCC, Cohen's κ, likelihood ratios, and heatmap SVG.
Cross-Validation
K-Fold, stratified, LOO, and train/val/test split — fold diagram, bias-variance tradeoff of k, CV score aggregation with CI.
Bias-Variance Tradeoff
Training vs validation error curves — optimal complexity finder, underfitting/overfitting zones, stacked error decomposition, bulls-eye diagram.
Regularization Calculator
L1 Lasso, L2 Ridge, and Elastic Net — coefficient shrinkage table, sparsity count, coefficient path SVG, and penalty geometry diagram.
Gradient Descent
Step-by-step GD on 1D polynomials — vanilla, momentum, Nesterov; animated path with prev/next/play controls, divergence & oscillation detection.
Learning Rate Finder
Smith (2017) LR range test — log-scale loss vs LR, steepest descent suggestion, cyclical LR range [LR_min, LR_max], warmup schedule SVG.
Loss Functions
Regression (MSE, RMSE, MAE, MAPE, Huber, R²) and classification (BCE, Hinge, Focal, KL) — per-sample breakdown, outlier sensitivity, loss landscape SVG.
Optimizer Comparator
SGD, Momentum, RMSProp, Adam, AdaGrad side by side — trajectory overlay on f(x), simultaneous loss curves, play/pause step controls.
Convergence Checker
Absolute, relative, and plateau convergence detection — EMA smoothing, exponential decay fit (L∞ + L₀e^{-λt}), extrapolated convergence point.
Activation Functions
Sigmoid, ReLU, Tanh, GELU, Swish, ELU, Leaky ReLU, Softmax — curve plots, derivative overlays, saturation / dead-neuron analysis at any x.
Layer Size Calculator
Build a network layer by layer — parameter counts, cumulative memory (MB), estimated max batch size given VRAM, network diagram SVG.
Backprop Stepper
Step through all 13 forward/backward-pass operations of a 2-layer MLP — gradients, weight updates, vanishing/exploding gradient warnings.
Dropout & Batch Norm
Dropout neuron grid (inverted scaling, training vs inference), BatchNorm forward pass (μ, σ², x̂, γ/β), running mean/variance via EMA.
Weight Initialization
Xavier Uniform/Normal, He Uniform/Normal, LeCun Normal, Random, Zeros, Ones — histogram of 20 samples vs theoretical PDF, per-activation recommendations.
K-Means Visualizer
K-Means++ initialization, step-through iterations watching centroids move, elbow method (k=1–8) with auto-detected elbow via max second derivative.
PCA Variance
Eigenvalue input or raw data matrix — QR algorithm covariance decomposition, scree plot, cumulative explained variance, components to reach threshold.
Distance Metrics
Euclidean, Manhattan, Chebyshev, Minkowski(p), Cosine, Hamming, Jaccard — per-dimension breakdown, radar/scatter visualization, dominant-dimension highlighting.
Silhouette Score
Per-point and per-cluster silhouette scores from (x, y, cluster_id) data — horizontal bar plot sorted by cluster, negative scores flagged in red.
Dimensionality Reduction
Curse of dimensionality: ball/cube volume ratio, expected nearest-neighbor distance, required sample blowup, Johnson-Lindenstrauss bound — log-scale curve chart.
I²C / SPI Timing
I²C rise time, pull-up validation, cable length. SPI clock, bit/byte periods — timing diagram SVG.