One page. One job. Done.
Mini Tools Collection
ToolPatch is a growing collection of focused utilities. Each page handles one task with clear inputs, fast results, and practical outputs.
Solve for distance, speed, or time using the standard motion formula.
Choose whether to solve for distance, speed, or time and provide the remaining values. Useful for travel planning, logistics estimation, and physics homework checks.
Approximate ODE solutions with the forward Euler method.
Numerically solve dy/dx = a*x + b*y + c from initial conditions, step size, and step count.
Model growth or decay over periods with compounding behavior.
Calculate exponential growth/decay trajectories using an initial value, periodic rate, and period count.
Compute n!, nPr, and nCr for combinatorics and probability problems.
Enter n and r to calculate factorial, permutations, and combinations in one place. Useful for exam prep, probability work, and algorithmic problem solving.
Fit a best-fit line from point data and compute r and R².
Enter x,y pairs to estimate slope, intercept, and correlation quality.
Analyze determinant, inverse, trace, and eigenvalues for 2x2 matrices.
Useful for linear algebra classes, engineering math, and matrix sanity checks.
Compute absolute and percentage increase/decrease between two values.
Enter initial and final values to calculate both absolute change and percent change instantly. Useful for pricing updates, KPI shifts, trend reports, and quick sanity checks.
Evaluate cubic polynomial derivatives and curvature at a chosen x value.
Compute f(x), f'(x), and f''(x) for ax^3+bx^2+cx+d with instant output.
Solve ax² + bx + c = 0 with real or complex roots.
Quickly compute discriminant and roots for quadratic equations with clear output formatting. Suitable for students, tutors, and engineering pre-checks.
Generate random numbers with range, count, and uniqueness options.
Create integer or decimal random samples with configurable bounds and uniqueness constraints.
Calculate mean, variance, and standard deviation for a dataset.
Paste numeric values to compute population and sample statistics quickly. Useful for analytics, classroom assignments, and data quality checks.
Integrate polynomial expressions symbolically and evaluate definite bounds.
Find antiderivatives for polynomial terms (e.g. 3x^2 - 4x + 7) and optionally compute definite integral values.
Analyze triangle validity, perimeter, area, angles, and type.
Enter side lengths to classify triangles and compute key geometry outputs for coursework and design.
Run dot product, angle, magnitude, sum, difference, and cross product.
Compute core 2D/3D vector operations for mechanics, graphics, and linear algebra tasks.
Find nth term and sum of an arithmetic progression from a, d, and n.
Solve arithmetic progression problems with first term, common difference, and number of terms. Great for school math, exam preparation, and quick sequence verification.
Compute exact and cumulative binomial probabilities for n, k, p.
Great for probability exercises, risk estimation, and stats exam prep.
Calculate diameter, circumference, and area from a circle radius.
Input radius and get all key circle measurements with precise decimal outputs. Suitable for geometry practice, engineering checks, and classroom demos.
Generate Fibonacci numbers and inspect nth term and sequence sum.
Choose how many terms to generate and instantly get the sequence, nth value, and total sum. Great for math practice, coding interviews, and algorithm demonstrations.
Reduce fractions to simplest form and convert to decimal instantly.
Enter numerator and denominator to simplify fractions using GCD and view decimal form. Helpful for math homework, tutoring sessions, and quick arithmetic checks.
Find greatest common divisor and least common multiple for two integers.
Input two integers to calculate GCD, LCM, and whether they are coprime. Great for number theory basics, classroom exercises, and programming prep.
Compute logarithms for custom base and value inputs.
Solve log_b(x) quickly and verify with exponent reconstruction.
Check whether a number is prime and view factors when it is not.
Enter an integer to test primality and classify the number quickly. Helpful for schoolwork, coding practice, and cryptography fundamentals.
Compute weighted average from value and weight lists.
Ideal for grading, portfolio weighting, KPI scoring, and multi-factor decision models.
Convert values to z-scores and estimate normal-distribution percentile.
Useful for test scores, benchmarking, and statistical interpretation.