Mini Tools Collection
Useful one-page tools for real work
ToolPatch is a growing collection of focused utilities. Each page handles one task with clear inputs, fast results, and practical outputs.
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Math
Featured
Cylinder Volume Calculator
Calculate cylinder volume and surface area from radius and height.
Compute volume, total surface area, lateral area, and base area from cylinder dimensions.
Math
Featured
Distance Speed Time Calculator
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.
Math
Featured
Euler Method ODE Solver
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.
Math
Featured
Exponential Growth Decay Calculator
Model growth or decay over periods with compounding behavior.
Calculate exponential growth/decay trajectories using an initial value, periodic rate, and period count.
Math
Featured
Factorial Permutation Combination Calculator
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.
Math
Featured
Linear Regression Calculator
Fit a best-fit line from point data and compute r and R².
Enter x,y pairs to estimate slope, intercept, and correlation quality.
Math
Featured
Matrix 2x2 Analyzer
Analyze determinant, inverse, trace, and eigenvalues for 2x2 matrices.
Useful for linear algebra classes, engineering math, and matrix sanity checks.
Math
Featured
Percentage Change Calculator
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.
Math
Featured
Polynomial Derivative Evaluator
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.
Math
Featured
Quadratic Equation Solver
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.
Math
Featured
Random Number Generator
Generate random numbers with range, count, and uniqueness options.
Create integer or decimal random samples with configurable bounds and uniqueness constraints.
Math
Featured
Sphere Volume Calculator
Calculate sphere volume and surface area from radius.
Compute volume, surface area, and diameter from sphere radius using standard geometric formulas.
Math
Featured
Standard Deviation Calculator
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.
Math
Featured
Symbolic Equation Solver
Solve linear and quadratic equations in x with symbolic steps.
Solve equations in one variable (`x`) on a single page and get both simplified form and final roots. This tool accepts equations such as `3x + 9 = 0` and `2x^2 - 5x - 3 = 0`, then normalizes terms to standard form, applies the correct method, and displays symbolic steps you can follow or reuse in notes. It is intended for algebra practice, quick verification before coding formulas, and engineering sanity checks. Current scope is polynomial equations up to degree 2 with real coefficients.
Math
Featured
Symbolic Integral Calculator
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.
Math
Featured
Triangle Analyzer
Analyze triangle validity, perimeter, area, angles, and type.
Enter side lengths to classify triangles and compute key geometry outputs for coursework and design.
Math
Featured
Vector Operations Calculator
Run dot product, angle, magnitude, sum, difference, and cross product.
Compute core 2D/3D vector operations for mechanics, graphics, and linear algebra tasks.
Math
Arithmetic Sequence Solver
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.
Math
Binomial Probability Calculator
Compute exact and cumulative binomial probabilities for n, k, p.
Great for probability exercises, risk estimation, and stats exam prep.
Math
Circle Calculator
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.
Math
Fibonacci Sequence Generator
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.
Math
Fraction Simplifier
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.
Math
GCD LCM Calculator
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.
Math
Logarithm Calculator
Compute logarithms for custom base and value inputs.
Solve log_b(x) quickly and verify with exponent reconstruction.
Math
Prime Number Checker
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.
Math
Weighted Average Calculator
Compute weighted average from value and weight lists.
Ideal for grading, portfolio weighting, KPI scoring, and multi-factor decision models.
Math
Z-Score Percentile Calculator
Convert values to z-scores and estimate normal-distribution percentile.
Useful for test scores, benchmarking, and statistical interpretation.